## CryptoDB

### Recent videos of IACR talks

**Year**

**Venue**

**Title**

2020

EUROCRYPT

Key-Homomorphic Pseudorandom Functions from LWE with Small Modulus
📺 Abstract

Pseudorandom functions (PRFs) are fundamental objects in cryptography that play a central role in symmetric-key cryptography. Although PRFs can be constructed from one-way functions generically, these black-box constructions are usually inefficient and require deep circuits to evaluate compared to direct PRF constructions that rely on specific algebraic assumptions. From lattices, one can directly construct PRFs from the Learning with Errors (LWE) assumption (or its ring variant) using the result of Banerjee, Peikert, and Rosen (Eurocrypt 2012) and its subsequent works. However, all existing PRFs in this line of work rely on the hardness of the LWE problem where the associated modulus is super-polynomial in the security parameter.
In this work, we provide two new PRF constructions from the LWE problem that each focuses on either minimizing the depth of its evaluation circuit or providing key-homomorphism while relying on the hardness of the LWE problem with only a polynomial modulus. Along the way, we introduce a new variant of the LWE problem called the Learning with Rounding and Errors (LWRE) problem. We show that for certain settings of parameters, the LWRE problem is as hard as the LWE problem. We then show that the hardness of the LWRE problem naturally induces a pseudorandom synthesizer that can be used to construct a low-depth PRF. The techniques that we introduce to study the LWRE problem can then be used to derive variants of existing key-homomorphic PRFs whose security can be reduced from the hardness of the LWE problem with a much smaller modulus.

2020

EUROCRYPT

Stacked Garbling for Disjunctive Zero-Knowledge Proofs
📺 Abstract

Zero-knowledge (ZK) proofs (ZKP) have received wide attention, focusing on non-interactivity, short proof size, and fast verification time. We focus on the fastest total proof time, in particular for large Boolean circuits. Under this metric, Garbled Circuit (GC)-based ZKP (Jawurek et al., [JKO], CCS 2013) remained the state-of-the-art technique due to the low-constant linear scaling of computing the garbling.
We improve GC-ZKP for proof statements with conditional clauses. Our communication is proportional to the longest branch rather than to the entire proof statement. This is most useful when the number m of branches is large, resulting in up to factor m× improvement over JKO.
In our proof-of-concept illustrative application, prover P demonstrates knowledge of a bug in a codebase consisting of any number of snippets of actual C code. Our computation cost is linear in the size of the code- base and communication is constant in the number of snippets. That is, we require only enough communication for a single largest snippet!
Our conceptual contribution is stacked garbling for ZK, a privacy-free circuit garbling scheme that can be used with the JKO GC-ZKP protocol to construct more efficient ZKP. Given a Boolean circuit C and computational security parameter k, our garbling is L · k bits long, where L is the length of the longest execution path in C. All prior concretely efficient garbling schemes produce garblings of size |C| · k. The computational cost of our scheme is not increased over prior state-of-the-art.
We implement our GC-ZKP and demonstrate significantly improved (m× over JKO) ZK performance for functions with branching factor m. Compared with recent ZKP (STARK, Libra, KKW, Ligero, Aurora, Bulletproofs), our scheme offers much better proof times for larger circuits (35-1000× or more, depending on circuit size and compared scheme). For our illustrative application, we consider four C code snippets, each of about 30-50 LOC; one snippet allows an invalid memory dereference. The entire proof takes 0.15 seconds and communication is 1.5 MB.

2020

EUROCRYPT

Lightweight Authenticated Encryption Mode Suitable for Threshold Implementation
📺 Abstract

This paper proposes tweakable block cipher (TBC) based modes \textsf{PFB}\_\textsf{Plus} and \textsf{PFB}$\omega$ that are efficient in threshold implementations (TI). Let $t$ be an algebraic degree of a target function, e.g. $t=1$ (resp. $t>1$) for linear (resp. non-linear) function. The $d$-th order TI encodes the internal state into $d t + 1$ shares. Hence, the area size increases proportionally to the number of shares. This implies that TBC based modes can be smaller than block cipher (BC) based modes in TI because TBC requires $s$-bit block to ensure $s$-bit security, e.g. \textsf{PFB} and \textsf{Romulus}, while BC requires $2s$-bit block. However, even with those TBC based modes, the minimum we can reach is 3 shares of $s$-bit state with $t=2$ and the first-order TI ($d=1$).
Our first design \textsf{PFB}\_\textsf{Plus} aims to break the barrier of the $3s$-bit state in TI. The block size of an underlying TBC is $s/2$ bits and the output of TBC is linearly expanded to $s$ bits. This expanded state requires only 2 shares in the first-order TI, which makes the total state size $2.5s$ bits. We also provide rigorous security proof of \textsf{PFB}\_\textsf{Plus}. Our second design \textsf{PFB}$\omega$ further increases a parameter $\omega$: a ratio of the security level $s$ to the block size of an underlying TBC. We prove security of \textsf{PFB}$\omega$ for any $\omega$ under some assumptions for an underlying TBC and for parameters used to update a state. Next, we show a concrete instantiation of \textsf{PFB}\_\textsf{Plus} for 128-bit security. It requires a TBC with 64-bit block, 128-bit key and 128-bit tweak, while no existing TBC can support it. We design a new TBC by extending \textsf{SKINNY} and provide basic security evaluation. Finally, we give hardware benchmarks of \textsf{PFB}\_\textsf{Plus} in the first-order TI to show that TI of \textsf{PFB}\_\textsf{Plus} is smaller than that of \textsf{PFB} by more than one thousand gates and is the smallest within the schemes having 128-bit security.

2020

EUROCRYPT

On Instantiating the Algebraic Group Model from Falsifiable Assumptions
📺 Abstract

We provide a standard-model implementation (of a relaxation) of the algebraic group model (AGM, [Fuchsbauer, Kiltz, Loss, CRYPTO 2018]). Specifically, we show that every algorithm that uses our group is algebraic, and hence "must know" a
representation of its output group elements in terms of its input group
elements. Here, "must know" means that a suitable extractor can extract such
a representation efficiently. We stress that our implementation relies only on
falsifiable assumptions in the standard model, and in particular does not use
any knowledge assumptions.
As a consequence, our group allows to transport a number of results obtained in
the AGM into the standard model, under falsifiable assumptions. For instance,
we show that in our group, several Diffie-Hellman-like assumptions (including
computational Diffie-Hellman) are equivalent to the discrete logarithm
assumption. Furthermore, we show that our group allows to prove the Schnorr
signature scheme tightly secure in the random oracle model.
Our construction relies on indistinguishability obfuscation, and hence should
not be considered as a practical group itself. However, our results show that
the AGM is a realistic computational model (since it can be instantiated in the
standard model), and that results obtained in the AGM are also possible with
standard-model groups.

2020

EUROCRYPT

How to Extract Useful Randomness from Unreliable Sources
📺 Abstract

For more than 30 years, cryptographers have been looking for public sources of uniform randomness in order to use them as a set-up to run appealing cryptographic protocols without relying on trusted third parties. Unfortunately, nowadays it is fair to assess that assuming the existence of physical phenomena producing public uniform randomness is far from reality.
It is known that uniform randomness cannot be extracted from a single weak source. A well-studied way to overcome this is to consider several independent weak sources. However, this means we must trust the various sampling processes of weak randomness from physical processes.
Motivated by the above state of affairs, this work considers a set-up where players can access multiple {\em potential} sources of weak randomness, several of which may be jointly corrupted by a computationally unbounded adversary. We introduce {\em SHELA} (Somewhere Honest Entropic Look Ahead) sources to model this situation.
We show that there is no hope of extracting uniform randomness from a {\em SHELA} source. Instead, we focus on the task of {\em Somewhere-Extraction} (i.e., outputting several candidate strings, some of which are uniformly distributed -- yet we do not know which). We give explicit constructions of {\em Somewhere-Extractors} for {\em SHELA} sources with good parameters.
Then, we present applications of the above somewhere-extractor where the public uniform randomness can be replaced by the output of such extraction from corruptible sources, greatly outperforming trivial solutions. The output of somewhere-extraction is also useful in other settings, such as a suitable source of random coins for many randomized algorithms.
In another front, we comprehensively study the problem of {\em Somewhere-Extraction} from a {\em weak} source, resulting in a series of bounds. Our bounds highlight the fact that, in most regimes of parameters (including those relevant for applications), {\em SHELA} sources significantly outperform {\em weak} sources of comparable parameters both when it comes to the process of {\em Somewhere-Extraction}, or in the task of amplification of success probability in randomized algorithms. Moreover, the low quality of somewhere-extraction from weak sources excludes its use in various efficient applications.

2020

EUROCRYPT

Everybody’s a Target: Scalability in Public-Key Encryption
📺 Abstract

For 1<=m<=n, we consider a natural m-out-of-n multi-instance scenario for a public-key encryption (PKE) scheme. An adversary, given n independent instances of PKE, wins if he breaks at least m out of the n instances. In this work, we are interested in the scaling factor of PKE schemes, SF, which measures how well the difficulty of breaking m out of the n instances scales in m. That is, a scaling factor SF=l indicates that breaking m out of n instances is at least l times more difficult than breaking one single instance. A PKE scheme with small scaling factor hence provides an ideal target for mass surveillance. In fact, the Logjam attack (CCS 2015) implicitly exploited, among other things, an almost constant scaling factor of ElGamal over finite fields (with shared group parameters).
For Hashed ElGamal over elliptic curves, we use the generic group model to describe how the scaling factor depends on the scheme's granularity. In low granularity, meaning each public key contains its independent group parameter, the scheme has optimal scaling factor SF=m; In medium and high granularity, meaning all public keys share the same group parameter, the scheme still has a reasonable scaling factor SF=sqrt(m). Our findings underline that instantiating ElGamal over elliptic curves should be preferred to finite fields in a multi-instance scenario.
As our main technical contribution, we derive new generic-group lower bounds of Omega(sqrt(mp)) on the complexity of solving both the m-out-of-n Gap Discrete Logarithm and the m-out-of-n Gap Computational Diffie-Hellman problem over groups of prime order p, extending a recent result by Yun (EUROCRYPT 2015). We establish the lower bound by studying the hardness of a related computational problem which we call the search-by-hypersurface problem.

2020

EUROCRYPT

OptORAMa: Optimal Oblivious RAM
📺 Abstract

Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC '87 and J. ACM '96) is a technique for provably obfuscating programs' access patterns, such that the access patterns leak no information about the programs' secret inputs. To compile a general program to an oblivious counterpart, it is well-known that $\Omega(\log N)$ amortized blowup is necessary, where $N$ is the size of the logical memory. This was shown in Goldreich and Ostrovksy's original ORAM work for statistical security and in a somewhat restricted model (the so called \emph{balls-and-bins} model), and recently by Larsen and Nielsen (CRYPTO '18) for computational security.
A long standing open question is whether there exists an optimal ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this paper, we resolve this problem and present the first secure ORAM with $O(\log N)$ amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS '18) who gave a construction with $O(\log N\cdot \log\log N)$ amortized blowup, assuming one-way functions.
One of our building blocks of independent interest is a linear-time deterministic oblivious algorithm for tight compaction: Given an array of $n$ elements where some elements are marked, we permute the elements in the array so that all marked elements end up in the front of the array. Our $O(n)$ algorithm improves the previously best known deterministic or randomized algorithms whose running time is $O(n \cdot\log n)$ or $O(n \cdot\log \log n)$, respectively.

2020

EUROCRYPT

Improving Key-Recovery in Linear Attacks: Application to 28-round PRESENT
📺 Abstract

Linear cryptanalysis is one of the most important tools in use for the security evaluation of symmetric primitives. Many improvements and refinements have been published since its introduction, and many applications on different ciphers have been found. Among these upgrades, Collard et al. proposed in 2007 an acceleration of the key-recovery part of Algorithm 2 for last-round attacks based on the FFT.
In this paper we present a generalized, matrix-based version of the previous algorithm which easily allows to take into consideration an arbitrary number of key-recovery rounds. We also provide efficient variants that exploit the key-schedule relations and that can be combined with multiple linear attacks.
Using our algorithms we provide some new cryptanalysis on PRESENT, including, to the best of our knowledge, the first attack on 28 rounds.

2020

EUROCRYPT

(One) failure is not an option: Bootstrapping the search for failures in lattice-based encryption schemes
📺 Abstract

Lattice-based encryption schemes are often subject to the possibility of decryption failures, in which valid encryptions are decrypted incorrectly. Such failures, in large number, leak information about the secret key, enabling an attack strategy alternative to pure lattice reduction. Extending the "failure boosting" technique of D'Anvers et al. in PKC 2019, we propose an approach that we call "directional failure boosting" that uses previously found "failing ciphertexts" to accelerate the search for new ones. We analyse in detail the case where the lattice is defined over polynomial ring modules quotiented by <X^N + 1> and demonstrate it on a simple Mod-LWE-based scheme parametrized à la Kyber768/Saber. We show that, using our technique, for a given secret key (single-target setting), the cost of searching for additional failing ciphertexts after one or more have already been found, can be sped up dramatically. We thus demonstrate that, in this single-target model, these schemes should be designed so that it is hard to even obtain one decryption failure. Besides, in a wider security model where there are many target secret keys (multi-target setting), our attack greatly improves over the state of the art.

2020

EUROCRYPT

Which Languages Have 4-Round Fully Black-Box Zero-Knowledge Arguments from One-Way Functions?
📺 Abstract

We prove that if a language $\cL$ has a 4-round fully black-box zero-knowledge argument with negligible soundness based on one-way functions, then $\overline{\cL} \in \MA$. Since $\coNP \subseteq \MA$ implies that the polynomial hierarchy collapses, our result implies that $\NP$-complete languages are unlikely to have 4-round fully black-box zero-knowledge arguments based on one-way functions. In TCC 2018, Hazay and Venkitasubramaniam, and Khurana, Ostrovsky, and Srinivasan demonstrated 4-round fully black-box zero-knowledge arguments for all languages in $\NP$ based on injective one-way functions.
Their results also imply a 5-round protocol based on one-way functions. In essence, our result resolves the round complexity of fully black-box zero-knowledge arguments based on one-way functions.

2020

EUROCRYPT

Modeling for Three-Subset Division Property without Unknown Subset -- Improved Cube Attacks against Trivium and Grain-128AEAD
📺 Abstract

A division property is a generic tool to search for integral distinguishers, and automatic tools such as MILP or SAT/SMT allow us to evaluate the propagation efficiently.
In the application to stream ciphers, it enables us to estimate the security of cube attacks theoretically, and it leads to the best key-recovery attacks against well-known stream ciphers.
However, it was reported that some of the key-recovery attacks based on the division property degenerate to distinguishing attacks due to the inaccuracy of the division property.
Three-subset division property (without unknown subset) is a promising method to solve this inaccuracy problem, and a new algorithm using automatic tools for the three-subset division property was recently proposed at Asiacrypt2019.
In this paper, we first show that this state-of-the-art algorithm is not always efficient and we cannot improve the existing key-recovery attacks.
Then, we focus on the feature of the three-subset division property without unknown subset and propose another new efficient algorithm using automatic tools.
Our algorithm is more efficient than existing algorithms, and it can improve existing key-recovery attacks.
In the application to Trivium, we show a 841-round key-recovery attack.
We also show that a 855-round key-recovery attack, which was proposed at CRYPTO2018, has a critical flaw and does not work.
As a result, our 841-round attack becomes the best key-recovery attack.
In the application to Grain-128AEAD, we show that the known 184-round key-recovery attack degenerates to distinguishing attacks.
Then, the distinguishing attacks are improved up to 189 rounds, and we also show the best key-recovery attack against 190 rounds.

2020

EUROCRYPT

Indistinguishability Obfuscation Without Maps: Attacks and Fixes for Noisy Linear FE
📺 Abstract

Candidates of Indistinguishability Obfuscation (iO) can be categorized as ``direct'' or ``bootstrapping based''. Direct constructions rely on high degree multilinear maps [GGH13,GGHRSW13] and provide heuristic guarantees, while bootstrapping based constructions [LV16,Lin17,LT17,AJLMS19,Agr19,JLMS19] rely, in the best case, on bilinear maps as well as new variants of the Learning With Errors (LWE) assumption and pseudorandom generators. Recent times have seen exciting progress in the construction of indistinguishability obfuscation (iO) from bilinear maps (along with other assumptions) [LT17,AJLMS19,JLMS19,Agr19].
As a notable exception, a recent work by Agrawal [Agr19] provided a construction for iO without using any maps. This work identified a new primitive, called Noisy Linear Functional Encryption (NLinFE) that provably suffices for iO and gave a direct construction of NLinFE from new assumptions on lattices. While a preliminary cryptanalysis for the new assumptions was provided in the original work, the author admitted the necessity of performing significantly more cryptanalysis before faith could be placed in the security of the scheme. Moreover, the author did not suggest concrete parameters for the construction.
In this work, we fill this gap by undertaking the task of thorough cryptanalytic study of NLinFE. We design two attacks that let the adversary completely break the security of the scheme. Our attacks are completely new and unrelated to attacks that were hitherto used to break other candidates of iO. To achieve this, we develop new cryptanalytic techniques which (we hope) will inform future designs of the primitive of NLinFE.
From the knowledge gained by our cryptanalytic study, we suggest modifications to the scheme. We provide a new scheme which overcomes the vulnerabilities identified before. We also provide a thorough analysis of all the security aspects of this scheme and argue why plausible attacks do not work. We additionally provide concrete parameters with which the scheme may be instantiated. We believe the security of NLinFE stands on significantly firmer footing as a result of this work.

2020

EUROCRYPT

Low Error Efficient Computational Extractors in the CRS Model
📺 Abstract

In recent years, there has been exciting progress on building two-source extractors for sources with low min-entropy. Unfortunately, all known explicit constructions of two-source extractors in the low entropy regime suffer from non-negligible error, and building such extractors with negligible error remains an open problem. We investigate this problem in the computational setting, and obtain the following results.
We construct an explicit 2-source extractor, and even an explicit non-malleable extractor, with negligible error, for sources with low min-entropy, under computational assumptions in the Common Random String (CRS) model. More specifically, we assume that a CRS is generated once and for all, and allow the min-entropy sources to depend on the CRS. We obtain our constructions by using the following transformations.
- Building on the technique of [BHK11], we show a general transformation for converting any computational 2-source extractor (in the CRS model) into a computational non-malleable extractor (in the CRS model), for sources with similar min-entropy.
We emphasize that the resulting computational non-malleable extractor is resilient to arbitrarily many tampering attacks (a property that is impossible to achieve information theoretically). This may be of independent interest.
This transformation uses cryptography, and in particular relies on the sub-exponential hardness of the Decisional Diffie Hellman (DDH) assumption.
- Next, using the blueprint of [BACD+17], we give a transformation converting our computational non-malleable extractor (in the CRS model) into a computational 2-source extractor for sources with low min-entropy (in the CRS model). Our 2-source extractor works for unbalanced sources: specifically, we require one of the sources to be larger than a specific polynomial in the other.
This transformation does not incur any additional assumptions. Our analysis makes a novel use of the leakage lemma of Gentry and Wichs [GW11].

2020

EUROCRYPT

The Price of Active Security in Cryptographic Protocols
📺 Abstract

We construct the first actively-secure Multi-Party Computation (MPC) protocols with an \emph{arbitrary} number of parties in the dishonest majority setting, for an \emph{arbitrary} field $\FF$ with \emph{constant communication overhead} over the ``passive-GMW'' protocol (Goldreich, Micali and Wigderson, STOC `87). Our protocols rely on passive implementations of Oblivious Transfer (OT) in the boolean setting and Oblivious Linear function Evaluation (OLE) in the arithmetic setting. Previously, such protocols were only known over sufficiently large fields (Genkin et al. STOC `14) or a constant number of parties (Ishai et al. CRYPTO `08).
Conceptually, our protocols are obtained via a new compiler from a passively-secure protocol for a distributed multiplication functionality $\cF_\mult$, to an actively-secure protocol for general functionalities. Roughly, $\cF_\mult$ is parameterized by a linear-secret sharing scheme $\cS$, where it takes $\cS$-shares of two secrets and returns $\cS$-shares of their product.
We show that our compilation is concretely efficient for sufficiently large fields, resulting in an overhead of 2 when securely computing natural circuits. Our compiler has two additional benefits: (1) it can rely on \emph{any} passive implementation of $\cF_\mult$, which, besides the standard implementation based on OT (for boolean) and OLE (for arithmetic) allows us to rely on implementations based on threshold cryptosystems (Cramer et al. Eurocrypt `01); and (2) it can rely on weaker-than-passive (i.e., imperfect/leaky) implementations, which in some parameter regimes yield actively-secure protocols with overhead less than 2.
Instantiating this compiler with an ``honest-majority'' implementations of $\cF_\mult$, we obtain the first honest-majority protocol with optimal corruption threshold for boolean circuits with constant communication overhead over the best passive protocol (Damg{\aa}rd and Nielsen, CRYPTO `07).

2020

EUROCRYPT

Transparent SNARKs from DARK Compilers
📺 Abstract

We construct a new polynomial commitment scheme for univariate and multivariate polynomials over finite fields, with public-coin evaluation proofs that have logarithmic communication and verification cost in the number of coefficients of the polynomial. The underlying technique is a Diophantine Argument of Knowledge (DARK), leveraging integer representations of polynomials and groups of unknown order. Security is shown from the strong RSA and the adaptive root assumption. Moreover, the scheme does not require a trusted setup if instantiated with class groups. We apply this new cryptographic compiler to a restricted class of algebraic linear IOPs in order to obtain doubly-efficient public-coin IPs with succinct communication and witness-extended emulation for any NP relation. Allowing for linear preprocessing, the online verifier's work is logarithmic in the circuit complexity of the relation.
Concretely, we obtain quasi-linear prover time when compiling the IOP employed in Sonic(MBKM, CCS 19). Applying the Fiat-Shamir transform in the random oracle model results in a SNARK system with quasi-linear preprocessing, quasi-linear (online) prover time, logarithmic proof size, and logarithmic (online) verification time for arbitrary circuits. The SNARK is also concretely efficient with 8.4KB proofs and 75ms verification time for circuits with 1 million gates. Most importantly, this SNARK is transparent: it does not require a trusted setup. We also obtain zk-SNARKs by applying a variant of our polynomial commitment scheme that is hiding and offers zero-knowledge evaluation proofs. This construction is the first transparent zk-SNARK that has both a practical prover time as well as strictly logarithmic proof size and verification time. We call our system Supersonic.

2020

EUROCRYPT

TNT: How to Tweak a Block Cipher
📺 Abstract

In this paper, we propose Tweak-aNd-Tweak (TNT for short) mode, which builds a tweakable block cipher from three independent block ciphers. TNT handles the tweak input by simply XOR-ing the unmodified tweak into the internal state of block ciphers twice. Due to its simplicity, TNT can also be viewed as a way of turning a block cipher into a tweakable block cipher by dividing the block cipher into three chunks, and adding the tweak at the two cutting points only. TNT is proven to be of beyond-birthday-bound $2^{2n/3}$ security, under the assumption that the three chunks are independent secure $n$-bit SPRPs. It clearly brings minimum possible overhead to both software and hardware implementations. To demonstrate this, an instantiation named TNT-AES with 6, 6, 6 rounds of AES as the underlying block ciphers is proposed. Besides the inherent proven security bound and tweak-independent rekeying feature of the TNT mode, the performance of TNT-AES is comparable with all existing TBCs designed through modular methods.

2020

EUROCRYPT

Quantum Security Analysis of CSIDH
📺 Abstract

CSIDH is a recent proposal for post-quantum non-interactive key-exchange, based on supersingular elliptic curve isogenies. It is similar in design to a previous scheme by Couveignes, Rostovtsev and Stolbunov, but aims at an improved balance between efficiency and security.
In the proposal, the authors suggest concrete parameters in order to meet some desired levels of quantum security. These parameters are based on the hardness of recovering a hidden isogeny between two elliptic curves, using a quantum subexponential algorithm of Childs, Jao and Soukharev. This algorithm combines two building blocks: first, a quantum algorithm for recovering a hidden shift in a commutative group. Second, a computation in superposition of all isogenies originating from a given curve, which the algorithm calls as a black box.
In this paper, we give a comprehensive security analysis of CSIDH. Our first step is to revisit three quantum algorithms for the abelian hidden shift problem from the perspective of non-asymptotic cost, with trade-offs between their quantum and classical complexities. Second, we complete the non-asymptotic study of the black box in the hidden shift algorithm. We give a quantum procedure that evaluates CSIDH-512 using less than 40~000 logical qubits.
This allows us to show that the parameters proposed by the authors of CSIDH do not meet their expected quantum security.

2020

EUROCRYPT

Continuous Verifiable Delay Functions
📺 Abstract

We introduce the notion of a continuous verifiable delay function (cVDF): a function g which is (a) iteratively sequential---meaning that evaluating the iteration $g^{(t)}$ of g (on a random input) takes time roughly t times the time to evaluate g, even with many parallel processors, and (b) (iteratively) verifiable---the output of $g^{(t)}$ can be efficiently verified (in time that is essentially independent of t). In other words, the iterated function $g^{(t)}$ is a verifiable delay function (VDF) (Boneh et al., CRYPTO '18), having the property that intermediate steps of the computation (i.e., $g^{(t')}$ for t'<t) are publicly and continuously verifiable.
We demonstrate that cVDFs have intriguing applications: (a) they can be used to construct public randomness beacons that only require an initial random seed (and no further unpredictable sources of randomness), (b) enable outsourceable VDFs where any part of the VDF computation can be verifiably outsourced, and (c) have deep complexity-theoretic consequences: in particular, they imply the existence of depth-robust moderately-hard Nash equilibrium problem instances, i.e. instances that can be solved in polynomial time yet require a high sequential running time.
Our main result is the construction of a cVDF based on the repeated squaring assumption and the soundness of the Fiat-Shamir (FS) heuristic for constant-round proofs.
We highlight that when viewed as a (plain) VDF, our construction requires a weaker FS assumption than previous ones (earlier constructions require the FS heuristic for either super-logarithmic round proofs, or for arguments).

2020

EUROCRYPT

Generic-Group Delay Functions Require Hidden-Order Groups
📺 Abstract

Despite the fundamental importance of delay functions, underlying both the classic notion of a time-lock puzzle and the more recent notion of a verifiable delay function, the only known delay function that offers both sufficient structure for realizing these two notions and a realistic level of practicality is the ``iterated squaring'' construction of Rivest, Shamir and Wagner. This construction, however, is based on rather strong assumptions in groups of hidden orders, such as the RSA group (which requires a trusted setup) or the class group of an imaginary quadratic number field (which is still somewhat insufficiently explored from the cryptographic perspective). For more than two decades, the challenge of constructing delay functions in groups of known orders, admitting a variety of well-studied instantiations, has eluded the cryptography community.
In this work we prove that there are no constructions of generic-group delay functions in cyclic groups of known orders: We show that for any delay function that does not exploit any particular property of the representation of the underlying group, there exists an attacker that completely breaks the function's sequentiality when given the group's order. As any time-lock puzzle and verifiable delay function give rise to a delay function, our result holds for these two notions we well, and explains the lack of success in resolving the above-mentioned long-standing challenge. Moreover, our result holds even if the underlying group is equipped with a d-linear map, for any constant d>=2 (and even for super-constant values of d under certain conditions).

2020

EUROCRYPT

Fractal: Post-Quantum and Transparent Recursive Proofs from Holography
📺 Abstract

We present a new methodology to efficiently realize recursive composition of succinct non-interactive arguments of knowledge (SNARKs). Prior to this work, the only known methodology relied on pairing-based SNARKs instantiated on cycles of pairing-friendly elliptic curves, an expensive algebraic object. Our methodology does not rely on any special algebraic objects and, moreover, achieves new desirable properties: it is post-quantum and it is transparent (the setup is public coin).
We exploit the fact that recursive composition is simpler for SNARKs with preprocessing, and the core of our work is obtaining a preprocessing zkSNARK for rank-1 constraint satisfiability (R1CS) that is post-quantum and transparent. We obtain this latter by establishing a connection between holography and preprocessing in the random oracle model, and then constructing a holographic proof for R1CS.
We experimentally validate our methodology, demonstrating feasibility in practice.

2020

EUROCRYPT

Finding Hash Collisions with Quantum Computers by Using Differential Trails with Smaller Probability than Birthday Bound
📺 Abstract

In this paper we spot light on dedicated quantum collision attacks on concrete hash functions, which has not received much attention so far.
In the classical setting, the generic complexity to find collisions of an $n$-bit hash function is $O(2^{n/2})$, thus classical collision attacks based on differential cryptanalysis such as rebound attacks build differential trails with probability higher than $2^{-n/2}$.
By the same analogy, generic quantum algorithms such as the BHT algorithm find collisions with complexity $O(2^{n/3})$.
With quantum algorithms, a pair of messages satisfying a differential trail with probability $p$ can be generated with complexity $p^{-1/2}$.
Hence, in the quantum setting, some differential trails with probability up to $2^{-2n/3}$ that cannot be exploited in the classical setting may be exploited to mount a collision attack in the quantum setting.
In particular, the number of attacked rounds may increase.
In this paper, we attack two international hash function standards: AES-MMO and Whirlpool.
For AES-MMO, we present a $7$-round differential trail with probability $2^{-80}$ and use it to find collisions with a quantum version of the rebound attack,
while only $6$ rounds can be attacked in the classical setting.
For Whirlpool, we mount a collision attack based on a $6$-round differential trail from a classical rebound distinguisher with a complexity higher than the birthday bound. This improves the best classical attack on 5 rounds by 1.
We also show that those trails are optimal in our approach.
Our results have two important implications.
First, there seems to exist a common belief that classically secure hash functions will remain secure against quantum adversaries. Indeed, several second-round candidates in the NIST post-quantum competition use existing hash functions, say SHA-3, as quantum secure ones. Our results disprove this common belief.
Second, our observation suggests that differential trail search should not stop with probability $2^{-n/2}$ but should consider up to $2^{-2n/3}$.
Hence it deserves to revisit the previous differential trail search activities.

2020

EUROCRYPT

Signatures from Sequential-OR Proofs
📺 Abstract

OR-proofs enable a prover to show that it knows the witness for one of many statements, or that one out of many statements is true. OR-proofs are a remarkably versatile tool, used to strengthen security properties, design group and ring signature schemes, and achieve tight security. The common technique to build OR-proofs is based on an approach introduced by Cramer, Damgaard, and Schoenmakers (CRYPTO'94), where the prover splits the verifier's challenge into random shares and computes proofs for each statement in parallel.
In this work we study a different, less investigated OR-proof technique, highlighted by Abe, Ohkubo, and Suzuki (ASIACRYPT'02). The difference is that the prover now computes the individual proofs sequentially. We show that such sequential OR-proofs yield signature schemes which can be proved secure in the non-programmable random oracle model. We complement this positive result with a black-box impossibility proof, showing that the same is unlikely to be the case for signatures derived from traditional OR-proofs. We finally argue that sequential-OR signature schemes can be proved secure in the quantum random oracle model, albeit with very loose bounds and by programming the random oracle.

2020

EUROCRYPT

Extracting Randomness from Extractor-Dependent Sources
📺 Abstract

We revisit the well-studied problem of extracting nearly uniform randomness from an arbitrary source of sufficient min-entropy. Strong seeded extractors solve this problem by relying on a public random seed, which is unknown to the source. Here, we consider a setting where the seed is reused over time and the source may depend on prior calls to the extractor with the same seed. Can we still extract nearly uniform randomness?
In more detail, we assume the seed is chosen randomly, but the source can make arbitrary oracle queries to the extractor with the given seed before outputting a sample. We require that the sample has entropy and differs from any of the previously queried values. The extracted output should look uniform even to a distinguisher that gets the seed. We consider two variants of the problem, depending on whether the source only outputs the sample, or whether it can also output some correlated public auxiliary information that preserves the sample's entropy. Our results are:
* Without Auxiliary Information: We show that every pseudo-random function (PRF) with a sufficiently high security level is a good extractor in this setting, even if the distinguisher is computationally unbounded. We further show that the source necessarily needs to be computationally bounded and that such extractors imply one-way functions.
* With Auxiliary Information: We construct secure extractors in this setting, as long as both the source and the distinguisher are computationally bounded. We give several constructions based on different intermediate primitives, yielding instantiations based on the DDH, DLIN, LWE or DCR assumptions. On the negative side, we show that one cannot prove security against computationally unbounded distinguishers in this setting under any standard assumption via a black-box reduction. Furthermore, even when restricting to computationally bounded distinguishers, we show that there exist PRFs that are insecure as extractors in this setting and that a large class of constructions cannot be proven secure via a black-box reduction from standard assumptions.

2020

EUROCRYPT

Measure-Rewind-Measure: Tighter Quantum Random Oracle Model Proofs for One-Way to Hiding and CCA Security
📺 Abstract

We introduce a new technique called `Measure-Rewind-Measure' (MRM) to achieve tighter security proofs in the quantum random oracle model (QROM).
We first apply our MRM technique to derive a new security proof for a variant of the `double-sided' quantum One-Way to Hiding Lemma (O2H) of Bindel et al. [TCC 2019] which, for the first time, avoids the square-root advantage loss in the security proof. In particular, it bypasses a previous `impossibility result' of Jiang, Zhang and Ma [IACR eprint 2019]. We then apply our new O2H Lemma to give a new tighter security proof for the Fujisaki-Okamoto transform for constructing a strong (INDCCA) Key Encapsulation Mechanism (KEM) from a weak (INDCPA) public-key encryption scheme satisfying a mild injectivity assumption.

2020

EUROCRYPT

Friet: an Authenticated Encryption Scheme with Built-in Fault Detection
📺 Abstract

In this work we present a duplex-based authenticated encryption scheme Friet based on a new permutation called Friet-P. We designed Friet-P with a novel approach for cryptographic permutations and block ciphers that takes fault-attack resistance into account and that we introduce in this paper.
In this method, we build a permutation f_C to be embedded in a larger one f. First, we define f as a sequence of steps that all abide a chosen error-correcting code C, i.e., that map C-codewords to C-codewords. Then, we embed f_C in f by first encoding its input to an element of C, applying f and then decoding back from C. This last step detects a fault when the output of f is not in C.
We motivate the design of the permutation we use in Friet and report on performance in soft- and hardware. We evaluate the fault-detection capabilities of the software and simulated hardware implementations with attacks. Finally, we perform a leakage evaluation.
Our code is available at https://github.com/thisimon/Friet.git.

2020

EUROCRYPT

New Slide Attacks on Almost Self-Similar Ciphers
📺 Abstract

The slide attack is a powerful cryptanalytic tool which has the unusual property that it can break iterated block ciphers with a complexity that does not depend on their number of rounds. However, it requires complete self similarity in the sense that all the rounds must be identical. While this can be the case in Feistel structures, this rarely happens in SP networks since the last round must end with an additional post-whitening subkey. In addition, in many SP networks the final round has additional asymmetries - for example, in AES the last round omits the MixColumns operation. Such asymmetry in the last round can make it difficult to utilize most of the advanced tools which were developed for slide attacks, such as deriving from one slid pair additional slid pairs by repeatedly
re-encrypting their ciphertexts. Consequently, almost all the successful applications of slide attacks against real cryptosystems (e.g., FF3, GOST,
SHACAL-1, etc.) had targeted Feistel structures rather than SP networks.
In this paper we overcome this last round problem by developing four new types of slide attacks. We demonstrate their power by applying them to many types of AES-like structures (with and without linear mixing in the last round, with known or secret S-boxes, with periodicity of 1,2 and 3 in their subkeys, etc).
In most of these cases, the time complexity of our attack is close to $2^{n/2}$, the smallest possible complexity for most slide attacks. Our new slide attacks have several unique properties: The first uses slid sets in which each plaintext from the first set forms a slid pair with some plaintext from the second set, but without knowing the exact correspondence. The second makes it possible to create from several slid pairs an exponential number of new slid pairs which form a hypercube spanned by the given pairs. The third has the unusual property that it is always successful, and the fourth can use known messages instead of chosen messages, with only slightly higher time complexity.

2020

EUROCRYPT

Formalizing Data Deletion in the Context of the Right to be Forgotten
📺 Abstract

The right of an individual to request the deletion of their personal data by an entity that might be storing it -- referred to as \emph{the right to be forgotten} -- has been explicitly recognized, legislated, and exercised in several jurisdictions across the world, including the European Union, Argentina, and California. However, much of the discussion surrounding this right offers only an intuitive notion of what it means for it to be fulfilled -- of what it means for such personal data to be deleted.
In this work, we provide a formal definitional framework for the right to be forgotten using tools and paradigms from cryptography. In particular, we provide a precise definition of what could be (or should be) expected from an entity that collects individuals' data when a request is made of it to delete some of this data. Our framework captures most, though not all, relevant aspects of typical systems involved in data processing. While it cannot be viewed as expressing the statements of current laws (especially since these are rather vague in this respect), our work offers technically precise definitions that represent possibilities for what the law could reasonably expect, and alternatives for what future versions of the law could explicitly require.
Finally, with the goal of demonstrating the applicability of our framework and definitions, we consider various natural and simple scenarios where the right to be forgotten comes up. For each of these scenarios, we highlight the pitfalls that arise even in genuine attempts at implementing systems offering deletion guarantees, and also describe technological solutions that provably satisfy our definitions. These solutions bring together techniques built by various communities.

2020

EUROCRYPT

PSI from PaXoS: Fast, Malicious Private Set Intersection
📺 Abstract

We present a 2-party private set intersection (PSI) protocol which provides security against malicious participants, yet is almost as fast as the fastest known semi-honest PSI protocol of Kolesnikov et al. (CCS 2016).
Our protocol is based on a new approach for two-party PSI, which can be instantiated to provide security against either malicious or semi-honest adversaries. The protocol is unique in that the only difference between the semi-honest and malicious versions is an instantiation with different parameters for a linear error-correction code. It is also the first PSI protocol which is concretely efficient while having linear communication and security against malicious adversaries, while running in the OT-hybrid model (assuming a non-programmable random oracle).
State of the art semi-honest PSI protocols take advantage of cuckoo hashing, but it has proven a challenge to use cuckoo hashing for malicious security. Our protocol is the first to use cuckoo hashing for malicious- secure PSI. We do so via a new data structure, called a probe-and-XOR of strings (PaXoS), which may be of independent interest. This abstraction captures important properties of previous data structures, most notably garbled Bloom filters. While an encoding by a garbled Bloom filter is larger by a factor of $\Omega(\lambda)$ than the original data, we describe a significantly improved PaXoS based on cuckoo hashing that achieves constant rate while being no worse in other relevant efficiency measures.

2020

EUROCRYPT

Efficient simulation of random states and random unitaries
📺 Abstract

We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access.
This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that t-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs.
In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar-random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error.
These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects.

2020

EUROCRYPT

Compact Adaptively Secure ABE from k-Lin: Beyond NC1 and towards NL
📺 Abstract

We present a new general framework for constructing compact and
adaptively secure attribute-based encryption (ABE) schemes from
k-Lin in asymmetric bilinear pairing groups. Previously, the only
construction [Kowalczyk and Wee, Eurocrypt '19] that simultaneously
achieves compactness and adaptive security from static assumptions supports
policies represented by Boolean formulae. Our framework enables
supporting more expressive policies represented by arithmetic
branching programs.
Our framework extends to ABE for policies represented by uniform models
of computation such as Turing machines. Such policies enjoy the feature
of being applicable to attributes of arbitrary lengths. We obtain the first
compact adaptively secure ABE for deterministic and non-deterministic finite
automata (DFA and NFA) from k-Lin, previously unknown from any static
assumptions. Beyond finite automata, we obtain the first ABE for large
classes of uniform computation, captured by deterministic and
non-deterministic logspace Turing machines (the complexity classes
L and NL) based on k-Lin. Our ABE scheme has compact
secret keys of size linear in the description size of the Turing machine M.
The ciphertext size grows linearly in the input length, but also linearly in
the time complexity, and exponentially in the space complexity.
Irrespective of compactness, we stress that our scheme is the first
that supports large classes of Turing machines based solely on standard
assumptions. In comparison, previous ABE for general Turing machines all
rely on strong primitives related to indistinguishability obfuscation.

2020

EUROCRYPT

Evolving Ramp Secret Sharing with a Small Gap
📺 Abstract

Evolving secret-sharing schemes, introduced by Komargodski, Naor, and Yogev (TCC 2016b), are secret-sharing schemes in which there is no a-priory upper bound on the number of parties that will participate. The parties arrive one by one and when a party arrives the dealer gives it a share; the dealer cannot update this share when other parties arrive. Motivated by the fact that when the number of parties is known, ramp secret-sharing schemes are more efficient than threshold secret-sharing schemes, we study evolving ramp secret-sharing schemes. Specifically, we study evolving $(b(j),g(j))$-ramp secret-sharing schemes, where $g,b: \NN\to \NN$ are non-decreasing functions. In such schemes, any set of parties that for some $j$ contains $g(j)$ parties from the first parties that arrive can reconstruct the secret, and any set such that for every $j$ contains less than $b(j)$ parties from the first $j$ parties that arrive cannot learn any information about the secret.
We focus on the case that the gap is small, namely $g(j)-b(j)=j^{\beta}$ for $0<\beta<1$. We show that there is an evolving ramp secret-sharing scheme with gap $t^{\beta}$, in which the share size of the $j$-th party is $\tilde{O}(j^{4-\frac{1}{\log^2 {1/\beta}}})$. Furthermore, we show that our construction results in much better share size for fixed values of $\beta$, i.e., there is an evolving ramp secret-sharing scheme with gap $\sqrt{j}$, in which the share size of the $j$-th party is $\tilde{O}(j)$. Our construction should be compared to the best known evolving $g(j)$-threshold secret-sharing schemes (i.e., when $b(j)=g(j)-1$) in which the share size of the $j$-th party is $\tilde{O}(j^4)$. Thus, our construction offers a significant improvement for every constant $\beta$, showing that allowing a gap between the sizes of the authorized and unauthorized sets can reduce the share size.
In addition, we present an evolving $(k/2,k)$-ramp secret-sharing scheme for a constant $k$ (which can be very big), where any set of parties of size at least $k$ can reconstruct the secret and any set of parties of size at most $k/2$ cannot learn any information about the secret. The share size of the $j$-th party in our construction is $O(\log k\log j)$. This is an improvement over the best known evolving $k$-threshold secret-sharing schemes in which the share size of the $j$-th party is $O(k\log j)$.

2020

EUROCRYPT

Quantum-access-secure message authentication via blind-unforgeability
📺 Abstract

Formulating and designing authentication of classical messages in the presence of adversaries with quantum query access has been a challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of ``predicting an unqueried value'' when the adversary can query in quantum superposition.
We propose a natural definition of unforgeability against quantum adversaries called blind unforgeability. This notion defines a function to be predictable if there exists an adversary who can use "partially blinded" oracle access to predict values in the blinded region. We support the proposal with a number of technical results. We begin by establishing that the notion coincides with EUF-CMA in the classical setting and go on to demonstrate that the notion is satisfied by a number of simple guiding examples, such as random functions and quantum-query-secure pseudorandom functions. We then show the suitability of blind unforgeability for supporting canonical constructions and reductions. We prove that the "hash-and-MAC" paradigm and the Lamport one-time digital signature scheme are indeed unforgeable according to the definition. In this setting, we additionally define and study a new variety of quantum-secure hash functions called Bernoulli-preserving.
Finally, we demonstrate that blind unforgeability is strictly stronger than a previous definition of Boneh and Zhandry [EUROCRYPT '13, CRYPTO '13] and resolve an open problem concerning this previous definition by constructing an explicit function family which is forgeable yet satisfies the definition.

2020

EUROCRYPT

He Gives C-Sieves on the CSIDH
📺 Abstract

Recently, Castryck, Lange, Martindale, Panny, and Renes proposed
\emph{CSIDH} (pronounced ``sea-side'') as a candidate post-quantum
``commutative group action.'' It has attracted much attention and
interest, in part because it enables noninteractive
Diffie--Hellman-like key exchange with quite small
communication. Subsequently, CSIDH has also been used as a foundation
for digital signatures.
In 2003--04, Kuperberg and then Regev gave asymptotically
subexponential quantum algorithms for ``hidden shift'' problems, which
can be used to recover the CSIDH secret key from a public key. In
late 2011, Kuperberg gave a follow-up quantum algorithm called the
\emph{collimation sieve} (``c-sieve'' for short), which improves the
prior ones, in particular by using exponentially less quantum memory
and offering more parameter tradeoffs. While recent works have
analyzed the concrete cost of the original algorithms (and variants)
against CSIDH, nothing of this nature was previously available for the
c-sieve.
This work fills that gap. Specifically, we generalize Kuperberg's
collimation sieve to work for arbitrary finite cyclic groups, provide
some practical efficiency improvements, give a classical (i.e.,
non-quantum) simulator, run experiments for a wide range of parameters
up to the actual CSIDH-512 group order, and concretely quantify the
complexity of the c-sieve against CSIDH.
Our main conclusion is that the proposed CSIDH parameters provide
relatively little quantum security beyond what is given by the cost of
quantumly evaluating the CSIDH group action itself (on a uniform
superposition). For example, the cost of CSIDH-512 key recovery is
only about~$2^{16}$ quantum evaluations using~$2^{40}$ bits of
quantumly accessible \emph{classical} memory (plus relatively small
other resources). This improves upon a prior estimate of~$2^{32.5}$
evaluations and~$2^{31}$ qubits of \emph{quantum} memory, for a
variant of Kuperberg's original sieve.
Under the plausible assumption that quantum evaluation does not cost
much more than what is given by a recent ``best case'' analysis,
CSIDH-512 can therefore be broken using significantly less
than~$2^{64}$ quantum T-gates. This strongly invalidates its claimed
NIST level~1 quantum security, especially when accounting for the
MAXDEPTH restriction. Moreover, under analogous assumptions for
CSIDH-1024 and -1792, which target higher NIST security levels, except
near the high end of the MAXDEPTH range even these instantiations fall
short of level~1.

2020

EUROCRYPT

Hardness of LWE on General Entropic Distributions
📺 Abstract

The hardness of the Learning with Errors (LWE) problem is by now a cornerstone of the cryptographic landscape, allowing to con- struct cryptographic schemes with properties unknown under other as- sumptions, and being conjectured to be resilient to quantum attacks. LWE is essentially the task of solving a noisy system of random linear equations over uniformly random secret variables (“the LWE secret”), evaluated modulo some integer. In applications the secret variables usu- ally correspond to the secret key of the cryptographic scheme.
It is therefore of great importance to understand what happens when the secret variables are not sampled uniformly (but still have some entropy). This is relevant for settings where an adversary manages to obtain partial information on the secret (a.k.a key leakage), for various theoretical ap- plications, and also for practical use where for efficiency or convenience it is easier to sample the secret from some non-uniform distribution. This so called “Entropic LWE” problem has been studied in a number of works, starting with Goldwasser et al. (ICS 2010). However, so far it was only known how to prove the hardness of Entropic LWE for secret distributions supported inside a ball of small radius.
In this work we resolve the hardness of Entropic LWE with arbitrary long secrets, in the following sense. We show an entropy bound that guarantees the security of arbitrary Entropic LWE. This bound is higher than what is required in the ball-bounded setting, but we show that this is essentially tight. Tightness is shown unconditionally for highly-composite moduli, and using black-box impossibility for arbitrary moduli. Technically, we show that the entropic hardness of LWE relies on a sim- ple to describe lossiness property of the distribution of secrets itself. This is simply the probability of recovering a random sample from this distri- bution s, given s + e, where e is Gaussian noise (i.e. the quality of the distribution of secrets as an error correcting code for Gaussian noise). We hope that this characterization will make it easier to derive entropic LWE results more easily in the future. We also use our techniques to show new results for the ball-bounded setting, essentially showing that under a strong enough assumption even polylogarithmic entropy suffices.

2020

EUROCRYPT

Candidate iO From Homomorphic Encryption Schemes
📺 Abstract

We propose a new approach to construct general-purpose indistinguishability obfuscation (iO). Our construction is obtained via a new intermediate primitive that we call split fully-homomorphic encryption (split FHE), which we show to be sufficient for constructing iO. Specifically, split FHE is FHE where decryption takes the following two-step syntactic form: (i) A secret decryption step uses the secret key and produces a hint which is (asymptotically) shorter than the length of the encrypted message, and (ii) a public decryption step that only requires the ciphertext and the previously generated hint (and not the entire secret key), and recovers the encrypted message. In terms of security, the hints for a set of ciphertexts should not allow one to violate semantic security for any other ciphertexts.
Next, we show a generic candidate construction of split FHE based on three building blocks: (i) A standard FHE scheme with linear decrypt-and-multiply (which can be instantiated with essentially all LWE-based constructions), (ii) a linearly homomorphic encryption scheme with short decryption hints (such as the Damgard-Jurik encryption scheme, based on the DCR problem), and (iii) a cryptographic hash function (which can be based on a variety of standard assumptions). Our approach is heuristic in the sense that our construction is not provably secure and makes implicit assumptions about the interplay between these underlying primitives. We show evidence that this construction is secure by providing an argument in an appropriately defined oracle model.
We view our construction as a big departure from the state-of-the-art constructions, and it is in fact quite simple.

2020

EUROCRYPT

Rational isogenies from irrational endomorphisms
📺 Abstract

In this paper, we introduce a polynomial-time algorithm to compute a connecting $\mathcal{O}$-ideal between two supersingular elliptic curves over $\mathbb{F}_p$ with common $\mathbb{F}_p$-endomorphism ring $\mathcal{O}$, given a description of their full endomorphism rings. This algorithm provides a reduction of the security of the CSIDH cryptosystem to the problem of computing endomorphism rings of supersingular elliptic curves. A similar reduction for SIDH appeared at Asiacrypt 2016, but relies on totally different techniques. Furthermore, we also show that any supersingular elliptic curve constructed using the complex-multiplication method can be located precisely in the supersingular isogeny graph by explicitly deriving a path to a known base curve. This result prohibits the use of such curves as a building block for a hash function into the supersingular isogeny graph.

2020

EUROCRYPT

Resource-Restricted Cryptography: Revisiting MPC Bounds in the Proof-of-Work Era
📺 Abstract

Traditional bounds on synchronous Byzantine agreement (BA) and secure multi-party computation (MPC) establish that in absence of a private correlated-randomness setup, such as a PKI,
protocols can tolerate up to $t<n/3$ of the parties being malicious. The introduction of ``Nakamoto style'' consensus, based on Proof-of-Work (PoW) blockchains, put forth a somewhat different flavor of BA,
showing that even a majority of corrupted parties
can be tolerated as long as the majority of the computation resources remain at honest hands. This assumption on honest majority of some resource was also extended to other resources such as stake, space, etc., upon which blockchains achieving Nakamoto-style consensus were built that violated the $t<n/3$ bound in terms of number of party corruptions. The above state of affairs
begs the question of whether the seeming mismatch is due to different goals and models, or whether the resource-restricting paradigm can be generically used to circumvent the $n/3$ lower bound.
In this work we study this question and formally demonstrate
how the above paradigm changes the rules of the game in cryptographic definitions.
First, we abstract the core properties that the resource-restricting paradigm offers by means of a functionality {\em wrapper}, in the UC framework, which when applied to a standard point-to-point network restricts the ability (of the adversary) to send new messages. We show that such a wrapped network can be implemented using the resource-restricting paradigm---concretely, using PoWs and honest majority of computing power---and that the traditional $t<n/3$ impossibility results fail when the parties have access to such a network. Our construction is in the {\em fresh} Common Reference String (CRS) model---i.e., it assumes a CRS which becomes available to the parties at the same time as to the adversary.
We then present constructions for BA and MPC, which given access to such a network tolerate $t<n/2$ corruptions without assuming a private correlated randomness setup. We also show how to remove the freshness assumption from the CRS by leveraging the power of a random oracle. Our MPC protocol achieves the standard notion of MPC security, where parties might have dedicated roles, as is for example the case in Oblivious Transfer protocols. This is in contrast to existing solutions basing MPC on PoWs, which associate roles to pseudonyms but do not link these pseudonyms with the actual parties.

2020

EUROCRYPT

Statistical ZAPR Arguments from Bilinear Maps
📺 Abstract

Dwork and Naor (FOCS '00) defined ZAPs as 2-message witness-indistinguishable proofs that are public-coin. We relax this to \emph{ZAPs with private Randomness} (ZAPRs), where the verifier can use private coins to sample the first message (independently of the statement being proved), but the proof must remain publicly verifiable given only the protocol transcript. In particular, ZAPRs are \emph{reusable}, meaning that the first message can be reused for multiple proofs without compromising security.
Known constructions of ZAPs from trapdoor permutations or bilinear maps are only computationally WI (and statistically sound). Two recent results of Badrinarayanan-Fernando-Jain-Khurana-Sahai and Goyal-Jain-Jin-Malavolta [EUROCRYPT '20] construct the first \emph{statistical ZAP arguments}, which are statistically WI (and computationally sound), from the quasi-polynomial LWE assumption. Here, we construct \emph{statistical ZAPR arguments} from the quasi-polynomial decision-linear (DLIN) assumption on groups with a bilinear map. Our construction relies on a combination of several tools including Groth-Ostrovsky-Sahai NIZK and NIWI [EUROCRYPT '06, CRYPTO '06, JACM '12], ``sometimes-binding statistically hiding commitments'' [Kalai-Khurana-Sahai, EUROCRYPT '18] and the ``MPC-in-the-head'' technique [Ishai-Kushilevitz-Ostrovsky-Sahai, STOC '07].

2020

EUROCRYPT

An Algebraic Attack on Rank Metric Code-Based Cryptosystems
📺 Abstract

The Rank metric decoding problem is the main problem considered in
cryptography based on codes in the rank metric. Very efficient schemes based
on this problem or quasi-cyclic versions of it have been proposed recently,
such as those in the submissions ROLLO and RQC currently at the second round
of the NIST Post-Quantum Cryptography Standardization Process. While
combinatorial attacks on this problem have been extensively studied and seem
now well understood, the situation is not as satisfactory for algebraic
attacks, for which previous work essentially suggested that they were
ineffective for cryptographic parameters.
In this paper, starting from Ourivski and Johansson's algebraic modelling of
the problem into a system of polynomial equations, we show how to augment
this system with easily computed equations so that the augmented system is
solved much faster via Gröbner bases. This happens because the augmented
system has solving degree $r$, $r+1$ or $r+2$ depending on the parameters,
where $r$ is the rank weight, which we show by extending results from Verbel
\emph{et al.} (PQCrypto 2019) on systems arising from the MinRank problem;
with target rank $r$, Verbel \emph{et al.} lower the solving degree to $r+2$,
and even less for some favorable instances that they call
``superdetermined''. We give complexity bounds for this approach as well as
practical timings of an implementation using \texttt{magma}. This improves
upon the previously known complexity estimates for both Gröbner basis and
(non-quantum) combinatorial approaches, and for example leads to an attack in
200 bits on ROLLO-I-256 whose claimed security was 256 bits.

2020

EUROCRYPT

SPARKs: Succinct Parallelizable Arguments of Knowledge
📺 Abstract

We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument system with the following three properties for computing and proving a time T (non-deterministic) computation:
- The prover's (parallel) running time is T + polylog T. (In other words, the prover's running time is essentially T for large computation times!)
- The prover uses at most polylog T processors.
- The communication complexity and verifier complexity are both polylog T.
While the third property is standard in succinct arguments, the combination of all three is desirable as it gives a way to leverage moderate parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover's parallel running time is not allowed.
Our main results are the following, all for non-deterministic polynomial-time RAM computation. We construct (1) an (interactive) SPARK based solely on the existence of collision-resistant hash functions, and (2) a non-interactive SPARK based on any collision-resistant hash function and any SNARK with quasi-linear overhead (as satisfied by recent SNARK constructions).

2020

EUROCRYPT

Statistical Zaps and New Oblivious Transfer Protocols
📺 Abstract

We study the problem of achieving statistical privacy in interactive proof systems and oblivious transfer -- two of the most well studied two-party protocols -- when limited rounds of interaction are available.
-- Statistical Zaps: We give the first construction of statistical Zaps, namely, two-round statistical witness-indistinguishable (WI) protocols with a public-coin verifier. Our construction achieves computational soundness based on the quasi-polynomial hardness of learning with errors assumption.
-- Three-Round Statistical Receiver-Private Oblivious Transfer: We give the first construction of a three-round oblivious transfer (OT) protocol -- in the plain model -- that achieves statistical privacy for receivers and computational privacy for senders against malicious adversaries, based on polynomial-time assumptions. The round-complexity of our protocol is optimal.
We obtain our first result by devising a public-coin approach to compress sigma protocols, without relying on trusted setup. To obtain our second result, we devise a general framework via a new notion of statistical hash commitments that may be of independent interest.

2020

EUROCRYPT

Impossibility Results for Lattice-Based Functional Encryption Schemes
📺 Abstract

Functional Encryption denotes a form of encryption where a master secret key-holder can control which functions a user can evaluate on encrypted data.
Learning With Errors (LWE) (Regev, STOC'05) is known to be a useful cryptographic hardness assumption which implies strong primitives such as, for example, fully homomorphic encryption (Brakerski et al., ITCS'12) and lockable obfuscation (Goyal et al., Wichs et al., FOCS'17). Despite its strength, however, there is just a limited number of functional encryption schemes which can be based on LWE. In fact, there are functional encryption schemes which can be achieved by using pairings but for which no secure instantiations from lattice-based assumptions are known: function-hiding inner product encryption (Lin, Baltico et al., CRYPTO'17) and compact quadratic functional encryption (Abdalla et al., CRYPTO'18). This raises the question whether there are some mathematical barriers which hinder us from realizing function-hiding and compact functional encryption schemes from lattice-based assumptions as LWE.
To study this problem, we prove an impossibility result for function-hiding functional encryption schemes which meet some algebraic restrictions at ciphertext encryption and decryption. Those restrictions are met by a lot of attribute-based, identity-based and functional encryption schemes whose security stems from LWE. Therefore, we see our results as important indications why it is hard to construct new functional encryption schemes from LWE and which mathematical restrictions have to be overcome to construct secure lattice-based functional encryption schemes for new functionalities.

2020

EUROCRYPT

Non-Interactive Zero-Knowledge in Pairing-Free Groups from Weaker Assumptions
📺 Abstract

We provide new constructions of non-interactive zero-knowledge arguments (NIZKs) for NP from discrete-logarithm-style assumptions over cyclic groups, without relying on pairings. A previous construction from (Canetti et al., Eurocrypt'18) achieves such NIZKs under the assumption that no efficient adversary can break the key-dependent message (KDM) security of (additive) ElGamal with respect to all (even inefficient) functions over groups of size $2^\lambda$, with probability better than $\poly(\lambda)/2^{\lambda}$. This is an extremely strong, non-falsifiable assumption. In particular, even mild (polynomial) improvements over the current best known attacks on the discrete logarithm problem would already contradict this assumption. (Canetti et al. STOC'19) describe how to improve the assumption to rely only on KDM security with respect to all efficient functions, therefore obtaining an assumption that is (in spirit) falsifiable.
Our first construction improves this state of affairs. We provide a construction of NIZKs for NP under the CDH assumption together with the assumption that no efficient adversary can break the key-dependent message one-wayness of ElGamal with respect to efficient functions over groups of size $2^\lambda$, with probability better than $\poly(\lambda)/2^{c\lambda}$ (denoted $2^{-c\lambda}$-OWKDM), for a constant $c = 3/4$. Unlike the previous assumption, our assumption leaves an exponential gap between the best known attack and the required security guarantee.
We also analyse whether we could build NIZKs when CDH does not hold. As a second contribution, we construct an infinitely often NIZK argument system for NP (where soundness and zero-knowledge are only guaranteed to hold for infinitely many security parameters), under the $2^{-c\lambda}$-OWKDM security of ElGamal with $c = 28/29+o(1)$, together with the existence of low-depth pseudorandom generators.

2020

EUROCRYPT

Succinct Non-Interactive Secure Computation
📺 Abstract

We present the first maliciously secure protocol for succinct non-interactive secure two-party computation (SNISC): Each player sends just a single message whose length is (essentially) independent of the running time of the function to be computed. The protocol does not require any trusted setup, satisfies superpolynomial-time simulation-based security (SPS), and is based on (subexponential) security of the Learning With Errors (LWE) assumption. We do not rely on SNARKs or "knowledge of exponent"-type assumptions.
Since the protocol is non-interactive, the relaxation to SPS security is needed, as standard polynomial-time simulation is impossible; however, a slight variant of our main protocol yields a SNISC with polynomial-time simulation in the CRS model.

2020

EUROCRYPT

Separate Your Domains: NIST PQC KEMs, Oracle Cloning and Read-Only Indifferentiability
📺 Abstract

It is convenient and common for schemes in the random oracle model to assume access to multiple random oracles (ROs), leaving to implementations the task --we call it oracle cloning-- of constructing them from a single RO. The first part of the paper is a case study of oracle cloning in KEM submissions to the NIST Post-Quantum Cryptography standardization process. We give key-recovery attacks on some submissions arising from mistakes in oracle cloning, and find other submissions using oracle cloning methods whose validity is unclear. Motivated by this, the second part of the paper gives a theoretical treatment of oracle cloning. We give a definition of what is an "oracle cloning method" and what it means for such a method to "work," in a framework we call read-only indifferentiability, a simple variant of classical indifferentiability that yields security not only for usage in single-stage games but also in multi-stage ones. We formalize domain separation, and specify and study many oracle cloning methods, including common domain-separating ones, giving some general results to justify (prove read-only indifferentiability of) certain classes of methods. We are not only able to validate the oracle cloning methods used in many of the unbroken NIST PQC KEMs, but also able to specify and validate oracle cloning methods that may be useful beyond that.

2020

EUROCRYPT

Efficient Constructions for Almost-everywhere Secure Computation
📺 Abstract

We study the problem of {\em almost-everywhere reliable message transmission}; a key component in designing efficient and secure MPC protocols for sparsely connected networks.
The goal is to design low-degree networks which allow a large fraction of honest nodes to communicate reliably even while linearly many nodes can experience byzantine corruption and deviate arbitrarily from the assigned protocol.\\
\noindent In this paper, we achieve a $\log$-degree network with a polylogarithmic work complexity protocol, thereby improving over the state-of-the-art result of Chandran {\em et al.} (ICALP 2010) who required a polylogarithmic-degree network and had a linear work complexity.
In addition, we also achieve:
\begin{itemize}
\item A work efficient version of Dwork et. al.'s (STOC 1986) butterfly network.
\item An improvement upon the state of the art protocol of Ben-or and Ron (Information Processing Letters 1996) in the randomized corruption model---both in work-efficiency and in resilience.

2020

EUROCRYPT

Broadcast-Optimal Two-Round MPC
📺 Abstract

An intensive effort by the cryptographic community to minimize the round complexity of secure multi-party computation (MPC) has recently led to optimal two-round protocols from minimal assumptions. Most of the proposed solutions, however, make use of a broadcast channel in every round, and it is unclear if the broadcast channel can be replaced by standard point-to-point communication in a round-preserving manner, and if so, at what cost on the resulting security.
In this work, we provide a complete characterization of the trade-off between number of broadcast rounds and achievable security level for two-round MPC tolerating arbitrarily many active corruptions. Specifically, we consider all possible combinations of broadcast and point-to-point rounds against the three standard levels of security for maliciously se- cure MPC protocols, namely, security with identifiable, unanimous, and selective abort. For each of these notions and each combination of broadcast and point-to-point rounds, we provide either a tight feasibility or an infeasibility result of two-round MPC. Our feasibility results hold assuming two-round OT in the CRS model, whereas our impossibility results hold given any correlated randomness.

2020

EUROCRYPT

Tornado: Automatic Generation of Probing-Secure Masked Bitsliced Implementations
📺 Abstract

Cryptographic implementations deployed in real world devices often aim at (provable) security against the powerful class of side-channel attacks while keeping reasonable performances. Last year at Asiacrypt, a new formal verification tool named tightPROVE was put forward to exactly determine whether a masked implementation is secure in the well-deployed probing security model for any given security order t. Also recently, a compiler named Usuba was proposed to automatically generate bitsliced implementations of cryptographic primitives.
This paper goes one step further in the security and performances achievements with a new automatic tool named Tornado. In a nutshell, from the high-level description of a cryptographic primitive, Tornado produces a functionally equivalent bitsliced masked implementation at any desired order proven secure in the probing model, but additionally in the so-called register probing model which much better fits the reality of software implementations. This framework is obtained by the integration of Usuba with tightPROVE+, which extends tightPROVE with the ability to verify the security of implementations in the register probing model and to fix them with inserting refresh gadgets at carefully chosen locations accordingly.
We demonstrate Tornado on the lightweight cryptographic primitives selected to the second round of the NIST competition and which somehow claimed to be masking friendly. It advantageously displays performances of the resulting masked implementations for several masking orders and prove their security in the register probing model.

2020

EUROCRYPT

Mathematics and Cryptography: A Marriage of Convenience?
📺 Abstract

★Invited Paper

Mathematics and cryptography have a long history together, with the ups and downs inherent in any long relationship. Whether it is a marriage of convenience or a love match, their progeny have lives of their own and have had an impact on the world. This invited lecture will briefly recall some high points from the past, give speculation and encouragement for the future of this marriage, and give counseling on how to improve communication, resolve conflicts, and play well together, based on personal experience and lessons learned.

2020

EUROCRYPT

Mind the Composition: Birthday Bound Attacks on EWCDMD and SoKAC21
📺 Abstract

In an early version of CRYPTO'17, Mennink and Neves proposed \textsf{EWCDMD}, a dual of \textsf{EWCDM}, and showed $n$-bit security, where $n$ is the block size of the underlying block cipher. In CRYPTO'19, Chen et al. proposed permutation based design \textsf{SoKAC21} and showed $2n/3$-bit security, where $n$ is the input size of the underlying permutation. In this paper we show birthday bound attacks on \textsf{EWCDMD} and \textsf{SoKAC21}, invalidating their security claims. Both attacks exploit an inherent composition nature present in the constructions.
Motivated by the above two attacks exploiting the composition nature, we consider some generic relevant composition based constructions of ideal primitives
(possibly in the ideal permutation and random oracle model) and present birthday bound distinguishers for them.
In particular, we demonstrate a birthday bound distinguisher against (1) a secret random permutation followed by a public random function and (2) composition of two secret random functions.
Our distinguishers for \textsf{SoKAC21} and \textsf{EWCDMD} are direct consequences of (1) and (2) respectively.

2020

EUROCRYPT

Double-Base Chains for Scalar Multiplications on Elliptic Curves
📺 Abstract

Double-base chains (DBCs) are widely used to speed up scalar multiplications on elliptic curves. We present three results of DBCs. First, we display a structure of the set containing all DBCs and propose an iterative algorithm to compute the number of DBCs for a positive integer. This is the first polynomial time algorithm to compute the number of DBCs for positive integers. Secondly, we present an asymptotic lower bound on average Hamming weights of DBCs $\frac{\log n}{8.25}$ for a positive integer $n$. This result answers an open question about the Hamming weights of DBCs. Thirdly, we propose a new algorithm to generate an optimal DBC for any positive integer. The time complexity of this algorithm is $\mathcal{O}\left(\left(\log n\right)^2 \log\log n\right)$ bit operations and the space complexity is $\mathcal{O}\left(\left(\log n\right)^{2}\right)$ bits of memory. This algorithm accelerates the recoding procedure by more than $6$ times compared to the state-of-the-art Bernstein, Chuengsatiansup, and Lange's work. The Hamming weights of optimal DBCs are over $60$\% smaller than those of NAFs. Experimental results show that scalar multiplication using our optimal DBC is about $13$\% faster than that using non-adjacent form on elliptic curves over large prime fields.

2020

EUROCRYPT

Low Weight Discrete Logarithms and Subset Sum in $2^{0.65n}$ with Polynomial Memory
📺 Abstract

We propose two heuristic polynomial memory collision finding algorithms for the low Hamming weight discrete logarithm problem in any abelian group $G$. The first one is a direct adaptation of the Becker-Coron-Joux (BCJ) algorithm for subset sum to the discrete logarithm setting. The second one significantly improves on this adaptation for all possible weights using a more involved application of the representation technique together with some new Markov chain analysis. In contrast to other low weight discrete logarithm algorithms, our second algorithm's time complexity interpolates to Pollard's $|G|^{\frac 1 2}$ bound for general discrete logarithm instances.
We also introduce a new heuristic subset sum algorithm with polynomial memory that improves on BCJ's $2^{0.72n}$ time bound for random subset sum instances $a_1, \ldots, a_n, t \in \Z_{2^n}$. Technically, we introduce a novel nested collision finding for subset sum -- inspired by the NestedRho algorithm from Crypto '16 -- that recursively produces collisions. We first show how to instantiate our algorithm with run time $2^{0.649n}$. Using further tricks, we are then able to improve its complexity down to $2^{0.645n}$.

2020

EUROCRYPT

Private Information Retrieval with Sublinear Online Time
📺 Abstract

★ Best Young Researcher Award

We present the first protocols for private information retrieval that allow fast (sublinear-time) database lookups without increasing the server-side storage requirements. To achieve these efficiency goals, our protocols work in an offline/online model. In an offline phase, which takes place before the client has decided which database bit it wants to read, the client fetches a short string from the servers. In a subsequent online phase, the client can privately retrieve its desired bit of the database by making a second query to the servers. By pushing the bulk of the server-side computation into the offline phase (which is independent of the client’s query), our protocols allow the online phase to complete very quickly—in time sublinear in the size of the database. Our protocols can provide statistical security in the two-server setting and computational security in the single-server setting. Finally, we prove that, in this model, our protocols are optimal in terms of the trade-off they achieve between communication and running time.

2020

EUROCRYPT

Side-channel Masking with Pseudo-Random Generator
📺 Abstract

High-order masking countermeasures against side-channel attacks usually require plenty of randomness during their execution. For security against t probes, the classical ISW countermeasure requires O(t^2 s) random bits, where s is the circuit size. However running a True Random Number Generator (TRNG) can be costly in practice and become a bottleneck on embedded devices. In [IKL+13] the authors introduced the notion of robust pseudo-random number generator (PRG), which must remain secure even against an adversary who can probe at most t wires. They showed that when embedding a robust PRG within a private circuit, the number of random bits can be reduced to O(t^4), that is independent of the circuit size s (up to a logarithmic factor). Using bipartite expander graphs, this can be further reduced to O(t^(3+eps)); however the resulting construction is unpractical.
In this paper we describe a practical construction where the number of random bits is only O(t^2) for security against t probes, without expander graphs; moreover the running time of each pseudo-random generation goes down from O(t^4) to O(t). Our technique consists in using multiple independent PRGs instead of a single one. We show that for ISW circuits, the robustness property of the PRG is not required anymore, which leads to simple and efficient constructions. For example, for AES we only need 48 bytes of randomness to get second-order security (t=2), instead of 2880 in the original Rivain-Prouff countermeasure; when implemented on an ARM-based embedded device with a relatively slow TRNG, we obtain a 50% speed-up compared to Rivain-Prouff.

2020

EUROCRYPT

Blackbox Secret Sharing Revisited: A Coding-Theoretic Approach with Application to Expansionless Near-Threshold Schemes
📺 Abstract

A {\em blackbox} secret sharing (BBSS) scheme works
in exactly the same way for all finite Abelian groups $G$; it can be instantiated for any such group $G$ and {\em only} black-box access to its group operations and to random group elements is required. A secret is a single group element and each of the $n$ players' shares is a vector of such elements. Share-computation and secret-reconstruction is by integer linear combinations. These do not depend on $G$, and neither do the privacy and reconstruction parameters $t,r$. This classical, fundamental primitive was introduced by Desmedt and Frankel (CRYPTO 1989) in their context of ``threshold cryptography.'' The expansion factor is the total number of group elements in a full sharing divided by $n$. For threshold BBSS with $t$-privacy ($1\leq t \leq n-1$), $t+1$-reconstruction and arbitrary $n$, constructions with minimal expansion $O(\log n)$ exist
(CRYPTO 2002, 2005).
These results are firmly rooted in number theory; each makes
(different) judicious choices of orders in number fields admitting
a vector of elements of very large length (in the number field degree) whose corresponding Vandermonde-determinant is sufficiently controlled
so as to enable BBSS by a suitable adaptation of Shamir's scheme.
Alternative approaches generally lead to very large expansion.
The state of the art of BBSS has not changed for the last 15 years.
Our contributions are two-fold.
(1) We introduce a novel, nontrivial, effective construction of BBSS based on {\em coding theory}
instead of number theory.
For threshold-BBSS we also achieve minimal expansion factor $O(\log n)$.
(2) Our method is more versatile. Namely, we show, for the first time, BBSS that is {\em near-threshold}, i.e.,
$r-t$ is an arbitrarily small
constant fraction of $n$, {\em and} that has expansion factor~$O(1)$, i.e.,
individual share-vectors of {\em constant} length (``asymptotically expansionless''). Threshold can be concentrated essentially freely
across full range. We also show expansion is minimal for near-threshold and that such BBSS cannot be attained by previous methods.
Our general construction is based on a well-known mathematical principle, the local-global principle. More precisely, we first construct BBSS over local rings through either Reed-Solomon or algebraic geometry codes. We then ``glue'' these schemes together in a dedicated manner to obtain a global secret sharing scheme, i.e., defined over the integers, which, as we finally prove using novel insights, has the desired BBSS properties. Though our main purpose here is advancing BBSS for its own sake, we also briefly address possible protocol applications.

2020

EUROCRYPT

Tight Security Bounds for Double-block Hash-then-Sum MACs
📺 Abstract

In this work, we study the security of deterministic MAC constructions with a double-block internal state, captured by the double-block hash-then-sum (DBH) paradigm. Most DBH constructions, including PolyMAC, SUM-ECBC, PMAC-Plus, 3kf9 and LightMAC-Plus, have been proved to be pseudorandom up to 2^{2n/3} queries when they are instantiated with an n-bit block cipher, while the best known generic attacks require 2^{3n/4} queries.
We close this gap by proving the PRF-security of DBH constructions up to 2^{3n/4} queries (ignoring the maximum message length). The core of the security proof is to refine Mirror theory that systematically estimates the number of solutions to a system of equations and non-equations, and apply it to prove the security of the finalization function. Then we identify security requirements of the internal hash functions to ensure 3n/4-bit security of the resulting constructions when combined with the finalization function.
Within this framework, we prove the security of DBH whose internal hash function is given as the concatenation of a universal hash function using two independent keys. This class of constructions include PolyMAC and SUM-ECBC. Moreover, we prove the security of PMAC-Plus, 3kf9 and LightMAC-Plus up to 2^{3n/4} queries.

2020

EUROCRYPT

On the Quantum Complexity of the Continuous Hidden Subgroup Problem
📺 Abstract

The Hidden Subgroup Problem (HSP) aims at capturing all problems that are susceptible to be solvable in quantum polynomial time following the blueprints of Shor's celebrated algorithm. Successful solutions to this problems over various commutative groups allow to efficiently perform number-theoretic tasks such as factoring or finding discrete logarithms.
The latest successful generalization (Eisenträger et al. STOC 2014) considers the problem of finding a full-rank lattice as the hidden subgroup of the continuous vector space R^m, even for large dimensions m. It unlocked new cryptanalytic algorithms (Biasse-Song SODA 2016, Cramer et al. EUROCRYPT 2016 and 2017), in particular to find mildly short vectors in ideal lattices.
The cryptanalytic relevance of such a problem raises the question of a more refined and quantitative complexity analysis. In the light of the increasing physical difficulty of maintaining a large entanglement of qubits, the degree of concern may be different whether the above algorithm requires only linearly many qubits or a much larger polynomial amount of qubits.
This is the question we start addressing with this work. We propose a detailed analysis of (a variation of) the aforementioned HSP algorithm, and conclude on its complexity as a function of all the relevant parameters. Our modular analysis is tailored to support the optimization of future specialization to cases of cryptanalytic interests. We suggest a few ideas in this direction.

2020

EUROCRYPT

Statistical ZAP Arguments
📺 Abstract

Dwork and Naor (FOCS'00) first introduced and constructed two message public coin witness indistinguishable proofs (ZAPs) for NP based on trapdoor permutations. Since then, ZAPs have also been obtained based on the decisional linear assumption on bilinear maps, and indistinguishability obfuscation, and have proven extremely useful in the design of several cryptographic primitives.
However, all known constructions of two-message public coin (or even publicly verifiable) proof systems only guarantee witness indistinguishability against computationally bounded verifiers.
In this paper, we construct the first public coin two message witness indistinguishable (WI) arguments for NP with {\em statistical} privacy, assuming quasi-polynomial hardness of the learning with errors (LWE) assumption. We also show that the same protocol has a super-polynomial simulator (SPS), which yields the first public-coin SPS statistical zero knowledge argument.
Prior to this, there were no known constructions of two-message publicly verifiable WI protocols under lattice assumptions, even satisfying the weaker notion of computational witness indistinguishability.

2020

EUROCRYPT

Tight Time-Space Lower Bounds for Finding Multiple Collision Pairs and Their Applications
📺 Abstract

We consider a \emph{collision search problem} (CSP), where given a parameter $C$, the goal is to find $C$ collision pairs in a random function $f:[N] \rightarrow [N]$ (where $[N] = \{0,1,\ldots,N-1\})$ using $S$ bits of memory. Algorithms for CSP have numerous cryptanalytic applications such as space-efficient attacks on double and triple encryption. The best known algorithm for CSP is \emph{parallel collision search} (PCS) published by van Oorschot and Wiener, which achieves the time-space tradeoff $T^2 \cdot S = \tilde{O}(C^2 \cdot N)$.
In this paper, we prove that any algorithm for CSP satisfies $T^2 \cdot S = \tilde{\Omega}(C^2 \cdot N)$, hence the best known time-space tradeoff is optimal (up to poly-logarithmic factors in $N$). On the other hand, we give strong evidence that proving similar unconditional time-space tradeoff lower bounds on CSP applications (such as breaking double and triple encryption) may be very difficult, and would imply a breakthrough in complexity theory. Hence, we propose a new restricted model of computation and prove that under this model, the best known time-space tradeoff attack on double encryption is optimal.

2020

EUROCRYPT

Integral Matrix Gram Root and Lattice Gaussian Sampling without Floats
📺 Abstract

Many advanced lattice based cryptosystems require to sample lattice points from Gaussian distributions. One challenge for this task is that all current algorithms resort to floating-point arithmetic (FPA) at some point, which has numerous drawbacks in practice: it requires numerical stability analysis, extra storage for high-precision, lazy/backtracking techniques for efficiency, and may suffer from weak determinism which can completely break certain schemes.
In this paper, we give techniques to implement Gaussian sampling over general lattices without using FPA. To this end, we revisit the approach of Peikert, using perturbation sampling. Peikert's approach uses continuous Gaussian sampling and some decomposition $\BSigma = \matA \matA^t$ of the target covariance matrix $\BSigma$. The suggested decomposition, e.g. the Cholesky decomposition, gives rise to a square matrix $\matA$ with real (not integer) entries. Our idea, in a nutshell, is to replace this decomposition by an integral one. While there is in general no integer solution if we restrict $\matA$ to being a square matrix, we show that such a decomposition can be efficiently found by allowing $\matA$ to be wider (say $n \times 9n$). This can be viewed as an extension of Lagrange's four-square theorem to matrices. In addition, we adapt our integral decomposition algorithm to the ring setting: for power-of-2 cyclotomics, we can exploit the tower of rings structure for improved complexity and compactness.

2020

EUROCRYPT

The Retracing Boomerang Attack
📺 Abstract

Boomerang attacks are extensions of differential attacks, that make it
possible to combine
two unrelated differential properties of the first and second part of a
cryptosystem with probabilities $p$ and $q$ into a new differential-like
property
of the whole cryptosystem with probability $p^2q^2$ (since each one of the
properties has to be satisfied twice). In this paper we describe a new
version of
boomerang attacks which uses the counterintuitive idea of throwing out most
of the data in order to force equalities between certain values
on the ciphertext side. In certain cases,
this creates a correlation between the four probabilistic events,
which increases the probability of the combined property to $p^2q$
and increases the signal to noise ratio of the resultant distinguisher.
We call this variant a {\it retracing boomerang attack} since we make
sure that the boomerang we throw follows the same path
on its forward and backward directions.
To demonstrate the power of the new
technique, we apply it to the case of 5-round AES. This version of AES was
repeatedly
attacked by a large variety of techniques, but for twenty years its
complexity had remained
stuck at $2^{32}$. At Crypto'18 it was finally reduced to $2^{24}$ (for full key recovery), and with
our
new technique we can further reduce the complexity of full key recovery to
the surprisingly low value of $2^{16.5}$
(i.e., only $90,000$ encryption/decryption operations are required for a full
key recovery on half the rounds of AES).
In addition to improving previous
attacks, our new technique unveils a hidden relationship between
boomerang attacks and two other cryptanalytic techniques, the yoyo game and
the recently introduced mixture differentials.

2020

EUROCRYPT

Optimal Merging in Quantum $k$-xor and $k$-sum Algorithms
📺 Abstract

The $k$-xor or Generalized Birthday Problem aims at finding, given $k$ lists of bit-strings, a $k$-tuple among them XORing to 0. If the lists are unbounded, the best classical (exponential) time complexity has withstood since Wagner's CRYPTO 2002 paper. If the lists are bounded (of the same size) and such that there is a single solution, the \emph{dissection algorithms} of Dinur \emph{et al.} (CRYPTO 2012) improve the memory usage over a simple meet-in-the-middle.
In this paper, we study quantum algorithms for the $k$-xor problem. With unbounded lists and quantum access, we improve previous work by Grassi \emph{et al.} (ASIACRYPT 2018) for almost all $k$. Next, we extend our study to lists of any size and with classical access only.
We define a set of ``merging trees'' which represent the best known strategies for quantum and classical merging in $k$-xor algorithms, and prove that our method is optimal among these. Our complexities are confirmed by a Mixed Integer Linear Program that computes the best strategy for a given $k$-xor problem. All our algorithms apply also when considering modular additions instead of bitwise xors.
This framework enables us to give new improved quantum $k$-xor algorithms for all $k$ and list sizes. Applications include the subset-sum problem, LPN with limited memory and the multiple-encryption problem.

2020

EUROCRYPT

Implementing Grover oracles for quantum key search on AES and LowMC
📺 Abstract

Grover's search algorithm gives a quantum attack against block ciphers by searching for a key that matches a small number of plaintext-ciphertext pairs. This attack uses O(N) calls to the cipher to search a key space of size N. Previous work in the specific case of AES derived the full gate cost by analyzing quantum circuits for the cipher, but focused on minimizing the number of qubits.
In contrast, we study the cost of quantum key search attacks under a depth restriction and introduce techniques that reduce the oracle depth, even if it requires more qubits. As cases in point, we design quantum circuits for the block ciphers AES and LowMC. Our circuits give a lower overall attack cost in both the gate count and depth-times-width cost models. In NIST's post-quantum cryptography standardization process, security categories are defined based on the concrete cost of quantum key search against AES. We present new, lower cost estimates for each category, so our work has immediate implications for the security assessment of post-quantum cryptography.
As part of this work, we release Q# implementations of the full Grover oracle for AES-128, -192, -256 and for the three LowMC instantiations used in Picnic, including unit tests and code to reproduce our quantum resource estimates. To the best of our knowledge, these are the first two such full implementations and automatic resource estimations.

2020

EUROCRYPT

Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS
📺 Abstract

We present a general methodology to construct preprocessing zkSNARKs where the structured reference string (SRS) is universal and updatable. This exploits a novel application of *holographic* IOPs, a natural generalization of holographic PCPs [Babai et al., STOC 1991].
We use our methodology to obtain a preprocessing zkSNARK where the SRS has linear size and arguments have constant size. Our construction improves on Sonic [Maller et al., CCS 2019], the prior state of the art in this setting, in all efficiency parameters: proving is an order of magnitude faster and verification is twice as fast, even with smaller SRS size and argument size. Our construction is most efficient when instantiated in the algebraic group model (also used by Sonic), but we also demonstrate how to realize it under concrete knowledge assumptions.
The core of our zkSNARK is a new holographic IOP for rank-1 constraint satisfiability (R1CS), which is the first to achieve linear proof length and constant query complexity (among other efficiency features).

2020

EUROCRYPT

Private Aggregation from Fewer Anonymous Messages
📺 Abstract

Consider the setup where $n$ parties are each given an element~$x_i$ in the finite field $\F_q$ and the goal is to compute the sum $\sum_i x_i$ in a secure fashion and with as little communication as possible.
We study this problem in the \emph{anonymized model} of Ishai et al.~(FOCS 2006) where each party may broadcast anonymous messages on an insecure channel.
We present a new analysis of the one-round ``split and mix'' protocol of Ishai et al.
In order to achieve the same security parameter, our analysis reduces the required number of messages by a $\Theta(\log n)$ multiplicative factor.
We also prove lower bounds showing that the dependence of the number of messages on the domain size, the number of parties, and the security parameter is essentially tight.
Using a reduction of Balle et al. (2019), our improved analysis of the protocol of Ishai et al. yields, in the same model, an $\left(\varepsilon, \delta\right)$-differentially private protocol for aggregation that, for any constant $\varepsilon > 0$ and any $\delta = \frac{1}{\poly(n)}$, incurs only a constant error and requires only a \emph{constant number of messages} per party. Previously, such a protocol was known only for $\Omega(\log n)$ messages per party.

2020

EUROCRYPT

Two-Round Oblivious Transfer from CDH or LPN
📺 Abstract

We show a new general approach for constructing maliciously-secure two-round oblivious transfer (OT). Specifically, we provide a generic sequence of transformations to upgrade a very basic notion of two-roundOT, which we call elementary OT, to UC-secure OT. We then give simple constructions of elementary OT under the Computational Diffie-Hellman(CDH) assumption or the Learning Parity with Noise (LPN) assumption, yielding the first constructions of malicious (UC-secure) two-round OT under these assumptions. Since two-round OT is complete for two-round 2-party and multi-party computation in the malicious setting, we also achieve the first constructions of the latter under these assumptions.

2020

EUROCRYPT

New Constructions of Statistical NIZKs: Dual-Mode DV-NIZKs and More
📺 Abstract

Non-interactive zero-knowledge proofs (NIZKs) are important primitives in cryptography. A major challenge since the early works on NIZKs has been to construct NIZKs with a statistical zero-knowledge guarantee against unbounded verifiers. In the common reference string (CRS) model, such "statistical NIZK arguments" are currently known from k-Lin in a pairing-group and from LWE. In the (reusable) designated-verifier model (DV-NIZK), where a trusted setup algorithm generates a reusable verification key for checking proofs, we also have a construction from DCR. If we relax our requirements to computational zero-knowledge, we additionally have NIZKs from factoring and CDH in a pairing group in the CRS model, and from nearly all assumptions that imply public-key encryption (e.g., CDH, LPN, LWE) in the designated-verifier model. Thus, there still remains a gap in our understanding of statistical NIZKs in both the CRS and the designated-verifier models.
In this work, we develop new techniques for constructing statistical NIZK arguments. First, we construct statistical DV-NIZK arguments from the k-Lin assumption in pairing-free groups, the QR assumption, and the DCR assumption. These are the first constructions in pairing-free groups and from QR that satisfy statistical zero-knowledge. All of our constructions are secure even if the verification key is chosen maliciously (i.e., they are "malicious-designated-verifier" NIZKs), and moreover, they satisfy a "dual-mode" property where the CRS can be sampled from two computationally indistinguishable distributions: one distribution yields statistical DV-NIZK arguments while the other yields computational DV-NIZK proofs. We then show how to adapt our k-Lin construction in a pairing group to obtain new publicly-verifiable statistical NIZK arguments from pairings with a qualitatively weaker assumption than existing constructions of pairing-based statistical NIZKs.
Our constructions follow the classic paradigm of Feige, Lapidot, and Shamir (FLS). While the FLS framework has traditionally been used to construct computational (DV)-NIZK proofs, we newly show that the same framework can be leveraged to construct dual-mode (DV)-NIZKs.

2020

EUROCRYPT

Combiners for Functional Encryption, Unconditionally
📺 Abstract

Functional encryption (FE) combiners allow one to combine many candidates for a functional encryption scheme, possibly based on different computational assumptions, into another functional encryption candidate with the guarantee that the resulting candidate is secure as long as at least one of the original candidates is secure. The fundamental question in this area is whether FE combiners exist.
There have been a series of works Ananth et. al. (CRYPTO '16), Ananth-Jain-Sahai (EUROCRYPT '17), Ananth et. al (TCC '19) on constructing FE combiners from various assumptions.
We give the first unconditional construction of combiners for functional encryption, resolving this question completely. Our construction immediately implies an unconditional universal functional encryption scheme, an FE scheme that is secure if such an FE scheme exists. Previously such results either relied on algebraic assumptions or required subexponential security assumptions.

2020

EUROCRYPT

On the Streaming Indistinguishability of a Random Permutation and a Random Function
📺 Abstract

An adversary with $S$ bits of
memory obtains a stream of $Q$ elements that are uniformly drawn from the set $\{1,2,\ldots,N\}$, either with or without replacement. This corresponds to sampling $Q$ elements using either a random function or a random permutation. The adversary's goal is to distinguish between these two cases.
This problem was first considered by Jaeger and Tessaro (EUROCRYPT 2019), which proved that the adversary's advantage is upper bounded by $\sqrt{Q \cdot S/N}$. Jaeger and Tessaro used this bound as a streaming switching lemma which allowed proving that known time-memory tradeoff attacks on several modes of operation (such as counter-mode) are optimal up to a factor of $O(\log N)$ if $Q \cdot S \approx N$. However, the bound's proof assumed an unproven combinatorial conjecture. Moreover,
if $Q \cdot S \ll N$ there is a gap between the upper bound of $\sqrt{Q \cdot S/N}$ and the $Q \cdot S/N$ advantage obtained by known attacks.
In this paper, we prove a tight upper bound (up to poly-logarithmic factors) of $O(\log Q \cdot Q \cdot S/N)$ on the adversary's advantage in the streaming distinguishing problem. The proof does not require a conjecture and is based on a hybrid argument that gives rise to a reduction from the unique-disjointness communication complexity problem to streaming.

2020

EUROCRYPT

Fault Template Attacks on Block Ciphers Exploiting Fault Propagation
📺 Abstract

Fault attacks (FA) are one of the potent practical threats to modern cryptographic implementations. Over the years the FA techniques have evolved, gradually moving towards the exploitation of device-centric properties of the faults. In this paper, we exploit the fact that activation and propagation of a fault through a given combinational circuit (i.e., observability of a fault) is data-dependent. Next, we show that this property of combinational circuits leads to powerful Fault Template Attacks (FTA), even for implementations having dedicated protections against both power and fault-based vulnerabilities. The attacks found in this work are applicable even if the fault injection is made at the middle rounds of a block cipher, which are out of reach for most of the
other existing fault analysis strategies. Quite evidently, they also work for
a known-plaintext scenario. Moreover, the middle round attacks are entirely blind in the sense that no access to the ciphertexts (correct/faulty) or plaintexts are required. The adversary is only assumed to have the power of repeating an unknown plaintext several times. Practical validation over a hardware implementation of SCA-FA protected PRESENT, and simulated evaluation on a public software implementation of protected AES prove the efficacy of the proposed attacks.

2020

EUROCRYPT

On the Memory-Tightness of Hashed ElGamal
📺 Abstract

We study the memory-tightness of security reductions in public-key
cryptography, focusing in particular on Hashed ElGamal. We prove that
any {\em straightline} (i.e., without rewinding) black-box reduction
needs memory which grows linearly with the number of queries of the
adversary it has access to, as long as this reduction treats the
underlying group generically. This makes progress towards proving a
conjecture by Auerbach {\em et al.} (CRYPTO 2017), and is also the
first lower bound on memory-tightness for a concrete cryptographic
scheme (as opposed to generalized reductions across security
notions). Our proof relies on compression arguments in the generic
group model.

2020

EUROCRYPT

On a Generalization of Substitution-Permutation Networks: The HADES Design Strategy
📺 Abstract

Keyed and unkeyed cryptographic permutations often iterate simple round functions. Substitution-permutation networks (SPNs) are an approach that is popular since the mid 1990s. One of the new directions in the design of these round functions is to reduce the substitution (S-Box) layer from a full one to a partial one, uniformly distributed over all the rounds. LowMC and Zorro are examples of this approach.
A relevant freedom in the design space is to allow for a highly non-uniform distribution of S-Boxes. However, choosing rounds that are so different from each other is very rarely done, as it makes security analysis and implementation much harder.
We develop the design strategy HADES and an analysis framework for it, which despite this increased complexity allows for security arguments against many classes of attacks, similar to earlier simpler SPNs.
The framework builds upon the wide trail design strategy, and it additionally allows for security arguments against algebraic attacks, which are much more of a concern when algebraically simple S-Boxes are used.
Subsequently, this is put into practice by concrete instances and benchmarks for a use case that generally benefits from a smaller number of S-Boxes and showcases the diversity of design options we support: A candidate cipher natively working with objects in GF(p), for securing data transfers with distributed databases using secure multiparty computation (MPC). Compared to the currently fastest design MiMC, we observe significant improvements in online bandwidth requirements and throughput with a simultaneous reduction of preprocessing effort, while having a comparable online latency.

2020

EUROCRYPT

Security of Hedged Fiat-Shamir Signatures under Fault Attacks
📺 Abstract

Deterministic generation of per-signature randomness has been a widely accepted solution to mitigate the catastrophic risk of randomness failure in Fiat--Shamir type signature schemes. However, recent studies have practically demonstrated that such de-randomized schemes, including EdDSA, are vulnerable to differential fault attacks, which enable adversaries to recover the entire secret signing key, by artificially provoking randomness reuse or corrupting computation in other ways. In order to balance concerns of both randomness failures and the threat of fault injection, some signature designs are advocating a ``hedged'' derivation of the per-signature randomness, by hashing the secret key, message, and a nonce. Despite the growing popularity of the hedged paradigm in practical signature schemes, to the best of our knowledge, there has been no attempt to formally analyze the fault resilience of hedged signatures.
We perform a formal security analysis of the fault resilience of signature schemes constructed via the Fiat--Shamir transform. We propose a model to characterize bit-tampering fault attacks, and investigate their impact across different steps of the signing operation. We prove that, for some types of faults, attacks are mitigated by the hedged paradigm, while attacks remain possible for others. As concrete case studies, we then apply our results to XEdDSA, a hedged version of EdDSA used in the Signal messaging protocol, and to Picnic2, a hedged Fiat--Shamir signature scheme in Round 2 of the NIST Post-Quantum standardization process.

2020

EUROCRYPT

Compact NIZKs from Standard Assumptions on Bilinear Maps
📺 Abstract

A non-interactive zero-knowledge (NIZK) protocol enables a prover to convince a verifier of the truth of a statement without leaking any other information by sending a single message. The main focus of this work is on exploring short pairing-based NIZKs for all NP languages based on standard assumptions. In this regime, the seminal work of Groth, Ostrovsky, and Sahai (J.ACM'12) (GOS-NIZK) is still considered to be the state-of-the-art. Although fairly efficient, one drawback of GOS-NIZK is that the proof size is multiplicative in the circuit size computing the NP relation. That is, the proof size grows by $O(|C|k)$, where $C$ is the circuit for the NP relation and $k$ is the security parameter.
By now, there have been numerous follow-up works focusing on shortening the proof size of pairing-based NIZKs, however, thus far, all works come at the cost of relying either on a non-standard knowledge-type assumption or a non-static $q$-type assumption. Specifically, improving the proof size of the original GOS-NIZK under the same standard assumption has remained as an open problem.
Our main result is a construction of a pairing-based NIZK for all of NP whose proof size is additive in $|C|$, that is, the proof size only grows by $|C| +poly(k)$, based on the decisional linear (DLIN) assumption. Since the DLIN assumption is the same assumption underlying GOS-NIZK, our NIZK is a strict improvement on their proof size.
As by-products of our main result, we also obtain the following two results: (1) We construct a perfectly zero-knowledge NIZK (NIPZK) for NP relations computable in NC1 with proof size $|w|poly(k)$ where $|w|$ is the witness length based on the DLIN assumption. This is the first pairing-based NIPZK for a non-trivial class of NP languages whose proof size is independent of $|C|$ based on a standard assumption. (2) We construct a universally composable (UC) NIZK for NP relations computable in NC1 in the erasure-free adaptive setting whose proof size is $|w|poly(k)$ from the DLIN assumption. This is an improvement over the recent result of Katsumata, Nishimaki, Yamada, and Yamakawa (CRYPTO'19), which gave a similar scheme based on a non-static $q$-type assumption.
The main building block for all of our NIZKs is a constrained signature scheme with decomposable online-offline efficiency. This is a property which we newly introduce in this paper and construct from the DLIN assumption. We believe this construction is of an independent interest.

2020

EUROCRYPT

Key Recovery from Gram--Schmidt Norm Leakage in Hash-and-Sign Signatures over NTRU Lattices
📺 Abstract

In this paper, we initiate the study of side-channel leakage in hash-and-sign lattice-based signatures, with particular emphasis on the two efficient implementations of the original GPV lattice-trapdoor paradigm for signatures, namely NIST second-round candidate Falcon and its simpler predecessor DLP. Both of these schemes implement the GPV signature scheme over NTRU lattices, achieving great speed-ups over the general lattice case. Our results are mainly threefold.
First, we identify a specific source of side-channel leakage in most implementations of those schemes, namely, the one-dimensional Gaussian sampling steps within lattice Gaussian sampling. It turns out that the implementations of these steps often leak the Gram--Schmidt norms of the secret lattice basis.
Second, we elucidate the link between this leakage and the secret key, by showing that the entire secret key can be efficiently reconstructed solely from those Gram--Schmidt norms. The result makes heavy use of the algebraic structure of the corresponding schemes, which work over a power-of-two cyclotomic field.
Third, we concretely demonstrate the side-channel attack against DLP (but not Falcon due to the different structures of the two schemes). The challenge is that timing information only provides an approximation of the Gram--Schmidt norms, so our algebraic recovery technique needs to be combined with pruned tree search in order to apply it to approximate values. Experimentally, we show that around $2^{35}$ DLP traces are enough to reconstruct the entire key with good probability.

2020

EUROCRYPT

Adaptively Secure ABE for DFA from k-Lin and More
📺 Abstract

In this work, we present:
- the first adaptively secure ABE for DFA from the k-Lin assumption in prime-order bilinear groups; this resolves one of open problems posed by Waters [CRYPTO'12];
- the first ABE for NFA from the k-Lin assumption, provided the number of accepting paths is smaller than the order of the underlying group; the scheme achieves selective security;
- the first compact adaptively secure ABE (supporting unbounded multi-use of attributes) for branching programs from the k-Lin assumption, which generalizes and simplifies the recent result of Kowalczyk and Wee for boolean formula (NC1) [EUROCRYPT'19].
Our adaptively secure ABE for DFA relies on a new combinatorial mechanism avoiding the exponential security loss in the number of states when naively combining two recent techniques from CRYPTO'19 and EUROCRYPT'19. This requires us to design a selectively secure ABE for NFA; we give a construction which is sufficient for our purpose and of independent interest. Our ABE for branching programs leverages insights from our ABE for DFA.

2020

EUROCRYPT

Blind Schnorr Signatures and Signed ElGamal Encryption in the Algebraic Group Model
📺 Abstract

The Schnorr blind signing protocol allows blind issuing of Schnorr signatures, one of the most widely used signatures. Despite its practical relevance, its security analysis is unsatisfactory. The only known security proof is informal and in the combination of the generic group model (GGM) and the random oracle model (ROM) assuming that the ``ROS problem'' is hard. The situation is similar for (Schnorr-)signed ElGamal encryption, a simple CCA2-secure variant of ElGamal.
We analyze the security of these schemes in the algebraic group model (AGM), an idealized model closer to the standard model than the GGM. We first prove tight security of Schnorr signatures from the discrete logarithm assumption (DL) in the AGM+ROM. We then give a rigorous proof for blind Schnorr signatures in the AGM+ROM assuming hardness of the one-more discrete logarithm problem and ROS.
As ROS can be solved in sub-exponential time using Wagner's algorithm, we propose a simple modification of the signing protocol, which leaves the signatures unchanged. It is therefore compatible with systems that already use Schnorr signatures, such as blockchain protocols. We show that the security of our modified scheme relies on the hardness of a problem related to ROS that appears much harder. Finally, we give tight reductions, again in the AGM+ROM, of the CCA2 security of signed ElGamal encryption to DDH and signed hashed ElGamal key encapsulation to DL.

2020

EUROCRYPT

Lower Bounds for Leakage-Resilient Secret Sharing
📺 Abstract

Threshold secret sharing allows a dealer to split a secret into $n$ shares such that any authorized subset of cardinality at least $t$ of those shares efficiently reveals the secret, while at the same time any unauthorized subset of cardinality less than $t$ contains no information about the secret. Leakage-resilience additionally requires that the secret remains hidden even if one is given a bounded amount of additional leakage from every share.
In this work, we study leakage-resilient secret sharing schemes and prove a lower bound on the share size and the required amount randomness of any information-theoretically secure scheme.
We prove that for any information-theoretically secure leakage-resilient secret sharing scheme either the amount of randomness across all shares or the share size has to be linear in $n$.
More concretely, for a secret sharing scheme with $p$-bit long shares, $\ell$-bit leakage per share, where $\widehat{t}$ shares uniquely define the remaining $n - \widehat{t}$ shares, it has to hold that $p \ge \frac{\ell (n - t)}{\widehat{t}}$.
We use this lower bound to gain further insights into a question that was recently posed by Benhamouda et al. (CRYPTO'18), who ask to what extend existing regular secret sharing schemes already provide protection against leakage.
The authors proved that Shamir's secret sharing is $1$-bit leakage-resilient for reconstruction thresholds $t \geq 0.85n$ and conjectured that it is also $1$-bit leakage-resilient for any other threshold that is a constant fraction of the total number of shares.
We do not disprove their conjecture, but show that it is the best one could possibly hope for.
Concretely, we show that for large enough $n$ and any constant $0< c < 1$ it holds that Shamir's secret sharing scheme is \emph{not} leakage-resilient for $t \leq \frac{cn}{\log n}$.
In contrast to the setting with information-theoretic security, we show that our lower bound does not hold in the computational setting.
That is, we show how to construct a leakage-resilient secret sharing scheme in the random oracle model that is secure against computationally bounded adversaries and violates the lower bound stated above.

2020

EUROCRYPT

Secure Multi-party Quantum Computation with a Dishonest Majority
📺 Abstract

The cryptographic task of secure multi-party (classical) computation has received a lot of attention in the last decades. Even in the extreme case where a computation is performed between k mutually distrustful players, and security is required even for the single honest player if all other players are colluding adversaries, secure protocols are known. For quantum computation, on the other hand, protocols allowing arbitrary dishonest majority have only been proven for k=2. In this work, we generalize the approach taken by Dupuis, Nielsen and Salvail (CRYPTO 2012) in the two-party setting to devise a secure, efficient protocol for multi-party quantum computation for any number of players k, and prove security against up to k-1 colluding adversaries. The quantum round complexity of the protocol for computing a quantum circuit of {CNOT, T} depth d is O(k (d + log n)), where n is the security parameter. To achieve efficiency, we develop a novel public verification protocol for the Clifford authentication code, and a testing protocol for magic-state inputs, both using classical multi-party computation.

2020

EUROCRYPT

Sigma protocols for MQ, PKP and SIS, and fishy signature schemes
📺 Abstract

This work presents sigma protocols to prove knowledge of:
- a solution to a system of quadratic polynomials,
- a solution to an instance of the Permuted Kernel Problem and
- a witness for a variety of lattice statements (including SIS).
Our sigma protocols have soundness error 1/q', where q' is any number bounded by the size of the underlying finite field. This is much better than existing proofs, which have soundness error 2/3 or (q'+1)/2q'. The prover and verifier time our proofs are O(q'). We achieve this by first constructing so-called sigma protocols with helper, which are sigma protocols where the prover and the verifier are assisted by a trusted third party, and then eliminating the helper from the proof with a "cut-and-choose" protocol. We apply the Fiat-Shamir transform to obtain signature schemes with security proof in the QROM. We show that the resulting signature schemes, which we call the "MUltivariate quaDratic FIat-SHamir" scheme (MUDFISH) and the "ShUffled Solution to Homogeneous linear SYstem FIat-SHamir" scheme (SUSHSYFISH), are more efficient than existing signatures based on the MQ problem and the Permuted Kernel Problem. Our proof system can be used to improve the efficiency of applications relying on (generalizations of) Stern's protocol. We show that the proof size of our SIS proof is smaller than that of Stern's protocol by an order of magnitude and that our proof is more efficient than existing post-quantum secure SIS proofs.

2020

PKC

Fast, Compact, and Expressive Attribute-Based Encryption
📺 Abstract

Attribute-based encryption (ABE) is an advanced cryptographic tool and useful to build various types of access control systems. Toward the goal of making ABE more practical, we propose key-policy (KP) and ciphertext-policy (CP) ABE schemes, which first support unbounded sizes of attribute sets and policies with negation and multi-use of attributes, allow fast decryption, and are adaptively secure under a standard assumption, simultaneously. Our schemes are more expressive than previous schemes and efficient enough. To achieve the adaptive security along with the other properties, we refine the technique introduced by Kowalczyk and Wee (Eurocrypt’19) so that we can apply the technique more expressive ABE schemes. Furthermore, we also present a new proof technique that allows us to remove redundant elements used in their ABE schemes. We implement our schemes in 128-bit security level and present their benchmarks for an ordinary personal computer and smartphones. They show that all algorithms run in one second with the personal computer when they handle any policy or attribute set with one hundred attributes.

2020

PKC

Adaptive Simulation Security for Inner Product Functional Encryption
📺 Abstract

Inner product functional encryption ( $${mathsf {IPFE}}$$ ) [ 1 ] is a popular primitive which enables inner product computations on encrypted data. In $${mathsf {IPFE}}$$ , the ciphertext is associated with a vector $$varvec{x}$$ , the secret key is associated with a vector $$varvec{y}$$ and decryption reveals the inner product $$langle varvec{x},varvec{y}
angle $$ . Previously, it was known how to achieve adaptive indistinguishability ( $$mathsf {IND}$$ ) based security for $${mathsf {IPFE}}$$ from the $$mathsf {DDH}$$ , $$mathsf {DCR}$$ and $$mathsf {LWE}$$ assumptions [ 8 ]. However, in the stronger simulation ( $$mathsf {SIM}$$ ) based security game, it was only known how to support a restricted adversary that makes all its key requests either before or after seeing the challenge ciphertext, but not both. In more detail, Wee [ 46 ] showed that the $$mathsf {DDH}$$ -based scheme of Agrawal et al. (Crypto 2016) achieves semi-adaptive simulation-based security, where the adversary must make all its key requests after seeing the challenge ciphertext. On the other hand, O’Neill showed that all $$mathsf {IND}$$ -secure $${mathsf {IPFE}}$$ schemes (which may be based on $$mathsf {DDH}$$ , $$mathsf {DCR}$$ and $$mathsf {LWE}$$ ) satisfy $$mathsf {SIM}$$ based security in the restricted model where the adversary makes all its key requests before seeing the challenge ciphertext. In this work, we resolve the question of $$mathsf {SIM}$$ -based security for $${mathsf {IPFE}}$$ by showing that variants of the $${mathsf {IPFE}}$$ constructions by Agrawal et al. , based on $$mathsf {DDH}$$ , Paillier and $$mathsf {LWE}$$ , satisfy the strongest possible adaptive $$mathsf {SIM}$$ -based security where the adversary can make an unbounded number of key requests both before and after seeing the (single) challenge ciphertext. This establishes optimal security of the $${mathsf {IPFE}}$$ schemes, under all hardness assumptions on which it can (presently) be based.

2020

PKC

Verifiable Inner Product Encryption Scheme
📺 Abstract

In the standard setting of functional encryption (FE), we assume both the Central Authority (CA) and the encryptors to run their respective algorithms faithfully. Badrinarayanan et al. [ASIACRYPT 2016] proposed the concept of verifiable FE, which essentially guarantees that dishonest encryptors and authorities, even when colluding together, are not able to generate ciphertexts and tokens that give “inconsistent” results. They also provide a compiler turning any perfectly correct FE into a verifiable FE, but do not give efficient constructions. In this paper we improve on this situation by considering Inner-Product Encryption (IPE), which is a special case of functional encryption and a primitive that has attracted wide interest from both practitioners and researchers in the last decade. Specifically, we construct the first efficient verifiable IPE (VIPE) scheme according to the inner-product functionality of Katz, Sahai and Waters [EUROCRYPT 2008]. To instantiate the general construction of Badrinarayanan et al. we need to solve several additional challenges. In particular, we construct the first efficient perfectly correct IPE scheme. Our VIPE satisfies unconditional verifiability, whereas its privacy relies on the DLin assumption.

2020

PKC

A New Paradigm for Public-Key Functional Encryption for Degree-2 Polynomials
📺 Abstract

We give the first public-key functional encryption that supports the generation of functional decryption keys for degree-2 polynomials, with succinct ciphertexts, whose semi-adaptive simulation-based security is proven under standard assumptions. At the heart of our new paradigm lies a so-called partially function-hiding functional encryption scheme for inner products, which admits public-key instances, and that is sufficient to build functional encryption for degree-2 polynomials. Doing so, we improve upon prior works, such as the constructions from Lin (CRYPTO 17) or Ananth Sahai (EUROCRYPT 17), both of which rely on function-hiding inner product FE, that can only exist in the private-key setting. The simplicity of our construction yields the most efficient FE for quadratic functions from standard assumptions (even those satisfying a weaker security notion). The interest of our methodology is that the FE for quadratic functions that builds upon any partially function-hiding FE for inner products inherits the security properties of the latter. In particular, we build a partially function-hiding FE for inner products that enjoys simulation security, in the semi-adaptive setting, where the challenge sent from the adversary can be chosen adaptively after seeing the public key (but before corrupting functional decryption keys). This is in contrast from prior public-key FE for quadratic functions from Baltico et al. (CRYPTO 17), which only achieved an indistinguishability-based, selective security. As a bonus, we show that we can obtain security against Chosen-Ciphertext Attacks straightforwardly. Even though this is the de facto security notion for encryption, this was not achieved by prior functional encryption schemes for quadratic functions, where the generic Fujisaki Okamoto transformation (CRYPTO 99) does not apply.

2020

PKC

Master-Key KDM-Secure IBE from Pairings
📺 Abstract

Identity-based encryption (IBE) is a generalization of public-key encryption (PKE) by allowing encryptions to be made to user identities. In this work, we seek to obtain IBE schemes that achieve key-dependent-message (KDM) security with respect to messages that depend on the master secret key. Previous KDM-secure schemes only achieved KDM security in simpler settings, in which messages may only depend on user secret keys. An important motivation behind studying master-KDM security is the application of this notion in obtaining generic constructions of KDM-CCA secure PKE, a primitive notoriously difficult to realize. We give the first IBE that achieves master-KDM security from standard assumptions in pairing groups. Our construction is modular and combines techniques from KDM-secure PKE based from hash-proof systems, together with IBE that admits a tight security proof in the multi-challenge setting, which happens to be unexpectedly relevant in the context of KDM security. In fact, to the best of our knowledge, this is the first setting where techniques developed in the context of realizing tightly secure cryptosystems have led to a new feasibility result. As a byproduct, our KDM-secure IBE, and thus the resulting KDM-CCA-secure PKE both enjoy a tight security reduction, independent of the number of challenge ciphertexts, which was not achieved before.

2020

PKC

Hierarchical Identity-Based Encryption with Tight Multi-challenge Security
📺 Abstract

We construct the first hierarchical identity-based encryption (HIBE) scheme with tight adaptive security in the multi-challenge setting, where adversaries are allowed to ask for ciphertexts for multiple adaptively chosen identities. Technically, we develop a novel technique that can tightly introduce randomness into user secret keys for hierarchical identities in the multi-challenge setting, which cannot be easily achieved by the existing techniques for tightly multi-challenge secure IBE. In contrast to the previous constructions, the security of our scheme is independent of the number of user secret key queries and that of challenge ciphertext queries. We prove the tight security of our scheme based on the Matrix Decisional Diffie-Hellman Assumption, which is an abstraction of standard and simple decisional Diffie-Hellman assumptions, such as the k -Linear and SXDH assumptions. Finally, we also extend our ideas to achieve tight chosen-ciphertext security and anonymity, respectively. These security notions for HIBE have not been tightly achieved in the multi-challenge setting before.

2020

PKC

The Usefulness of Sparsifiable Inputs: How to Avoid Subexponential iO
📺 Abstract

We consider the problem of removing subexponential reductions to indistinguishability obfuscation (iO) in the context of obfuscating probabilistic programs. Specifically, we show how to apply complexity absorption (Zhandry Crypto 2016) to the recent notion of probabilistic indistinguishability obfuscation (piO, Canetti et al. TCC 2015). As a result, we obtain a variant of piO which allows to obfuscate a large class of probabilistic programs, from polynomially secure indistinguishability obfuscation and extremely lossy functions. Particularly, our piO variant is able to obfuscate circuits with specific input domains regardless of the performed computation. We then revisit several (direct or indirect) applications of piO, and obtain – a fully homomorphic encryption scheme (without circular security assumptions), – a multi-key fully homomorphic encryption scheme with threshold decryption, – an encryption scheme secure under arbitrary key-dependent messages, – a spooky encryption scheme for all circuits, – a function secret sharing scheme with additive reconstruction for all circuits, all from polynomially secure iO, extremely lossy functions, and, depending on the scheme, also other (but polynomial and comparatively mild) assumptions. All of these assumptions are implied by polynomially secure iO and the (non-polynomial, but very well-investigated) exponential DDH assumption. Previously, all the above applications required to assume the subexponential security of iO (and more standard assumptions).

2020

PKC

Witness Maps and Applications
📺 Abstract

We introduce the notion of Witness Maps as a cryptographic notion of a proof system. A Unique Witness Map (UWM) deterministically maps all witnesses for an $$mathbf {NP}$$ statement to a single representative witness, resulting in a computationally sound, deterministic-prover, non-interactive witness independent proof system. A relaxation of UWM, called Compact Witness Map (CWM), maps all the witnesses to a small number of witnesses, resulting in a “lossy” deterministic-prover, non-interactive proof-system. We also define a Dual Mode Witness Map (DMWM) which adds an “extractable” mode to a CWM. Our main construction is a DMWM for all $$mathbf {NP}$$ relations, assuming sub-exponentially secure indistinguishability obfuscation ( $${imathcal {O}}$$ ), along with standard cryptographic assumptions. The DMWM construction relies on a CWM and a new primitive called Cumulative All-Lossy-But-One Trapdoor Functions (C-ALBO-TDF), both of which are in turn instantiated based on $${imathcal {O}}$$ and other primitives. Our instantiation of a CWM is in fact a UWM; in turn, we show that a UWM implies Witness Encryption. Along the way to constructing UWM and C-ALBO-TDF, we also construct, from standard assumptions, Puncturable Digital Signatures and a new primitive called Cumulative Lossy Trapdoor Functions (C-LTDF). The former improves up on a construction of Bellare et al. (Eurocrypt 2016), who relied on sub-exponentially secure $${imathcal {O}}$$ and sub-exponentially secure OWF. As an application of our constructions, we show how to use a DMWM to construct the first leakage and tamper-resilient signatures with a deterministic signer , thereby solving a decade old open problem posed by Katz and Vaikunthanathan (Asiacrypt 2009), by Boyle, Segev and Wichs (Eurocrypt 2011), as well as by Faonio and Venturi (Asiacrypt 2016). Our construction achieves the optimal leakage rate of $$1 - o(1)$$ .

2020

PKC

Memory-Tight Reductions for Practical Key Encapsulation Mechanisms
📺 Abstract

The efficiency of a black-box reduction is an important goal of modern cryptography. Traditionally, the time complexity and the success probability were considered as the main aspects of efficiency measurements. In CRYPTO 2017, Auerbach et al. introduced the notion of memory-tightness in cryptographic reductions and showed a memory-tight reduction of the existential unforgeability of the RSA-FDH signature scheme. Unfortunately, their techniques do not extend directly to the reductions involving intricate RO-programming. The problem seems to be inherent as all the other existing results on memory-tightness are lower bounds and impossibility results. In fact, Auerbach et al. conjectured that a memory-tight reduction for security of Hashed-ElGamal KEM is impossible. We refute the above conjecture. Using a simple RO simulation technique, we provide memory-tight reductions of security of the Cramer-Shoup and the ECIES version of Hashed-ElGamal KEM. We prove memory-tight reductions for different variants of Fujisaki-Okamoto Transformation. We analyze the modular transformations introduced by Hofheinz, Hövermanns and Kiltz (TCC 2017). In addition to the constructions involving implicit rejection, we present a memory-tight reduction for the security of the transformation $$mathsf{ ext {QFO}_m^perp }$$ . Our techniques can withstand correctness-errors, and applicable to several lattice-based KEM candidates.

2020

PKC

Toward RSA-OAEP Without Random Oracles
📺 Abstract

We show new partial and full instantiation results under chosen-ciphertext security for the widely implemented and standardized RSA-OAEP encryption scheme of Bellare and Rogaway (EUROCRYPT 1994) and two variants. Prior work on such instantiations either showed negative results or settled for “passive” security notions like IND-CPA. More precisely, recall that RSA-OAEP adds redundancy and randomness to a message before composing two rounds of an underlying Feistel transform, whose round functions are modeled as random oracles (ROs), with RSA. Our main results are: Either of the two oracles (while still modeling the other as a RO) can be instantiated in RSA-OAEP under IND-CCA2 using mild standard-model assumptions on the round functions and generalizations of algebraic properties of RSA shown by Barthe, Pointcheval, and Báguelin (CCS 2012). The algebraic properties are only shown to hold at practical parameters for small encryption exponent ( $$e=3$$ ), but we argue they have value for larger e as well. Both oracles can be instantiated simultaneously for two variants of RSA-OAEP, called “ t -clear” and “ s -clear” RSA-OAEP. For this we use extractability-style assumptions in the sense of Canetti and Dakdouk (TCC 2010) on the round functions, as well as novel yet plausible “XOR-type” assumptions on RSA. While admittedly strong, such assumptions may nevertheless be necessary at this point to make positive progress. In particular, our full instantiations evade impossibility results of Shoup (J. Cryptology 2002), Kiltz and Pietrzak (EUROCRYPT 2009), and Bitansky et al. (STOC 2014). Moreover, our results for s -clear RSA-OAEP yield the most efficient RSA-based encryption scheme proven IND-CCA2 in the standard model (using bold assumptions on cryptographic hashing) to date.

2020

PKC

Public-Key Puncturable Encryption: Modular and Compact Constructions
📺 Abstract

We revisit the method of designing public-key puncturable encryption schemes and present a generic conversion by leveraging the techniques of distributed key-distribution and revocable encryption. In particular, we first introduce a refined version of identity-based revocable encryption, named key-homomorphic identity-based revocable key encapsulation mechanism with extended correctness . Then, we propose a generic construction of puncturable key encapsulation mechanism from the former by merging the idea of distributed key-distribution. Compared to the state-of-the-art, our generic construction supports unbounded number of punctures and multiple tags per message, thus achieving more fine-grained revocation of decryption capability. Further, it does not rely on random oracles , not suffer from non-negligible correctness error, and results in a variety of efficient schemes with distinct features. More precisely, we obtain the first scheme with very compact ciphertexts in the standard model, and the first scheme with support for both unbounded size of tags per ciphertext and unbounded punctures as well as constant-time puncture operation. Moreover, we get a comparable scheme proven secure under the standard DBDH assumption, which enjoys both faster encryption and decryption than previous works based on the same assumption, especially when the number of tags associated with the ciphertext is large.

2020

PKC

Flexible Authenticated and Confidential Channel Establishment (fACCE): Analyzing the Noise Protocol Framework
📺 Abstract

The Noise protocol framework is a suite of channel establishment protocols, of which each individual protocol ensures various security properties of the transmitted messages, but keeps specification, implementation, and configuration relatively simple. Implementations of the Noise protocols are themselves, due to the employed primitives, very performant. Thus, despite its relative youth, Noise is already used by large-scale deployed applications such as WhatsApp and Slack. Though the Noise specification describes and claims the security properties of the protocol patterns very precisely, there has been no computational proof yet. We close this gap. Noise uses only a limited number of cryptographic primitives which makes it an ideal candidate for reduction-based security proofs. Due to its patterns’ characteristics as channel establishment protocols, and the usage of established keys within the handshake, the authenticated and confidential channel establishment (ACCE) model (Jager et al. CRYPTO 2012) seems to perfectly fit for an analysis of Noise. However, the ACCE model strictly divides protocols into two non-overlapping phases: the pre-accept phase (i.e., the channel establishment) and post-accept phase (i.e., the channel). In contrast, Noise allows the transmission of encrypted messages as soon as any key is established (for instance, before authentication between parties has taken place), and then incrementally increases the channel’s security guarantees. By proposing a generalization of the original ACCE model, we capture security properties of such staged channel establishment protocols flexibly – comparably to the multi-stage key exchange model (Fischlin and Günther CCS 2014). We give security proofs for eight of the 15 basic Noise patterns in the full version (EPRINT 2019/436) and exemplify them by the proof of the XK pattern in this article.

2020

PKC

Limits on the Efficiency of (Ring) LWE Based Non-interactive Key Exchange
📺 Abstract

$$mathsf {LWE}$$ based key-exchange protocols lie at the heart of post-quantum public-key cryptography. However, all existing protocols either lack the non-interactive nature of Diffie-Hellman key-exchange or polynomial $$mathsf {LWE}$$ -modulus, resulting in unwanted efficiency overhead. We study the possibility of designing non-interactive $$mathsf {LWE}$$ -based protocols with polynomial $$mathsf {LWE}$$ -modulus. To this end, We identify and formalize simple non-interactive and polynomial $$mathsf {LWE}$$ -modulus variants of existing protocols, where Alice and Bob simultaneously exchange one or more (ring) $$mathsf {LWE}$$ samples with polynomial $$mathsf {LWE}$$ -modulus and then run individual key reconciliation functions to obtain the shared key. We point out central barriers and show that such non-interactive key-exchange protocols are impossible if: (1) the reconciliation functions first compute the inner product of the received $$mathsf {LWE}$$ sample with their private $$mathsf {LWE}$$ secret. This impossibility is information theoretic. (2) One of the reconciliation functions does not depend on the error of the transmitted $$mathsf {LWE}$$ sample. This impossibility assumes hardness of $$mathsf {LWE}$$ . We give further evidence that progress in either direction, of giving an $$mathsf {LWE}$$ -based $$mathrm {NIKE}$$ protocol or proving impossibility of one will lead to progress on some other well-studied questions in cryptography. Overall, our results show possibilities and challenges in designing simple (ring) $$mathsf {LWE}$$ -based non-interactive key exchange protocols.

2020

PKC

PAKEs: New Framework, New Techniques and More Efficient Lattice-Based Constructions in the Standard Model
📺 Abstract

Password-based authenticated key exchange (PAKE) allows two parties with a shared password to agree on a session key. In the last decade, the design of PAKE protocols from lattice assumptions has attracted lots of attention. However, existing solutions in the standard model do not have appealing efficiency. In this work, we first introduce a new PAKE framework. We then provide two realizations in the standard model, under the Learning With Errors (LWE) and Ring-LWE assumptions, respectively. Our protocols are much more efficient than previous proposals, thanks to three novel technical ingredients that may be of independent interests. The first ingredient consists of two approximate smooth projective hash (ASPH) functions from LWE, as well as two ASPHs from Ring-LWE. The latter are the first ring-based constructions in the literature, one of which only has a quasi-linear runtime while its function value contains $$varTheta (n)$$ field elements (where n is the degree of the polynomial defining the ring). The second ingredient is a new key conciliation scheme that is approximately rate-optimal and that leads to a very efficient key derivation for PAKE protocols. The third one is a new authentication code that allows to verify a MAC with a noisy key.

2020

PKC

Constraining and Watermarking PRFs from Milder Assumptions
📺 Abstract

Constrained pseudorandom functions (C-PRFs) let the possessor of a secret key delegate the ability to evaluate the function on certain authorized inputs, while keeping the remaining function values pseudorandom. A constraint-hiding constrained PRF (CHC-PRF) additionally conceals the predicate that determines which inputs are authorized. These primitives have a wealth of applications, including watermarking schemes, symmetric deniable encryption, and updatable garbled circuits. Recent works have constructed (CH)C-PRFs from rather aggressive parameterizations of Learning With Errors (LWE) with subexponential modulus-noise ratios, even for relatively simple “puncturing” or $$ ext {NC}^{1}$$ circuit constraints. This corresponds to strong lattice assumptions and inefficient constructions, and stands in contrast to LWE-based unconstrained PRFs and fully homomorphic encryption schemes, which can be based on quasi-polynomial or even (nearly) polynomial modulus-noise ratios. In this work we considerably improve the LWE assumptions needed for building (constraint-hiding) constrained PRFs and watermarking schemes. In particular, for CHC-PRFs and related watermarking schemes we improve the modulus-noise ratio to $$lambda ^{O((d+log lambda ) log lambda )}$$ for depth- d circuit constraints, which is merely quasi-polynomial for $$ ext {NC}^{1}$$ circuits and closely related watermarking schemes. For (constraint-revealing) C-PRFs for $$ ext {NC}^{1}$$ we do even better, obtaining a nearly polynomial $$lambda ^{omega (1)}$$ ratio. These improvements are partly enabled by slightly modifying the definition of C-PRFs, in a way that is still compatible with many of their applications. Finally, as a contribution of independent interest we build CHC-PRFs for special constraint classes from generic , weaker assumptions: we obtain bit-fixing constraints based on the minimal assumption of one-way functions, and hyperplane-membership constraints based on key-homomorphic PRFs.

2020

PKC

Bringing Order to Chaos: The Case of Collision-Resistant Chameleon-Hashes
📺 Abstract

Chameleon-hash functions, introduced by Krawczyk and Rabin at NDSS 2000, are trapdoor collision-resistant hash-functions parametrized by a public key. If the corresponding secret key is known, arbitrary collisions for the hash function can be efficiently found. Chameleon-hash functions have prominent applications in the design of cryptographic primitives, such as lifting non-adaptively secure signatures to adaptively secure ones. Recently, this primitive also received a lot of attention as a building block in more complex cryptographic applications ranging from editable blockchains to advanced signature and encryption schemes. We observe that in latter applications various different notions of collision-resistance are used, and it is not always clear if the respective notion does really cover what seems intuitively required by the application. Therefore, we revisit existing collision-resistance notions in the literature, study their relations, and—using the example of the recent redactable blockchain proposals—discuss which practical impact different notions of collision-resistance might have. Moreover, we provide a stronger, and arguably more desirable, notion of collision-resistance than what is known from the literature. Finally, we present a surprisingly simple and efficient black-box construction of chameleon-hash functions achieving this strong notion.

2020

PKC

Concretely-Efficient Zero-Knowledge Arguments for Arithmetic Circuits and Their Application to Lattice-Based Cryptography
📺 Abstract

In this work we present a new interactive Zero-Knowledge Argument of knowledge for general arithmetic circuits. Our protocol is based on the “MPC-in-the-head”-paradigm of Ishai et al. (STOC 2009) and follows the recent “MPC-in-the-head with Preprocessing” as proposed by Katz, Kolesnikov and Wang (ACM CCS 2018). However, in contrast to Katz et al. who used the “cut-and-choose” approach for pre-processing, we show how to incorporate the well-known “sacrificing” paradigm into “MPC-in-the-head”, which reduces the proof size when working over arithmetic circuits. Our argument system uses only lightweight symmetric-key primitives and utilizes a simplified version of the so-called SPDZ-protocol. Based on specific properties of our protocol we then show how it can be used to construct an efficient Zero-Knowledge Argument of Knowledge for instances of the Short Integer Solution (SIS) problem. We present different protocols that are tailored to specific uses of SIS, while utilizing the advantages of our scheme. In particular, we present a variant of our argument system that allows the parties to sample the circuit “on the fly”, which may be of independent interest. We furthermore implemented our Zero-Knowledge argument for SIS and show that using our protocols it is possible to run a complete interactive proof, even for general SIS instances which result in a circuit with $${>}10^6$$ gates, in less than 0.5 s .

2020

PKC

Updateable Inner Product Argument with Logarithmic Verifier and Applications
📺 Abstract

We propose an improvement for the inner product argument of Bootle et al. (EUROCRYPT’16). The new argument replaces the unstructured common reference string (the commitment key) by a structured one. We give two instantiations of this argument, for two different distributions of the CRS. In the designated verifier setting, this structure can be used to reduce verification from linear to logarithmic in the circuit size. The argument can be compiled to the publicly verifiable setting in asymmetric bilinear groups. The new common reference string can easily be updateable. The argument can be directly used to improve verification of Bulletproofs range proofs (IEEE SP’18). On the other hand, to use the improved argument to prove circuit satisfiability with logarithmic verification, we adapt recent techniques from Sonic (ACM CCS’19) to work with the new common reference string. The resulting argument is secure under standard assumptions (in the Random Oracle Model), in contrast with Sonic and recent works that improve its efficiency (Plonk, Marlin, AuroraLight), which, apart from the Random Oracle Model, need either the Algebraic Group Model or Knowledge Type assumptions.

2020

PKC

On Black-Box Extensions of Non-interactive Zero-Knowledge Arguments, and Signatures Directly from Simulation Soundness
📺 Abstract

Highly efficient non-interactive zero-knowledge arguments (NIZK) are often constructed for limited languages and it is not known how to extend them to cover wider classes of languages in general. In this work we initiate a study on black-box language extensions for conjunctive and disjunctive relations, that is, building a NIZK system for $${mathcal L}diamond hat{{mathcal L}}$$ (with $$diamond in {wedge , vee }$$ ) based on NIZK systems for languages $${mathcal L}$$ and $$hat{{mathcal L}}$$ . While the conjunctive extension of NIZKs is straightforward by simply executing the given NIZKs in parallel, it is not known how disjunctive extensions could be achieved in a black-box manner. Besides, observe that the simple conjunctive extension does not work in the case of simulation-sound NIZKs (SS-NIZKs), as pointed out by Sahai (Sahai, FOCS 1999). Our main contribution is an impossibility result that negates the existence of the above extensions and implies other non-trivial separations among NIZKs, SS-NIZKs, and labelled SS-NIZKs. Motivated by the difficulty of such transformations, we additionally present an efficient construction of signature schemes based on unbounded simulation-sound NIZKs (USS-NIZKs) for any language without language extensions.

2020

PKC

On QA-NIZK in the BPK Model
📺 Abstract

Recently, Bellare et al. defined subversion-resistance (security in the case the CRS creator may be malicious) for NIZK. In particular, a Sub-ZK NIZK is zero-knowledge, even in the case of subverted CRS. We study Sub-ZK QA-NIZKs, where the CRS can depend on the language parameter. First, we observe that subversion zero-knowledge (Sub-ZK) in the CRS model corresponds to no-auxiliary-string non-black-box NIZK in the Bare Public Key model, and hence, the use of non-black-box techniques is needed to obtain Sub-ZK. Second, we give a precise definition of Sub-ZK QA-NIZKs that are (knowledge-)sound if the language parameter but not the CRS is subverted and zero-knowledge even if both are subverted. Third, we prove that the most efficient known QA-NIZK for linear subspaces by Kiltz and Wee is Sub-ZK under a new knowledge assumption that by itself is secure in (a weaker version of) the algebraic group model. Depending on the parameter setting, it is (knowledge-)sound under different non-falsifiable assumptions, some of which do not belong to the family of knowledge assumptions.

2020

PKC

Improved Discrete Gaussian and Subgaussian Analysis for Lattice Cryptography
📺 Abstract

Discrete Gaussian distributions over lattices are central to lattice-based cryptography, and to the computational and mathematical aspects of lattices more broadly. The literature contains a wealth of useful theorems about the behavior of discrete Gaussians under convolutions and related operations. Yet despite their structural similarities, most of these theorems are formally incomparable, and their proofs tend to be monolithic and written nearly “from scratch,” making them unnecessarily hard to verify, understand, and extend. In this work we present a modular framework for analyzing linear operations on discrete Gaussian distributions. The framework abstracts away the particulars of Gaussians, and usually reduces proofs to the choice of appropriate linear transformations and elementary linear algebra. To showcase the approach, we establish several general properties of discrete Gaussians, and show how to obtain all prior convolution theorems (along with some new ones) as straightforward corollaries. As another application, we describe a self-reduction for Learning With Errors (LWE) that uses a fixed number of samples to generate an unlimited number of additional ones (having somewhat larger error). The distinguishing features of our reduction are its simple analysis in our framework, and its exclusive use of discrete Gaussians without any loss in parameters relative to a prior mixed discrete-and-continuous approach. As a contribution of independent interest, for subgaussian random matrices we prove a singular value concentration bound with explicitly stated constants, and we give tighter heuristics for specific distributions that are commonly used for generating lattice trapdoors. These bounds yield improvements in the concrete bit-security estimates for trapdoor lattice cryptosystems.

2020

PKC

Almost Tight Security in Lattice with Polynomial Moduli - PRF, IBE, All-but-many LTF, and More
📺 Abstract

Achieving tight security is a fundamental task in cryptography. While one of the most important purposes of this task is to improve the overall efficiency of a construction (by allowing smaller security parameters), many current lattice-based instantiations do not completely achieve the goal. Particularly, a super-polynomial modulus seems to be necessary in all prior work for (almost) tight schemes that allow the adversary to conduct queries, such as PRF, IBE, and Signatures. As the super-polynomial modulus would affect the noise-to-modulus ratio and thus increase the parameters, this might cancel out the advantages (in efficiency) brought from the tighter analysis. To determine the full power of tight security/analysis in lattices, it is necessary to determine whether the super-polynomial modulus restriction is inherent. In this work, we remove the super-polynomial modulus restriction for many important primitives – PRF, IBE, All-but-many Lossy Trapdoor Functions, and Signatures. The crux relies on an improvement over the framework of Boyen and Li (Asiacrypt 16), and an almost tight reduction from LWE to LWR, which improves prior work by Alwen et al. (Crypto 13), Bogdanov et al. (TCC 16), and Bai et al. (Asiacrypt 15). By combining these two advances, we are able to derive these almost tight schemes under LWE with a polynomial modulus.

2020

PKC

The Randomized Slicer for CVPP: Sharper, Faster, Smaller, Batchier
📺 Abstract

Following the recent line of work on solving the closest vector problem with preprocessing (CVPP) using approximate Voronoi cells, we improve upon previous results in the following ways: We derive sharp asymptotic bounds on the success probability of the randomized slicer, by modelling the behaviour of the algorithm as a random walk on the coset of the lattice of the target vector. We thereby solve the open question left by Doulgerakis–Laarhoven–De Weger [PQCrypto 2019] and Laarhoven [MathCrypt 2019]. We obtain better trade-offs for CVPP and its generalisations (strictly, in certain regimes), both with and without nearest neighbour searching, as a direct result of the above sharp bounds on the success probabilities. We show how to reduce the memory requirement of the slicer, and in particular the corresponding nearest neighbour data structures, using ideas similar to those proposed by Becker–Gama–Joux [Cryptology ePrint Archive, 2015]. Using $$2^{0.185d + o(d)}$$ memory, we can solve a single CVPP instance in $$2^{0.264d + o(d)}$$ time. We further improve on the per-instance time complexities in certain memory regimes, when we are given a sufficiently large batch of CVPP problem instances for the same lattice. Using $$2^{0.208d + o(d)}$$ memory, we can heuristically solve CVPP instances in $$2^{0.234d + o(d)}$$ amortized time, for batches of size at least $$2^{0.058d + o(d)}$$ . Our random walk model for analysing arbitrary-step transition probabilities in complex step-wise algorithms may be of independent interest, both for deriving analytic bounds through convexity arguments, and for computing optimal paths numerically with a shortest path algorithm. As a side result we apply the same random walk model to graph-based nearest neighbour searching, where we improve upon results of Laarhoven [SOCG 2018] by deriving sharp bounds on the success probability of the corresponding greedy search procedure.

2020

PKC

Tweaking the Asymmetry of Asymmetric-Key Cryptography on Lattices: KEMs and Signatures of Smaller Sizes
📺 Abstract

Currently, lattice-based cryptosystems are less efficient than their number-theoretic counterparts (based on RSA, discrete logarithm, etc.) in terms of key and ciphertext (signature) sizes. For adequate security the former typically needs thousands of bytes while in contrast the latter only requires at most hundreds of bytes. This significant difference has become one of the main concerns in replacing currently deployed public-key cryptosystems with lattice-based ones. Observing the inherent asymmetries in existing lattice-based cryptosystems, we propose asymmetric variants of the (module-)LWE and (module-)SIS assumptions, which yield further size-optimized KEM and signature schemes than those from standard counterparts. Following the framework of Lindner and Peikert (CT-RSA 2011) and the Crystals-Kyber proposal (EuroS&P 2018), we propose an IND-CCA secure KEM scheme from the hardness of the asymmetric module-LWE (AMLWE), whose asymmetry is fully exploited to obtain shorter public keys and ciphertexts. To target at a 128-bit quantum security, the public key (resp., ciphertext) of our KEM only has 896 bytes (resp., 992 bytes). Our signature scheme bears most resemblance to and improves upon the Crystals-Dilithium scheme (ToCHES 2018). By making full use of the underlying asymmetric module-LWE and module-SIS assumptions and carefully selecting the parameters, we construct an SUF-CMA secure signature scheme with shorter public keys and signatures. For a 128-bit quantum security, the public key (resp., signature) of our signature scheme only has 1312 bytes (resp., 2445 bytes). We adapt the best known attacks and their variants to our AMLWE and AMSIS problems and conduct a comprehensive and thorough analysis of several parameter choices (aiming at different security strengths) and their impacts on the sizes, security and error probability of lattice-based cryptosystems. Our analysis demonstrates that AMLWE and AMSIS problems admit more flexible and size-efficient choices of parameters than the respective standard versions.

2020

PKC

MPSign: A Signature from Small-Secret Middle-Product Learning with Errors
📺 Abstract

We describe a digital signature scheme $$mathsf {MPSign}$$ , whose security relies on the conjectured hardness of the Polynomial Learning With Errors problem ( $$mathsf {PLWE}$$ ) for at least one defining polynomial within an exponential-size family (as a function of the security parameter). The proposed signature scheme follows the Fiat-Shamir framework and can be viewed as the Learning With Errors counterpart of the signature scheme described by Lyubashevsky at Asiacrypt 2016, whose security relies on the conjectured hardness of the Polynomial Short Integer Solution ( $$mathsf {PSIS}$$ ) problem for at least one defining polynomial within an exponential-size family. As opposed to the latter, $$mathsf {MPSign}$$ enjoys a security proof from $$mathsf {PLWE}$$ that is tight in the quantum-access random oracle model. The main ingredient is a reduction from $$mathsf {PLWE}$$ for an arbitrary defining polynomial among exponentially many, to a variant of the Middle-Product Learning with Errors problem ( $$mathsf {MPLWE}$$ ) that allows for secrets that are small compared to the working modulus. We present concrete parameters for $$mathsf {MPSign}$$ using such small secrets, and show that they lead to significant savings in signature length over Lyubashevsky’s Asiacrypt 2016 scheme (which uses larger secrets) at typical security levels. As an additional small contribution, and in contrast to $$mathsf {MPSign}$$ (or $$mathsf {MPLWE}$$ ), we present an efficient key-recovery attack against Lyubashevsky’s scheme (or the inhomogeneous $$mathsf {PSIS}$$ problem), when it is used with sufficiently small secrets, showing the necessity of a lower bound on secret size for the security of that scheme.

2020

PKC

Witness Indistinguishability for Any Single-Round Argument with Applications to Access Control
📺 Abstract

Consider an access policy for some resource which only allows access to users of the system who own a certain set of attributes. Specifically, we consider the case where such an access structure is defined by some monotone function $$f:{0,1}^N
ightarrow {0,1}$$ , belonging to some class of function $$F$$ (e.g. conjunctions, space bounded computation), where N is the number of possible attributes. In this work we show that any succinct single-round delegation scheme for the function class $$F$$ can be converted into a succinct single-round private access control protocol. That is, a verifier can be convinced that an approved user (i.e. one which holds an approved set of attributes) is accessing the system, without learning any additional information about the user or the set of attributes. As a main tool of independent interest, we show that assuming a quasi-polynomially secure two-message oblivious transfer scheme with statistical sender privacy (which can be based on quasi-polynomial hardness of the DDH, QR, DCR or LWE assumptions), we can convert any single-round protocol into a witness indistinguishable one, with similar communication complexity.

2020

PKC

Boosting Verifiable Computation on Encrypted Data
📺 Abstract

We consider the setting in which an untrusted server stores a collection of data and is asked to compute a function over it. In this scenario, we aim for solutions where the untrusted server does not learn information about the data and is prevented from cheating. This problem is addressed by verifiable and private delegation of computation, proposed by Gennaro, Gentry and Parno (CRYPTO’10), a notion that is close to both the active areas of homomorphic encryption and verifiable computation (VC). However, in spite of the efficiency advances in the respective areas, VC protocols that guarantee privacy of the inputs are still expensive. The only exception is a protocol by Fiore, Gennaro and Pastro (CCS’14) that supports arithmetic circuits of degree at most 2. In this paper we propose new efficient protocols for VC on encrypted data that improve over the state of the art solution of Fiore et al. in multiple aspects. First, we can support computations of degree higher than 2. Second, we achieve public delegatability and public verifiability whereas Fiore et al. need the same secret key to encode inputs and verify outputs. Third, we achieve a new property that guarantees that verifiers can be convinced about the correctness of the outputs without learning information on the inputs. The key tool to obtain our new protocols is a new SNARK that can efficiently handle computations over a quotient polynomial ring, such as the one used by Ring-LWE somewhat homomorphic encryption schemes. This SNARK in turn relies on a new commit-and-prove SNARK for proving evaluations on the same point of several committed polynomials. We propose a construction of this scheme under an extractability assumption over bilinear groups in the random oracle model.

2020

PKC

Lossy CSI-FiSh: Efficient Signature Scheme with Tight Reduction to Decisional CSIDH-512
📺 Abstract

Recently, Beullens, Kleinjung, and Vercauteren (Asiacrypt’19) provided the first practical isogeny-based digital signature, obtained from the Fiat-Shamir (FS) paradigm. They worked with the CSIDH-512 parameters and passed through a new record class group computation. However, as with all standard FS signatures, the security proof is highly non-tight and the concrete parameters are set under the heuristic that the only way to attack the scheme is by finding collisions for a hash function. In this paper, we propose an FS-style signature scheme, called Lossy CSI-FiSh, constructed using the CSIDH-512 parameters and with a security proof based on the “Lossy Keys” technique introduced by Kiltz, Lyubashevsky and Schaffner (Eurocrypt’18). Lossy CSI-FiSh is provably secure under the same assumption which underlies the security of the key exchange protocol CSIDH (Castryck et al. (Asiacrypt’18)) and is almost as efficient as CSI-FiSh. For instance, aiming for small signature size, our scheme is expected to take around $$approx 800$$ ms to sign/verify while producing signatures of size $$approx 280$$ bytes. This is only twice slower than CSI-FiSh while having similar signature size for the same parameter set. As an additional benefit, our scheme is by construction secure both in the classical and quantum random oracle model.

2020

PKC

Threshold Schemes from Isogeny Assumptions
📺 Abstract

We initiate the study of threshold schemes based on the Hard Homogeneous Spaces (HHS) framework of Couveignes. Quantum-resistant HHS based on supersingular isogeny graphs have recently become usable thanks to the record class group precomputation performed for the signature scheme CSI-FiSh. Using the HHS equivalent of the technique of Shamir’s secret sharing in the exponents , we adapt isogeny based schemes to the threshold setting. In particular we present threshold versions of the CSIDH public key encryption, and the CSI-FiSh signature schemes. The main highlight is a threshold version of CSI-FiSh which runs almost as fast as the original scheme, for message sizes as low as 1880 B, public key sizes as low as 128 B, and thresholds up to 56; other speed-size-threshold compromises are possible.

2020

PKC

Topology-Hiding Computation for Networks with Unknown Delays
📺 Abstract

Topology-Hiding Computation (THC) allows a set of parties to securely compute a function over an incomplete network without revealing information on the network topology. Since its introduction in TCC’15 by Moran et al., the research on THC has focused on reducing the communication complexity, allowing larger graph classes, and tolerating stronger corruption types. All of these results consider a fully synchronous model with a known upper bound on the maximal delay of all communication channels. Unfortunately, in any realistic setting this bound has to be extremely large, which makes all fully synchronous protocols inefficient. In the literature on multi-party computation, this is solved by considering the fully asynchronous model. However, THC is unachievable in this model (and even hard to define), leaving even the definition of a meaningful model as an open problem. The contributions of this paper are threefold. First, we introduce a meaningful model of unknown and random communication delays for which THC is both definable and achievable. The probability distributions of the delays can be arbitrary for each channel, but one needs to make the (necessary) assumption that the delays are independent. The existing fully-synchronous THC protocols do not work in this setting and would, in particular, leak information about the topology. Second, in the model with trusted stateless hardware boxes introduced at Eurocrypt’18 by Ball et al., we present a THC protocol that works for any graph class. Third, we explore what is achievable in the standard model without trusted hardware and present a THC protocol for specific graph types (cycles and trees) secure under the DDH assumption. The speed of all protocols scales with the actual (unknown) delay times, in contrast to all previously known THC protocols whose speed is determined by the assumed upper bound on the network delay.

2020

PKC

Sublinear-Round Byzantine Agreement Under Corrupt Majority
📺 Abstract

Although Byzantine Agreement (BA) has been studied for three decades, perhaps somewhat surprisingly, there still exist significant gaps in our understanding regarding its round complexity. A long-standing open question is the following: can we achieve BA with sublinear round complexity under corrupt majority? Due to the beautiful works by Garay et al. (FOCS’07) and Fitzi and Nielsen (DISC’09), we have partial and affirmative answers to this question albeit for the narrow regime $$f = n/2 + o(n)$$ where f is the number of corrupt nodes and n is the total number of nodes. So far, no positive result is known about the setting $$f > 0.51n$$ even for static corruption! In this paper, we make progress along this somewhat stagnant front. We show that there exists a corrupt-majority BA protocol that terminates in $$O(frac{1}{epsilon } log frac{1}{delta })$$ rounds in the worst case, satisfies consistency with probability at least $$1 - delta $$ , and tolerates $$(1-epsilon )$$ fraction of corrupt nodes. Our protocol secures against an adversary that can corrupt nodes adaptively during the protocol execution but cannot perform “after-the-fact” removal of honest messages that have already been sent prior to corruption. Our upper bound is optimal up to a logarithmic factor in light of the elegant $$varOmega (1/epsilon )$$ lower bound by Garay et al. (FOCS’07).

2020

PKC

Bandwidth-Efficient Threshold EC-DSA
📺 Abstract

Threshold Signatures allow n parties to share the power of issuing digital signatures so that any coalition of size at least $$t+1$$ can sign, whereas groups of t or less players cannot. Over the last few years many schemes addressed the question of realizing efficient threshold variants for the specific case of EC-DSA signatures. In this paper we present new solutions to the problem that aim at reducing the overall bandwidth consumption. Our main contribution is a new variant of the Gennaro and Goldfeder protocol from ACM CCS 2018 that avoids all the required range proofs, while retaining provable security against malicious adversaries in the dishonest majority setting. Our experiments show that – for all levels of security – our signing protocol reduces the bandwidth consumption of best previously known secure protocols for factors varying between 4.4 and 9, while key generation is consistently two times less expensive. Furthermore compared to these same protocols, our signature generation is faster for 192-bits of security and beyond.

2020

PKC

Blazing Fast OT for Three-Round UC OT Extension
📺 Abstract

Oblivious Transfer (OT) is an important building block for multi-party computation (MPC). Since OT requires expensive public-key operations, efficiency-conscious MPC protocols use an OT extension (OTE) mechanism [Beaver 96, Ishai et al. 03] to provide the functionality of many independent OT instances with the same sender and receiver, using only symmetric-key operations plus few instances of some base OT protocol. Consequently there is significant interest in constructing OTE friendly protocols, namely protocols that, when used as base-OT for OTE, result in extended OT that are both round-efficient and cost-efficient. We present the most efficient OTE-friendly protocol to date. Specifically: Our base protocol incurs only 3 exponentiations per instance. Our base protocol results in a 3 round extended OT protocol. The extended protocol is UC secure in the Observable Random Oracle Model (ROM) under the CDH assumption. For comparison, the state of the art for base OTs that result in 3-round OTE are proven only in the programmable ROM, and require 4 exponentiations under Interactive DDH or 6 exponentiations under DDH [Masney-Rindal 19]. We also implement our protocol and benchmark it against the Simplest OT protocol [Chou and Orlandi, Latincrypt 2015], which is the most efficient and widely used OT protocol but not known to suffice for OTE. The computation cost is roughly the same in both cases. Interestingly, our base OT is also 3 rounds. However, we slightly modify the extension mechanism (which normally adds a round) so as to preserve the number of rounds in our case.

2020

PKC

Going Beyond Dual Execution: MPC for Functions with Efficient Verification
📺 Abstract

The dual execution paradigm of Mohassel and Franklin (PKC’06) and Huang, Katz and Evans (IEEE ’12) shows how to achieve the notion of 1-bit leakage security at roughly twice the cost of semi-honest security for the special case of two-party secure computation . To date, there are no multi-party computation (MPC) protocols that offer such a strong trade-off between security and semi-honest performance. Our main result is to address this shortcoming by designing 1-bit leakage protocols for the multi-party setting, albeit for a special class of functions. We say that function f ( x , y ) is efficiently verifiable by g if the running time of g is always smaller than f and $$g(x,y,z)=1$$ if and only if $$f(x,y)=z$$ . In the two-party setting, we first improve dual execution by observing that the “second execution” can be an evaluation of g instead of f , and that by definition, the evaluation of g is asymptotically more efficient. Our main MPC result is to construct a 1-bit leakage protocol for such functions from any passive protocol for f that is secure up to additive errors and any active protocol for g . An important result by Genkin et al. (STOC ’14) shows how the classic protocols by Goldreich et al. (STOC ’87) and Ben-Or et al. (STOC ’88) naturally support this property, which allows to instantiate our compiler with two-party and multi-party protocols. A key technical result we prove is that the passive protocol for distributed garbling due to Beaver et al. (STOC ’90) is in fact secure up to additive errors against malicious adversaries, thereby, yielding another powerful instantiation of our paradigm in the constant-round multi-party setting. As another concrete example of instantiating our approach, we present a novel protocol for computing perfect matching that is secure in the 1-bit leakage model and whose communication complexity is less than the honest-but-curious implementations of textbook algorithms for perfect matching.

2020

PKC

Mon$\mathbb {Z}_{2^{k}}$a: Fast Maliciously Secure Two Party Computation on $\mathbb {Z}_{2^{k}}$
📺 Abstract

In this paper we present a new 2-party protocol for secure computation over rings of the form $$mathbb {Z}_{2^k}$$ . As many recent efficient MPC protocols supporting dishonest majority, our protocol consists of a heavier (input-independent) pre-processing phase and a very efficient online stage. Our offline phase is similar to BeDOZa (Bendlin et al. Eurocrypt 2011) but employs Joye-Libert (JL, Eurocrypt 2013) as underlying homomorphic cryptosystem and, notably, it can be proven secure without resorting to the expensive sacrifice step. JL turns out to be particularly well suited for the ring setting as it naturally supports $$mathbb {Z}_{2^k}$$ as underlying message space. Moreover, it enjoys several additional properties (such as valid ciphertext-verifiability and efficiency) that make it a very good fit for MPC in general. As a main technical contribution we show how to take advantage of all these properties (and of more properties that we introduce in this work, such as a ZK proof of correct multiplication) in order to design a two-party protocol that is efficient, fast and easy to implement in practice. Our solution is particularly well suited for relatively large choices of k ( e.g. $$k=128$$ ), but compares favorably with the state of the art solution of SPD $$mathbb {Z}_{2^k}$$ (Cramer et al. Crypto 2018) already for the practically very relevant case of $$mathbb {Z}_{2^{64}}$$ .

2020

PKC

Generic Authenticated Key Exchange in the Quantum Random Oracle Model
📺 Abstract

We propose $$mathsf {FO_mathsf {AKE}}$$ , a generic construction of two-message authenticated key exchange (AKE) from any passively secure public key encryption (PKE) in the quantum random oracle model (QROM). Whereas previous AKE constructions relied on a Diffie-Hellman key exchange or required the underlying PKE scheme to be perfectly correct, our transformation allows arbitrary PKE schemes with non-perfect correctness. Dealing with imperfect schemes is one of the major difficulties in a setting involving active attacks. Our direct construction, when applied to schemes such as the submissions to the recent NIST post-quantum competition, is more natural than previous AKE transformations. Furthermore, we avoid the use of (quantum-secure) digital signature schemes which are considerably less efficient than their PKE counterparts. As a consequence, we can instantiate our AKE transformation with any of the submissions to the recent NIST competition, e.g., ones based on codes and lattices. $$mathsf {FO_mathsf {AKE}}$$ can be seen as a generalisation of the well known Fujisaki-Okamoto transformation (for building actively secure PKE from passively secure PKE) to the AKE setting. As a helper result, we also provide a security proof for the Fujisaki-Okamoto transformation in the QROM for PKE with non-perfect correctness which is tighter and tolerates a larger correctness error than previous proofs.

2020

PKC

Threshold Ring Signatures: New Definitions and Post-quantum Security
📺 Abstract

A t -out-of- N threshold ring signature allows t parties to jointly and anonymously compute a signature on behalf on N public keys, selected in an arbitrary manner among the set of all public keys registered in the system. Existing definitions for t -out-of- N threshold ring signatures guarantee security only when the public keys are honestly generated, and many even restrict the ability of the adversary to actively participate in the computation of the signatures. Such definitions do not capture the open settings envisioned for threshold ring signatures, where parties can independently add themselves to the system, and join other parties for the computation of the signature. Furthermore, known constructions of threshold ring signatures are not provably secure in the post-quantum setting, either because they are based on non-post quantum secure problems (e.g. Discrete Log, RSA), or because they rely on transformations such as Fiat-Shamir, that are not always secure in the quantum random oracle model (QROM). In this paper, we provide the first definition of t -out-of- N threshold ring signatures against active adversaries who can participate in the system and arbitrarily deviate from the prescribed procedures. Second, we present a post-quantum secure realization based on any (post-quantum secure) trapdoor commitment, which we prove secure in the QROM. Our construction is black-box and it can be instantiated with any trapdoor commitment, thus allowing the use of a variety of hardness assumptions.

2020

PKC

Tight and Optimal Reductions for Signatures Based on Average Trapdoor Preimage Sampleable Functions and Applications to Code-Based Signatures
📺 Abstract

The GPV construction [ GPV08 ] presents a generic construction of signature schemes in the Hash and Sign paradigm and is used in some lattice based signatures. This construction requires a family $$mathcal {F}$$ of trapdoor preimage sampleable functions (TPSF). In this work we extend this notion to the weaker Average TPSF (ATPSF) and show that the GPV construction also holds for ATPSF in the Random Oracle Model (ROM). We also introduce the problem of finding a Claw with a random function (Claw(RF)) and present a tight security reduction to the Claw(RF) problem. Our reduction is also optimal meaning that an algorithm that solves the Claw(RF) problem breaks the scheme. We extend these results to the quantum setting and prove this same tight and optimal reduction in the QROM. Finally, we apply these results to code-based signatures, notably the Wave signature scheme and prove security for it in the ROM and the QROM, improving and extending the original analysis of [ DST19a ].

2020

PKC

Faster Cofactorization with ECM Using Mixed Representations
📺 Abstract

This paper introduces a novel implementation of the elliptic curve factoring method specifically designed for medium-size integers such as those arising by billions in the cofactorization step of the Number Field Sieve. In this context, our algorithm requires fewer modular multiplications than any other publicly available implementation. The main ingredients are: the use of batches of primes, fast point tripling, optimal double-base decompositions and Lucas chains, and a good mix of Edwards and Montgomery representations.

2020

PKC

Improved Classical Cryptanalysis of SIKE in Practice
📺 Abstract

The main contribution of this work is an optimized implementation of the van Oorschot-Wiener (vOW) parallel collision finding algorithm. As is typical for cryptanalysis against conjectured hard problems (e. g. factoring or discrete logarithms), challenges can arise in the implementation that are not captured in the theory, making the performance of the algorithm in practice a crucial element of estimating security. We present a number of novel improvements, both to generic instantiations of the vOW algorithm finding collisions in arbitrary functions, and to its instantiation in the context of the supersingular isogeny key encapsulation (SIKE) protocol, that culminate in an improved classical cryptanalysis of the computational supersingular isogeny (CSSI) problem. In particular, we present a scalable implementation that can be applied to the Round-2 parameter sets of SIKE that can be used to give confidence in their security levels.

2020

PKC

A Short-List of Pairing-Friendly Curves Resistant to Special TNFS at the 128-Bit Security Level
📺 Abstract

There have been notable improvements in discrete logarithm computations in finite fields since 2015 and the introduction of the Tower Number Field Sieve algorithm (TNFS) for extension fields. The Special TNFS is very efficient in finite fields that are target groups of pairings on elliptic curves, where the characteristic is special (e.g. sparse). The key sizes for pairings should be increased, and alternative pairing-friendly curves can be considered. We revisit the Special variant of TNFS for pairing-friendly curves. In this case the characteristic is given by a polynomial of moderate degree (between 4 and 38) and tiny coefficients, evaluated at an integer (a seed). We present a polynomial selection with a new practical trade-off between degree and coefficient size. As a consequence, the security of curves computed by Barbulescu, El Mrabet and Ghammam in 2019 should be revised: we obtain a smaller estimated cost of STNFS for all curves except BLS12 and BN. To obtain TNFS-secure curves, we reconsider the Brezing–Weng generic construction of families of pairing-friendly curves and estimate the cost of our new Special TNFS algorithm for these curves. This improves on the work of Fotiadis and Konstantinou, Fotiadis and Martindale, and Barbulescu, El Mrabet and Ghammam. We obtain a short-list of interesting families of curves that are resistant to the Special TNFS algorithm, of embedding degrees 10 to 16 for the 128-bit security level. We conclude that at the 128-bit security level, BLS-12 and Fotiadis–Konstantinou–Martindale curves with $$k=12$$ over a 440 to 448-bit prime field seem to be the best choice for pairing efficiency. We also give hints at the 192-bit security level.

2020

PKC

Privacy-Preserving Authenticated Key Exchange and the Case of IKEv2
📺 Abstract

In this paper, we present a strong, formal, and general-purpose cryptographic model for privacy-preserving authenticated key exchange (PPAKE) protocols. PPAKE protocols are secure in the traditional AKE sense but additionally guarantee the confidentiality of the identities used in communication sessions. Our model has several useful and novel features, among others: it is a proper extension of classical AKE models, guarantees in a strong sense that the confidentiality of session keys is independent from the secrecy of the used identities, and it is the first to support what we call dynamic modes, where the responsibility of selecting the identities of the communication partners may vary over several protocol runs. We show the validity of our model by applying it to the cryptographic core of IPsec IKEv2 with signature-based authentication where the need for dynamic modes is practically well-motivated. In our analysis, we not only show that this protocol provides strong classical AKE security guarantees but also that the identities that are used by the parties remain hidden in successful protocol runs. Historically, the Internet Key Exchange (IKE) protocol was the first real-world AKE to incorporate privacy-preserving techniques. However, lately privacy-preserving techniques have gained renewed interest in the design process of important protocols like TLS 1.3 (with encrypted SNI) and NOISE. We believe that our new model can be a solid foundation to analyze these and other practical protocols with respect to their privacy guarantees, in particular, in the now so wide-spread scenario where multiple virtual servers are hosted on a single machine.

2020

PKC

Linearly-Homomorphic Signatures and Scalable Mix-Nets
📺 Abstract

Anonymity is a primary ingredient for our digital life. Several tools have been designed to address it such as, for authentication, blind signatures, group signatures or anonymous credentials and, for confidentiality, randomizable encryption or mix-nets. When it comes to complex electronic voting schemes, random shuffling of authenticated ciphertexts with mix-nets is the only known tool. However, it requires huge and complex zero-knowledge proofs to guarantee the actual permutation of the initial ciphertexts in a privacy-preserving way. In this paper, we propose a new approach for proving correct shuffling of signed ElGamal ciphertexts: the mix-servers can simply randomize individual ballots, which means the ciphertexts, the signatures, and the verification keys, with an additional global proof of constant size, and the output will be publicly verifiable. The security proof is in the generic bilinear group model. The computational complexity for the each mix-server is linear in the number of ballots. Verification is also linear in the number of ballots, but independent of the number of rounds of mixing. This leads to a new highly scalable technique. Our construction makes use of linearly-homomorphic signatures, with new features, that are of independent interest.

2020

PKC

Efficient Redactable Signature and Application to Anonymous Credentials
📺 Abstract

Let us assume that Alice has received a constant-size signature on a set of messages $${m_i}_{i=1}^n$$ from some organization. Depending on the situation, Alice might need to disclose, prove relations about or hide some of these messages. Ideally, the complexity of the corresponding protocols should not depend on the hidden messages. In particular, if Alice wants to disclose only k messages, then the authenticity of the latter should be verifiable in at most O ( k ) operations. Many solutions were proposed over the past decades, but they only provide a partial answer to this problem. In particular, we note that they suffer either from the need to prove knowledge of the hidden elements or from the inability to prove that the latter satisfy some relations. In this paper, we propose a very efficient constant-size redactable signature scheme that addresses all the problems above. Signatures can indeed be redacted to remain valid only on a subset of k messages included in $${m_i}_{i=1}^n$$ . The resulting redacted signature consists of 4 elements and can be verified with essentially k exponentiations. Different shows of the same signature can moreover be made unlinkable leading to a very efficient anonymous credentials system.

2019

CHES

RISCV and Security: how, when and why?
📺 Abstract

★Invited talk

In this talk we will provide an overview of the current activities of the RISCV Foundation, including the creation of a Security Standing Committee about a year ago which is in charge of assessing new threats and opportunities in security in the RISCV world; we will discuss progress being made by the security-related task groups. The first one is working on specifying extensions of the base instruction set architecture (ISA) that will enable high-performance and high security cryptographic operations (AES, SHA-2, Public Key Cryptography); the second one is looking at creating extensions and hardware/software specifications to enable a trusted execution environment built on top of a RISCV processor; we will also provide details on the activities of the Security Standing Committee itself, and what some of the plans are to tackle the newest microarchitectural cache timing side-channel attacks such as Spectre, Meltdown, Foreshadow, etc. We will review some additional work on secure RISCV and existing security extension initiatives by academia around the world. Finally, we will describe some approaches of how a side-channel and DPA-resistant RISCV CPU could be built and elaborate on the research we have been focused on in the past months.

2019

CHES

Developing High-Performance Mechanically-Verified Cryptographic Code
📺 Abstract

★Invited talk

Project Everest is constructing a high-performance, standards-compliant, formally verified implementation of the HTTPS ecosystem, including TLS, X.509, and the core cryptographic algorithms. This talk will present an overview of how we verify our implementations are correct, cryptographically secure, and resilient to basic side channels. We will focus on our EverCrypt cryptographic provider, a comprehensive collection of verified, high-performance cryptographic functionalities available via a carefully designed API. The API provably supports agility (choosing between multiple algorithms for the same functionality) and multiplexing (choosing between multiple implementations of the same algorithm). Through a combination of abstraction and zero-cost generic programming, we show how agility can simplify verification without sacrificing performance, and we demonstrate how C and assembly can be composed and verified against shared specifications. The result is several functionalities whose performance matches or exceeds the best unverified implementations. Altogether, EverCrypt consists of over 100K verified lines of specs, code, and proofs, and it produces over 45K lines of C and assembly code.

2019

CRYPTO

Cryptanalysis of OCB2: Attacks on Authenticity and Confidentiality
📺 Abstract

★ Best paper

We present practical attacks on OCB2. This mode of operation of a blockcipher was designed with the aim to provide particularly efficient and provably-secure authenticated encryption services, and since its proposal about 15 years ago it belongs to the top performers in this realm. OCB2 was included in an ISO standard in 2009.An internal building block of OCB2 is the tweakable blockcipher obtained by operating a regular blockcipher in $$ \text {XEX} ^*$$ mode. The latter provides security only when evaluated in accordance with certain technical restrictions that, as we note, are not always respected by OCB2. This leads to devastating attacks against OCB2’s security promises: We develop a range of very practical attacks that, amongst others, demonstrate universal forgeries and full plaintext recovery. We complete our report with proposals for (provably) repairing OCB2. To our understanding, as a direct consequence of our findings, OCB2 is currently in a process of removal from ISO standards. Our attacks do not apply to OCB1 and OCB3, and our privacy attacks on OCB2 require an active adversary.

2019

CRYPTO

Quantum Cryptanalysis in the RAM Model: Claw-Finding Attacks on SIKE
📺 Abstract

★ Best Young Researcher Paper

We introduce models of computation that enable direct comparisons between classical and quantum algorithms. Incorporating previous work on quantum computation and error correction, we justify the use of the gate-count and depth-times-width cost metrics for quantum circuits. We demonstrate the relevance of these models to cryptanalysis by revisiting, and increasing, the security estimates for the Supersingular Isogeny Diffie–Hellman (SIDH) and Supersingular Isogeny Key Encapsulation (SIKE) schemes. Our models, analyses, and physical justifications have applications to a number of memory intensive quantum algorithms.

2019

CRYPTO

Fully Secure Attribute-Based Encryption for t-CNF from LWE
📺 Abstract

★ Best young researcher

Attribute-based Encryption (ABE), first introduced by [SW05, GPSW06], is a public key encryption system that can support multiple users with varying decryption permissions. One of the main properties of such schemes is the supported function class of policies. While there are fully secure constructions from bilinear maps for a fairly large class of policies, the situation with lattice-based constructions is less satisfactory and many efforts were made to close this gap. Prior to this work the only known fully secure lattice construction was for the class of point functions (also known as IBE).In this work we construct for the first time a lattice-based (ciphertext-policy) ABE scheme for the function class t-CNF, which consists of CNF formulas where each clause depends on at most t bits of the input, for any constant t. This class includes NP-verification policies, bit-fixing policies and t-threshold policies. Towards this goal we also construct a fully secure single-key constrained PRF from OWF for the same function class, which might be of independent interest.

2019

CRYPTO

Noninteractive Zero Knowledge for NP from (Plain) Learning with Errors
📺 Abstract

We finally close the long-standing problem of constructing a noninteractive zero-knowledge (NIZK) proof system for any NP language with security based on the plain Learning With Errors (LWE) problem, and thereby on worst-case lattice problems. Our proof system instantiates the framework recently developed by Canetti et al. [EUROCRYPT’18], Holmgren and Lombardi [FOCS’18], and Canetti et al. [STOC’19] for soundly applying the Fiat–Shamir transform using a hash function family that is correlation intractable for a suitable class of relations. Previously, such hash families were based either on “exotic” assumptions (e.g., indistinguishability obfuscation or optimal hardness of certain LWE variants) or, more recently, on the existence of circularly secure fully homomorphic encryption (FHE). However, none of these assumptions are known to be implied by plain LWE or worst-case hardness.Our main technical contribution is a hash family that is correlation intractable for arbitrary size-S circuits, for any polynomially bounded S, based on plain LWE (with small polynomial approximation factors). The construction combines two novel ingredients: a correlation-intractable hash family for log-depth circuits based on LWE (or even the potentially harder Short Integer Solution problem), and a “bootstrapping” transform that uses (leveled) FHE to promote correlation intractability for the FHE decryption circuit to arbitrary (bounded) circuits. Our construction can be instantiated in two possible “modes,” yielding a NIZK that is either computationally sound and statistically zero knowledge in the common random string model, or vice-versa in the common reference string model.

2019

CRYPTO

Lattice-Based Zero-Knowledge Proofs: New Techniques for Shorter and Faster Constructions and Applications
📺 Abstract

We devise new techniques for design and analysis of efficient lattice-based zero-knowledge proofs (ZKP). First, we introduce one-shot proof techniques for non-linear polynomial relations of degree $$k\ge 2$$, where the protocol achieves a negligible soundness error in a single execution, and thus performs significantly better in both computation and communication compared to prior protocols requiring multiple repetitions. Such proofs with degree $$k\ge 2$$ have been crucial ingredients for important privacy-preserving protocols in the discrete logarithm setting, such as Bulletproofs (IEEE S&P ’18) and arithmetic circuit arguments (EUROCRYPT ’16). In contrast, one-shot proofs in lattice-based cryptography have previously only been shown for the linear case ($$k=1$$) and a very specific quadratic case ($$k=2$$), which are obtained as a special case of our technique.Moreover, we introduce two speedup techniques for lattice-based ZKPs: a CRT-packing technique supporting “inter-slot” operations, and “NTT-friendly” tools that permit the use of fully-splitting rings. The former technique comes at almost no cost to the proof length, and the latter one barely increases it, which can be compensated for by tweaking the rejection sampling parameters while still having faster computation overall.To illustrate the utility of our techniques, we show how to use them to build efficient relaxed proofs for important relations, namely proof of commitment to bits, one-out-of-many proof, range proof and set membership proof. Despite their relaxed nature, we further show how our proof systems can be used as building blocks for advanced cryptographic tools such as ring signatures.Our ring signature achieves a dramatic improvement in length over all the existing proposals from lattices at the same security level. The computational evaluation also shows that our construction is highly likely to outperform all the relevant works in running times. Being efficient in both aspects, our ring signature is particularly suitable for both small-scale and large-scale applications such as cryptocurrencies and e-voting systems. No trusted setup is required for any of our proposals.

2019

CRYPTO

Efficient Lattice-Based Zero-Knowledge Arguments with Standard Soundness: Construction and Applications
📺 Abstract

We provide new zero-knowledge argument of knowledge systems that work directly for a wide class of language, namely, ones involving the satisfiability of matrix-vector relations and integer relations commonly found in constructions of lattice-based cryptography. Prior to this work, practical arguments for lattice-based relations either have a constant soundness error $$(2/3)$$, or consider a weaker form of soundness, namely, extraction only guarantees that the prover is in possession of a witness that “approximates” the actual witness. Our systems do not suffer from these limitations.The core of our new argument systems is an efficient zero-knowledge argument of knowledge of a solution to a system of linear equations, where variables of this solution satisfy a set of quadratic constraints. This argument enjoys standard soundness, a small soundness error $$(1/poly)$$, and a complexity linear in the size of the solution. Using our core argument system, we construct highly efficient argument systems for a variety of statements relevant to lattices, including linear equations with short solutions and matrix-vector relations with hidden matrices.Based on our argument systems, we present several new constructions of common privacy-preserving primitives in the standard lattice setting, including a group signature, a ring signature, an electronic cash system, and a range proof protocol. Our new constructions are one to three orders of magnitude more efficient than the state of the art (in standard lattice). This illustrates the efficiency and expressiveness of our argument system.

2019

CRYPTO

Algebraic Techniques for Short(er) Exact Lattice-Based Zero-Knowledge Proofs
📺 Abstract

A key component of many lattice-based protocols is a zero-knowledge proof of knowledge of a vector
$$\vec {s}$$
with small coefficients satisfying
$$A\vec {s}=\vec {u}\bmod \,q$$
. While there exist fairly efficient proofs for a relaxed version of this equation which prove the knowledge of
$$\vec {s}'$$
and c satisfying
$$A\vec {s}'=\vec {u}c$$
where
$$\Vert \vec {s}'\Vert \gg \Vert \vec {s}\Vert $$
and c is some small element in the ring over which the proof is performed, the proofs for the exact version of the equation are considerably less practical. The best such proof technique is an adaptation of Stern’s protocol (Crypto ’93), for proving knowledge of nearby codewords, to larger moduli. The scheme is a
$$\varSigma $$
-protocol, each of whose iterations has soundness error
$$2{/}3$$
, and thus requires over 200 repetitions to obtain soundness error of
$$2^{-128}$$
, which is the main culprit behind the large size of the proofs produced.
In this paper, we propose the first lattice-based proof system that significantly outperforms Stern-type proofs for proving knowledge of a short
$$\vec {s}$$
satisfying
$$A\vec {s}=\vec {u}\bmod \,q$$
. Unlike Stern’s proof, which is combinatorial in nature, our proof is more algebraic and uses various relaxed zero-knowledge proofs as sub-routines. The main savings in our proof system comes from the fact that each round has soundness error of
$$1{/}n$$
, where n is the number of columns of A. For typical applications, n is a few thousand, and therefore our proof needs to be repeated around 10 times to achieve a soundness error of
$$2^{-128}$$
. For concrete parameters, it produces proofs that are around an order of magnitude smaller than those produced using Stern’s approach.

2019

CRYPTO

Seedless Fruit Is the Sweetest: Random Number Generation, Revisited
📺 Abstract

The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks.A recent important line of work (initiated by Dodis et al., CCS ’13) focuses on the notion of robustness for pseudorandom number generators (PRNGs) with inputs. These are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and adversarial control of entropy sources. However, the achievability of robustness inherently depends on a seed, or, alternatively, on an ideal primitive (e.g., a random oracle), independent of the source of entropy. Both assumptions are problematic: seed generation requires randomness to start with, and it is arguable whether the seed or the ideal primitive can be kept independent of the source.
This paper resolves this dilemma by putting forward new notions of robustness which enable both (1) seedless PRNGs and (2) primitive-dependent adversarial sources of entropy. To bypass obvious impossibility results, we make a realistic compromise by requiring that the source produce sufficient entropy even given its evaluations of the underlying primitive. We also provide natural, practical, and provably secure constructions based on hash-function designs from compression functions, block ciphers, and permutations. Our constructions can be instantiated with minimal changes to industry-standard hash functions SHA-2 and SHA-3, or key derivation function HKDF, and can be downgraded to (online) seedless randomness extractors, which are of independent interest.On the way we consider both a computational variant of robustness, where attackers only make a bounded number of queries to the ideal primitive, as well as a new information-theoretic variant, which dispenses with this assumption to a certain extent, at the price of requiring a high rate of injected weak randomness (as it is, e.g., plausible on Intel’s on-chip RNG). The latter notion enables applications such as everlasting security. Finally, we show that the CBC extractor, used by Intel’s on-chip RNG, is provably insecure in our model.

2019

CRYPTO

Nonces Are Noticed: AEAD Revisited
📺 Abstract

We draw attention to a gap between theory and usage of nonce-based symmetric encryption, under which the way the former treats nonces can result in violation of privacy in the latter. We bridge the gap with a new treatment of nonce-based symmetric encryption that modifies the syntax (decryption no longer takes a nonce), upgrades the security goal (asking that not just messages, but also nonces, be hidden) and gives simple, efficient schemes conforming to the new definitions. We investigate both basic security (holding when nonces are not reused) and advanced security (misuse resistance, providing best-possible guarantees when nonces are reused).

2019

CRYPTO

How to Build Pseudorandom Functions from Public Random Permutations
📺 Abstract

Pseudorandom functions are traditionally built upon block ciphers, but with the trend of permutation based cryptography, it is a natural question to investigate the design of pseudorandom functions from random permutations. We present a generic study of how to build beyond birthday bound secure pseudorandom functions from public random permutations. We first show that a pseudorandom function based on a single permutation call cannot be secure beyond the $$2^{n/2}$$ birthday bound, where n is the state size of the function. We next consider the Sum of Even-Mansour (SoEM) construction, that instantiates the sum of permutations with the Even-Mansour construction. We prove that SoEM achieves tight $$2n{/}3$$-bit security if it is constructed from two independent permutations and two randomly drawn keys. We also demonstrate a birthday bound attack if either the permutations or the keys are identical. Finally, we present the Sum of Key Alternating Ciphers (SoKAC) construction, a translation of Encrypted Davies-Meyer Dual to a public permutation based setting, and show that SoKAC achieves tight $$2n{/}3$$-bit security even when a single key is used.

2019

CRYPTO

New Results on Modular Inversion Hidden Number Problem and Inversive Congruential Generator
📺 Abstract

The Modular Inversion Hidden Number Problem (MIHNP), introduced by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001, is briefly described as follows: Let $${\mathrm {MSB}}_{\delta }(z)$$ refer to the $$\delta $$ most significant bits of z. Given many samples $$\left( t_{i}, {\mathrm {MSB}}_{\delta }((\alpha + t_{i})^{-1} \bmod {p})\right) $$ for random $$t_i \in \mathbb {Z}_p$$, the goal is to recover the hidden number $$\alpha \in \mathbb {Z}_p$$. MIHNP is an important class of Hidden Number Problem.In this paper, we revisit the Coppersmith technique for solving a class of modular polynomial equations, which is respectively derived from the recovering problem of the hidden number $$\alpha $$ in MIHNP. For any positive integer constant d, let integer $$n=d^{3+o(1)}$$. Given a sufficiently large modulus p, $$n+1$$ samples of MIHNP, we present a heuristic algorithm to recover the hidden number $$\alpha $$ with a probability close to 1 when $$\delta /\log _2 p>\frac{1}{d\,+\,1}+o(\frac{1}{d})$$. The overall time complexity of attack is polynomial in $$\log _2 p$$, where the complexity of the LLL algorithm grows as $$d^{\mathcal {O}(d)}$$ and the complexity of the Gröbner basis computation grows as $$(2d)^{\mathcal {O}(n^2)}$$. When $$d> 2$$, this asymptotic bound outperforms $$\delta /\log _2 p>\frac{1}{3}$$ which is the asymptotic bound proposed by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001. It is the first time that a better bound for solving MIHNP is given, which implies that the conjecture that MIHNP is hard whenever $$\delta /\log _2 p<\frac{1}{3}$$ is broken. Moreover, we also get the best result for attacking the Inversive Congruential Generator (ICG) up to now.

2019

CRYPTO

On the Shortness of Vectors to Be Found by the Ideal-SVP Quantum Algorithm
📺 Abstract

The hardness of finding short vectors in ideals of cyclotomic number fields (hereafter, Ideal-SVP) can serve as a worst-case assumption for numerous efficient cryptosystems, via the average-case problems Ring-SIS and Ring-LWE. For a while, it could be assumed the Ideal-SVP problem was as hard as the analog problem for general lattices (SVP), even when considering quantum algorithms.But in the last few years, a series of works has lead to a quantum algorithm for Ideal-SVP that outperforms what can be done for general SVP in certain regimes. More precisely, it was demonstrated (under certain hypotheses) that one can find in quantum polynomial time a vector longer by a factor at most
$$\alpha = \exp ({\widetilde{O}(n^{1/2})})$$
than the shortest non-zero vector in a cyclotomic ideal lattice, where n is the dimension.In this work, we explore the constants hidden behind this asymptotic claim. While these algorithms have quantum steps, the steps that impact the approximation factor
$$\alpha $$
are entirely classical, which allows us to estimate it experimentally using only classical computing. Moreover, we design heuristic improvements for those steps that significantly decrease the hidden factors in practice. Finally, we derive new provable effective lower bounds based on volumetric arguments.This study allows to predict the crossover point with classical lattice reduction algorithms, and thereby determine the relevance of this quantum algorithm in any cryptanalytic context. For example we predict that this quantum algorithm provides shorter vectors than BKZ-300 (roughly the weakest security level of NIST lattice-based candidates) for cyclotomic rings of rank larger than about 24000.

2019

CRYPTO

Proofs of Replicated Storage Without Timing Assumptions
📺 Abstract

In this paper we provide a formal treatment of proof of replicated storage, a novel cryptographic primitive recently proposed in the context of a novel cryptocurrency, namely Filecoin.In a nutshell, proofs of replicated storage is a solution to the following problem: A user stores a file m on n different servers to ensure that the file will be available even if some of the servers fail. Using proof of retrievability, the user could check that every server is indeed storing the file. However, what if the servers collude and, in order to save on resources, decide to only store one copy of the file? A proof of replicated storage guarantees that, unless the (potentially colluding) servers are indeed reserving the space necessary to store n copies of the file, the user will not accept the proofs. While some candidate proofs of replicated storage have already been proposed, their soundness relies on timing assumptions i.e., the user must reject the proof if the prover does not reply within a certain time-bound.In this paper we provide the first construction of a proof of replication which does not rely on any timing assumptions.

2019

CRYPTO

Simple Proofs of Space-Time and Rational Proofs of Storage
📺 Abstract

We introduce a new cryptographic primitive: Proofs of Space-Time (PoSTs) and construct an extremely simple, practical protocol for implementing these proofs. A PoST allows a prover to convince a verifier that she spent a “space-time” resource (storing data—space—over a period of time). Formally, we define the PoST resource as a trade-off between CPU work and space-time (under reasonable cost assumptions, a rational user will prefer to use the lower-cost space-time resource over CPU work).Compared to a proof-of-work, a PoST requires less energy use, as the “difficulty” can be increased by extending the time period over which data is stored without increasing computation costs. Our definition is very similar to “Proofs of Space” [ePrint 2013/796, 2013/805] but, unlike the previous definitions, takes into account amortization attacks and storage duration. Moreover, our protocol uses a very different (and much simpler) technique, making use of the fact that we explicitly allow a space-time tradeoff, and doesn’t require any non-standard assumptions (beyond random oracles). Unlike previous constructions, our protocol allows incremental difficulty adjustment, which can gracefully handle increases in the price of storage compared to CPU work. In addition, we show how, in a crypto-currency context, the parameters of the scheme can be adjusted using a market-based mechanism, similar in spirit to the difficulty adjustment for PoW protocols.

2019

CRYPTO

Non-malleable Codes for Decision Trees
📺 Abstract

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by decision trees of depth
$$d= n^{1/4-o(1)}$$
. In particular, each bit of the tampered codeword is set arbitrarily after adaptively reading up to d arbitrary locations within the original codeword. Prior to this work, no efficient unconditional non-malleable codes were known for decision trees beyond depth
$$O(\log ^2 n)$$
.Our result also yields efficient, unconditional non-malleable codes that are
$$\exp (-n^{\varOmega (1)})$$
-secure against constant-depth circuits of
$$\exp (n^{\varOmega (1)})$$
-size. Prior work of Chattopadhyay and Li (STOC 2017) and Ball et al. (FOCS 2018) only provide protection against
$$\exp (O(\log ^2n))$$
-size circuits with
$$\exp (-O(\log ^2n))$$
-security.We achieve our result through simple non-malleable reductions of decision tree tampering to split-state tampering. As an intermediary, we give a simple and generic reduction of leakage-resilient split-state tampering to split-state tampering with improved parameters. Prior work of Aggarwal et al. (TCC 2015) only provides a reduction to split-state non-malleable codes with decoders that exhibit particular properties.

2019

CRYPTO

Explicit Rate-1 Non-malleable Codes for Local Tampering
📺 Abstract

This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider $$\delta $$-local tampering functions; namely, each output bit of the tampering function is a function of (at most) $$\delta $$ input bits. This work presents the first explicit and efficient rate-1 non-malleable code for $$\delta $$-local tampering functions, where $$\delta =\xi \lg n$$ and $$\xi <1$$ is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC$$^0$$ tampering functions.Before our work, no explicit construction for a constant-rate non-malleable code was known even for the simplest 1-local tampering functions. Ball et al. (EUROCRYPT–2016), and Chattopadhyay and Li (STOC–2017) provided the first explicit non-malleable codes against $$\delta $$-local tampering functions. However, these constructions are rate-0 even when the tampering functions have 1-locality. In the CRS model, Faust et al. (EUROCRYPT–2014) constructed efficient rate-1 non-malleable codes for $$\delta = O(\log n)$$ local tampering functions.Our main result is a general compiler that bootstraps a rate-0 non-malleable code against leaky input and output local tampering functions to construct a rate-1 non-malleable code against $$\xi \lg n$$-local tampering functions, for any positive constant $$\xi < 1$$. Our explicit construction instantiates this compiler using an appropriate encoding by Ball et al. (EUROCRYPT–2016).

2019

CRYPTO

Continuous Space-Bounded Non-malleable Codes from Stronger Proofs-of-Space
📺 Abstract

Non-malleable codes are encoding schemes that provide protections against various classes of tampering attacks. Recently Faust et al. (CRYPTO 2017) initiated the study of space-bounded non-malleable codes that provide such protections against tampering within small-space devices. They put forward a construction based on any non-interactive proof-of-space(NIPoS). However, the scheme only protects against an a priori bounded number of tampering attacks.We construct non-malleable codes that are resilient to an unbounded polynomial number of space-bounded tamperings. Towards that we introduce a stronger variant of $$\text {NIPoS}$$ called proof-extractable$$\text {NIPoS}$$ ($$\text {PExt-NIPoS}$$), and propose two approaches of constructing such a primitive. Using a new proof strategy we show that the generic encoding scheme of Faust et al. achieves unbounded tamper-resilience when instantiated with a $$\text {PExt-NIPoS}$$. We show two methods to construct $$\text {PExt-NIPoS}$$:1.The first method uses a special family of “memory-hard” graphs, called challenge-hard graphs (CHG), a notion we introduce here. We instantiate such family of graphs based on an extension of stack of localized expanders (first used by Ren and Devadas in the context of proof-of-space). In addition, we show that the graph construction used as a building block for the proof-of-space by Dziembowski et al. (CRYPTO 2015) satisfies challenge-hardness as well. These two CHG-instantiations lead to continuous space-bounded NMC with different features in the random oracle model.2.Our second instantiation relies on a new measurable property, called uniqueness of $$\text {NIPoS}$$. We show that standard extractability can be upgraded to proof-extractability if the $$\text {NIPoS}$$ also has uniqueness. We propose a simple heuristic construction of $$\text {NIPoS}$$, that achieves (partial) uniqueness, based on a candidate memory-hard function in the standard model and a publicly verifiable computation with small-space verification. Instantiating the encoding scheme of Faust et al. with this $$\text {NIPoS}$$, we obtain a continuous space-bounded NMC that supports the “most practical” parameters, complementing the provably secure but “relatively impractical” CHG-based constructions. Additionally, we revisit the construction of Faust et al. and observe that due to the lack of uniqueness of their $$\text {NIPoS}$$, the resulting encoding schemes yield “highly impractical” parameters in the continuous setting.
We conclude the paper with a comparative study of all our non-malleable code constructions with an estimation of concrete parameters.

2019

CRYPTO

Synchronous, with a Chance of Partition Tolerance
📺 Abstract

Murphy, Murky, Mopey, Moody, and Morose decide to write a paper together over the Internet and submit it to the prestigious CRYPTO’19 conference that has the most amazing PC. They encounter a few problems. First, not everyone is online every day: some are lazy and go skiing on Mondays; others cannot use git correctly and they are completely unaware that they are losing messages. Second, a small subset of the co-authors may be secretly plotting to disrupt the project (e.g., because they are writing a competing paper in stealth).Suppose that each day, sufficiently many honest co-authors are online (and use git correctly); moreover, suppose that messages checked into git on Monday can be correctly received by honest and online co-authors on Tuesday or any future day. Can the honest co-authors successfully finish the paper in a small number of days such that they make the CRYPTO deadline; and perhaps importantly, can all the honest co-authors, including even those who are lazy and those who sometimes use git incorrectly, agree on the final theorem?

2019

CRYPTO

Subvector Commitments with Application to Succinct Arguments
📺 Abstract

We put forward the notion of subvector commitments (SVC): An SVC allows one to open a committed vector at a set of positions, where the opening size is independent of length of the committed vector and the number of positions to be opened. We propose two constructions under variants of the root assumption and the CDH assumption, respectively. We further generalize SVC to a notion called linear map commitments (LMC), which allows one to open a committed vector to its images under linear maps with a single short message, and propose a construction over pairing groups.Equipped with these newly developed tools, we revisit the “CS proofs” paradigm [Micali, FOCS 1994] which turns any arguments with public-coin verifiers into non-interactive arguments using the Fiat-Shamir transform in the random oracle model. We propose a compiler that turns any (linear, resp.) PCP into a non-interactive argument, using exclusively SVCs (LMCs, resp.). For an approximate 80 bits of soundness, we highlight the following new implications:1.There exists a succinct non-interactive argument of knowledge (SNARK) with public-coin setup with proofs of size 5360 bits, under the adaptive root assumption over class groups of imaginary quadratic orders against adversaries with runtime $$2^{128}$$. At the time of writing, this is the shortest SNARK with public-coin setup.2.There exists a non-interactive argument with private-coin setup, where proofs consist of 2 group elements and 3 field elements, in the generic bilinear group model.

2019

CRYPTO

Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains
📺 Abstract

We present batching techniques for cryptographic accumulators and vector commitments in groups of unknown order. Our techniques are tailored for distributed settings where no trusted accumulator manager exists and updates to the accumulator are processed in batches. We develop techniques for non-interactively aggregating membership proofs that can be verified with a constant number of group operations. We also provide a constant sized batch non-membership proof for a large number of elements. These proofs can be used to build the first positional vector commitment (VC) with constant sized openings and constant sized public parameters. As a core building block for our batching techniques we develop several succinct proof systems in groups of unknown order. These extend a recent construction of a succinct proof of correct exponentiation, and include a succinct proof of knowledge of an integer discrete logarithm between two group elements. We circumvent an impossibility result for Sigma-protocols in these groups by using a short trapdoor-free CRS. We use these new accumulator and vector commitment constructions to design a stateless blockchain, where nodes only need a constant amount of storage in order to participate in consensus. Further, we show how to use these techniques to reduce the size of IOP instantiations, such as STARKs. The full version of the paper is available online [BBF18b].

2019

CRYPTO

On the Plausibility of Fully Homomorphic Encryption for RAMs
📺 Abstract

We initiate the study of fully homomorphic encryption for RAMs (RAM-FHE). This is a public-key encryption scheme where, given an encryption of a large database D, anybody can efficiently compute an encryption of P(D) for an arbitrary RAM program P. The running time over the encrypted data should be as close as possible to the worst case running time of P, which may be sub-linear in the data size.A central difficulty in constructing a RAM-FHE scheme is hiding the sequence of memory addresses accessed by P. This is particularly problematic because an adversary may homomorphically evaluate many programs over the same ciphertext, therefore effectively “rewinding” any mechanism for making memory accesses oblivious.We identify a necessary prerequisite towards constructing RAM-FHE that we call rewindable oblivious RAM (rewindable ORAM), which provides security even in this strong adversarial setting. We show how to construct rewindable ORAM using symmetric-key doubly efficient PIR (SK-DEPIR) (Canetti-Holmgren-Richelson, Boyle-Ishai-Pass-Wootters: TCC ’17). We then show how to use rewindable ORAM, along with virtual black-box (VBB) obfuscation for specific circuits, to construct RAM-FHE. The latter primitive can be heuristically instantiated using existing indistinguishability obfuscation candidates. Overall, we obtain a RAM-FHE scheme where the multiplicative overhead in running time is polylogarithmic in the database size N. Our basic scheme is single-hop, but we also extend it to obtain multi-hop RAM-FHE with overhead
$$N^\epsilon $$
for arbitrarily small
$$\epsilon >0$$
.We view our work as the first evidence that RAM-FHE is likely to exist.

2019

CRYPTO

Homomorphic Time-Lock Puzzles and Applications
📺 Abstract

Time-lock puzzles allow one to encrypt messages for the future, by efficiently generating a puzzle with a solution s that remains hidden until time $$\mathcal {T}$$ has elapsed. The solution is required to be concealed from the eyes of any algorithm running in (parallel) time less than $$\mathcal {T}$$. We put forth the concept of homomorphic time-lock puzzles, where one can evaluate functions over puzzles without solving them, i.e., one can manipulate a set of puzzles with solutions $$(s_1, \dots , s_n)$$ to obtain a puzzle that solves to $$f(s_1, \ldots , s_n)$$, for any function f. We propose candidate constructions under concrete cryptographic assumptions for different classes of functions. Then we show how homomorphic time-lock puzzles overcome the limitations of classical time-lock puzzles by proposing new protocols for applications of interest, such as e-voting, multi-party coin flipping, and fair contract signing.

2019

CRYPTO

Symmetric Primitives with Structured Secrets
📺 Abstract

Securely managing encrypted data on an untrusted party is a challenging problem that has motivated the study of a wide variety of cryptographic primitives. A special class of such primitives allows an untrusted party to transform a ciphertext encrypted under one key to a ciphertext under another key, using some auxiliary information that does not leak the underlying data. Prominent examples of such primitives in the symmetric setting are key-homomorphic (weak) PRFs, updatable encryption, and proxy re-encryption. Although these primitives differ significantly in terms of their constructions and security requirements, they share two important properties: (a) they have secrets with structure or extra functionality, and (b) all known constructions of these primitives satisfying reasonably strong definitions of security are based on concrete public-key assumptions, e.g., DDH and LWE.
This raises the question of whether these objects inherently belong to the world of public-key primitives, or they can potentially be built from simple symmetric-key objects such as pseudorandom functions. In this work, we show that the latter possibility is unlikely. More specifically, we show that:Any (bounded) key-homomorphic weak PRF with an abelian output group implies a (bounded) input-homomorphic weak PRF, which has recently been shown to imply not only public-key encryption but also a variety of primitives such as PIR, lossy TDFs, and even IBE.Any ciphertext-independent updatable encryption scheme that is forward and post-compromise secure implies PKE. Moreover, any symmetric-key proxy re-encryption scheme with reasonably strong security guarantees implies a forward and post-compromise secure ciphertext-independent updatable encryption, and hence PKE.
In addition, we show that unbounded (or exact) key-homomorphic weak PRFs over abelian groups are impossible in the quantum world. In other words, over abelian groups, bounded key-homomorphism is the best that we can hope for in terms of post-quantum security. Our attack also works over other structured primitives with abelian groups and exact homomorphisms, including homomorphic one-way functions and input-homomorphic weak PRFs.

2019

CRYPTO

Unifying Leakage Models on a Rényi Day
📺 Abstract

In the last decade, several works have focused on finding the best way to model the leakage in order to obtain provably secure implementations. One of the most realistic models is the noisy leakage model, introduced in [PR13, DDF14] together with secure constructions. These works suffer from various limitations, in particular the use of ideal leak-free gates in [PR13] and an important loss (in the size of the field) in the reduction in [DDF14].In this work, we provide new strategies to prove the security of masked implementations and start by unifying the different noisiness metrics used in prior works by relating all of them to a standard notion in information theory: the pointwise mutual information. Based on this new interpretation, we define two new natural metrics and analyze the security of known compilers with respect to these metrics. In particular, we prove (1) a tighter bound for reducing the noisy leakage models to the probing model using our first new metric, (2) better bounds for amplification-based security proofs using the second metric.To support that the improvements we obtain are not only a consequence of the use of alternative metrics, we show that for concrete representation of leakage (e.g., “Hamming weight + Gaussian noise”), our approach significantly improves the parameters compared to prior works. Finally, using the Rényi divergence, we quantify concretely the advantage of an adversary in attacking a block cipher depending on the number of leakage acquisitions available to it.

2019

CRYPTO

Leakage Certification Revisited: Bounding Model Errors in Side-Channel Security Evaluations
📺 Abstract

Leakage certification aims at guaranteeing that the statistical models used in side-channel security evaluations are close to the true statistical distribution of the leakages, hence can be used to approximate a worst-case security level. Previous works in this direction were only qualitative: for a given amount of measurements available to an evaluation laboratory, they rated a model as “good enough” if the model assumption errors (i.e., the errors due to an incorrect choice of model family) were small with respect to the model estimation errors. We revisit this problem by providing the first quantitative tools for leakage certification. For this purpose, we provide bounds for the (unknown) Mutual Information metric that corresponds to the true statistical distribution of the leakages based on two easy-to-compute information theoretic quantities: the Perceived Information, which is the amount of information that can be extracted from a leaking device thanks to an estimated statistical model, possibly biased due to estimation and assumption errors, and the Hypothetical Information, which is the amount of information that would be extracted from an hypothetical device exactly following the model distribution. This positive outcome derives from the observation that while the estimation of the Mutual Information is in general a hard problem (i.e., estimators are biased and their convergence is distribution-dependent), it is significantly simplified in the case of statistical inference attacks where a target random variable (e.g., a key in a cryptographic setting) has a constant (e.g., uniform) probability. Our results therefore provide a general and principled path to bound the worst-case security level of an implementation. They also significantly speed up the evaluation of any profiled side-channel attack, since they imply that the estimation of the Perceived Information, which embeds an expensive cross-validation step, can be bounded by the computation of a cheaper Hypothetical Information, for any estimated statistical model.

2019

CRYPTO

Security in the Presence of Key Reuse: Context-Separable Interfaces and Their Applications
📺 Abstract

Key separation is often difficult to enforce in practice. While key reuse can be catastrophic for security, we know of a number of cryptographic schemes for which it is provably safe. But existing formal models, such as the notions of joint security (Haber-Pinkas, CCS ’01) and agility (Acar et al., EUROCRYPT ’10), do not address the full range of key-reuse attacks—in particular, those that break the abstraction of the scheme, or exploit protocol interactions at a higher level of abstraction. This work attends to these vectors by focusing on two key elements: the game that codifies the scheme under attack, as well as its intended adversarial model; and the underlying interface that exposes secret key operations for use by the game. Our main security experiment considers the implications of using an interface (in practice, the API of a software library or a hardware platform such as TPM) to realize the scheme specified by the game when the interface is shared with other unspecified, insecure, or even malicious applications. After building up a definitional framework, we apply it to the analysis of two real-world schemes: the EdDSA signature algorithm and the Noise protocol framework. Both provide some degree of context separability, a design pattern for interfaces and their applications that aids in the deployment of secure protocols.

2019

CRYPTO

The Communication Complexity of Threshold Private Set Intersection
📺 Abstract

Threshold private set intersection enables Alice and Bob who hold sets
$$S_{\mathsf {A}}$$
and
$$S_{\mathsf {B}}$$
of size n to compute the intersection
$$S_{\mathsf {A}} \cap S_{\mathsf {B}} $$
if the sets do not differ by more than some threshold parameter
$$t$$
. In this work, we investigate the communication complexity of this problem and we establish the first upper and lower bounds. We show that any protocol has to have a communication complexity of
$$\varOmega (t)$$
. We show that an almost matching upper bound of
$$\tilde{\mathcal {O}}(t)$$
can be obtained via fully homomorphic encryption. We present a computationally more efficient protocol based on weaker assumptions, namely additively homomorphic encryption, with a communication complexity of
$$\tilde{\mathcal {O}}(t ^2)$$
. For applications like biometric authentication, where a given fingerprint has to have a large intersection with a fingerprint from a database, our protocols may result in significant communication savings.Prior to this work, all previous protocols had a communication complexity of
$$\varOmega (n)$$
. Our protocols are the first ones with communication complexities that mainly depend on the threshold parameter
$$t$$
and only logarithmically on the set size n.

2019

CRYPTO

Adaptively Secure MPC with Sublinear Communication Complexity
📺 Abstract

A central challenge in the study of MPC is to balance between security guarantees, hardness assumptions, and resources required for the protocol. In this work, we study the cost of tolerating adaptive corruptions in MPC protocols under various corruption thresholds. In the strongest setting, we consider adaptive corruptions of an arbitrary number of parties (potentially all) and achieve the following results:A two-round secure function evaluation (SFE) protocol in the CRS model, assuming LWE and indistinguishability obfuscation (iO). The communication, the CRS size, and the online-computation are sublinear in the size of the function. The iO assumption can be replaced by secure erasures. Previous results required either the communication or the CRS size to be polynomial in the function size.Under the same assumptions, we construct a “Bob-optimized” 2PC (where Alice talks first, Bob second, and Alice learns the output). That is, the communication complexity and total computation of Bob are sublinear in the function size and in Alice’s input size. We prove impossibility of “Alice-optimized” protocols.Assuming LWE, we bootstrap adaptively secure NIZK arguments to achieve proof size sublinear in the circuit size of the NP-relation.
On a technical level, our results are based on laconic function evaluation (LFE) (Quach, Wee, and Wichs, FOCS’18) and shed light on an interesting duality between LFE and FHE.Next, we analyze adaptive corruptions of all-but-one of the parties and show a two-round SFE protocol in the threshold PKI model (where keys of a threshold FHE scheme are pre-shared among the parties) with communication complexity sublinear in the circuit size, assuming LWE and NIZK. Finally, we consider the honest-majority setting, and show a two-round SFE protocol with guaranteed output delivery under the same constraints.

2019

CRYPTO

Communication Lower Bounds for Statistically Secure MPC, With or Without Preprocessing
📺 Abstract

We prove a lower bound on the communication complexity of unconditionally secure multiparty computation, both in the standard model with
$$n=2t+1$$
parties of which t are corrupted, and in the preprocessing model with
$$n=t+1$$
. In both cases, we show that for any
$$g \in \mathbb {N}$$
there exists a Boolean circuit C with g gates, where any secure protocol implementing C must communicate
$$\varOmega (n g)$$
bits, even if only passive and statistical security is required. The results easily extends to constructing similar circuits over any fixed finite field. This shows that for all sizes of circuits, the O(n) overhead of all known protocols when t is maximal is inherent. It also shows that security comes at a price: the circuit we consider could namely be computed among n parties with communication only O(g) bits if no security was required. Our results extend to the case where the threshold t is suboptimal. For the honest majority case, this shows that the known optimizations via packed secret-sharing can only be obtained if one accepts that the threshold is
$$t= (1/2 - c)n$$
for a constant c. For the honest majority case, we also show an upper bound that matches the lower bound up to a constant factor (existing upper bounds are a factor
$$\lg n$$
off for Boolean circuits).

2019

CRYPTO

Communication-Efficient Unconditional MPC with Guaranteed Output Delivery
📺 Abstract

We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold
$$t < n/3$$
. We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive for over a decade.We resolve the above question in the affirmative by providing an MPC with communication complexity
$$O(Cn\kappa + n^3\kappa )$$
where
$$\kappa $$
is the size of an element in the field, C is the size of the (arithmetic) circuit, and, n is the number of parties. This represents a strict improvement over the previously best known communication complexity of
$$O(Cn\kappa +D_Mn^2\kappa +n^3\kappa )$$
where
$$D_M$$
is the multiplicative depth of the circuit. To obtain this result, we introduce a novel technique called 4-consistent tuples of sharings which we believe to be of independent interest.

2019

CRYPTO

Efficient Collision Attack Frameworks for RIPEMD-160
📺 Abstract

RIPEMD-160 is an ISO/IEC standard and has been applied to generate the Bitcoin address with SHA-256. Due to the complex dual-stream structure, the first collision attack on reduced RIPEMD-160 presented by Liu, Mendel and Wang at Asiacrypt 2017 only reaches 30 steps, having a time complexity of $$2^{70}$$. Apart from that, several semi-free-start collision attacks have been published for reduced RIPEMD-160 with the start-from-the-middle method. Inspired from such start-from-the middle structures, we propose two novel efficient collision attack frameworks for reduced RIPEMD-160 by making full use of the weakness of its message expansion. Those two frameworks are called dense-left-and-sparse-right (DLSR) framework and sparse-left-and-dense-right (SLDR) framework. As it turns out, the DLSR framework is more efficient than SLDR framework since one more step can be fully controlled, though with extra $$2^{32}$$ memory complexity. To construct the best differential characteristics for the DLSR framework, we carefully build the linearized part of the characteristics and then solve the corresponding nonlinear part using a guess-and-determine approach. Based on the newly discovered differential characteristics, we provide colliding messages pairs for the first practical collision attacks on 30 and 31 (out of 80) steps of RIPEMD-160 with time complexity $$2^{35.9}$$ and $$2^{41.5}$$ respectively. In addition, benefiting from the partial calculation, we can attack 33 and 34 (out of 80) steps of RIPEMD-160 with time complexity $$2^{67.1}$$ and $$2^{74.3}$$ respectively. When applying the SLDR framework to the differential characteristic used in the Asiacrypt 2017 paper, we significantly improve the time complexity by a factor of $$2^{13}$$. However, it still cannot compete with the results obtained from the DLSR framework. To the best of our knowledge, these are the best collision attacks on reduced RIPEMD-160 with respect to the number of steps, including the first colliding message pairs for 30 and 31 steps of RIPEMD-160.

2019

CRYPTO

Improving Attacks on Round-Reduced Speck32/64 Using Deep Learning
📺 Abstract

This paper has four main contributions. First, we calculate the predicted difference distribution of Speck32/64 with one specific input difference under the Markov assumption completely for up to eight rounds and verify that this yields a globally fairly good model of the difference distribution of Speck32/64. Secondly, we show that contrary to conventional wisdom, machine learning can produce very powerful cryptographic distinguishers: for instance, in a simple low-data, chosen plaintext attack on nine rounds of Speck, we present distinguishers based on deep residual neural networks that achieve a mean key rank roughly five times lower than an analogous classical distinguisher using the full difference distribution table. Thirdly, we develop a highly selective key search policy based on a variant of Bayesian optimization which, together with our neural distinguishers, can be used to reduce the remaining security of 11-round Speck32/64 to roughly 38 bits. This is a significant improvement over previous literature. Lastly, we show that our neural distinguishers successfully use features of the ciphertext pair distribution that are invisible to all purely differential distinguishers even given unlimited data.While our attack is based on a known input difference taken from the literature, we also show that neural networks can be used to rapidly (within a matter of minutes on our machine) find good input differences without using prior human cryptanalysis. Supplementary code and data for this paper is available at https://github.com/agohr/deep_speck.

2019

CRYPTO

Correlation of Quadratic Boolean Functions: Cryptanalysis of All Versions of Full $\mathsf {MORUS}$
📺 Abstract

We show that the correlation of any quadratic Boolean function can be read out from its so-called disjoint quadratic form. We further propose a polynomial-time algorithm that can transform an arbitrary quadratic Boolean function into its disjoint quadratic form. With this algorithm, the exact correlation of quadratic Boolean functions can be computed efficiently.We apply this method to analyze the linear trails of $$\mathsf {MORUS}$$ (one of the seven finalists of the CAESAR competition), which are found with the help of a generic model for linear trails of $$\mathsf {MORUS}$$-like key-stream generators. In our model, any tool for finding linear trails of block ciphers can be used to search for trails of $$\mathsf {MORUS}$$-like key-stream generators. As a result, a set of trails with correlation $$2^{-38}$$ is identified for all versions of full $$\mathsf {MORUS}$$, while the correlations of previously published best trails for $$\mathsf {MORUS}$$-640 and $$\mathsf {MORUS}$$-1280 are $$2^{-73}$$ and $$2^{-76}$$ respectively (ASIACRYPT 2018). This significantly improves the complexity of the attack on $$\mathsf {MORUS}$$-1280-256 from $$2^{152}$$ to $$2^{76}$$. These new trails also lead to the first distinguishing and message-recovery attacks on $$\mathsf {MORUS}$$-640-128 and $$\mathsf {MORUS}$$-1280-128 with surprisingly low complexities around $$2^{76}$$.Moreover, we observe that the condition for exploiting these trails in an attack can be more relaxed than previously thought, which shows that the new trails are superior to previously published ones in terms of both correlation and the number of ciphertext blocks involved.

2019

CRYPTO

Low-Memory Attacks Against Two-Round Even-Mansour Using the 3-XOR Problem
📺 Abstract

The iterated Even-Mansour construction is an elegant construction that idealizes block cipher designs such as the AES. In this work we focus on the simplest variant, the 2-round Even-Mansour construction with a single key. This is the most minimal construction that offers security beyond the birthday bound: there is a security proof up to $$2^{2n/3}$$ evaluations of the underlying permutations and encryption, and the best known attacks have a complexity of roughly $$2^n/n$$ operations.We show that attacking this scheme with block size n is related to the 3-XOR problem with element size $$\ell = 2n$$, an important algorithmic problem that has been studied since the nineties. In particular the 3-XOR problem is known to require at least $$2^{\ell /3}$$ queries, and the best known algorithms require around $$2^{\ell /2}/\ell $$ operations: this roughly matches the known bounds for the 2-round Even-Mansour scheme.Using this link we describe new attacks against the 2-round Even-Mansour scheme. In particular, we obtain the first algorithms where both the data and the memory complexity are significantly lower than $$2^{n}$$. From a practical standpoint, previous works with a data and/or memory complexity close to $$2^n$$ are unlikely to be more efficient than a simple brute-force search over the key. Our best algorithm requires just $$\lambda n$$ known plaintext/ciphertext pairs, for some constant $$0< \lambda < 1$$, $$2^n/\lambda n$$ time, and $$2^{\lambda n}$$ memory. For instance, with $$n=64$$ and $$\lambda = 1/2$$, the memory requirement is practical, and we gain a factor 32 over brute-force search. We also describe an algorithm with asymptotic complexity $$\mathcal {O}(2^{n} \ln ^2 n/n^2)$$, improving the previous asymptotic complexity of $$\mathcal {O}(2^n/n)$$, using a variant of the 3-SUM algorithm of Baran, Demaine, and Pǎtraşcu.

2019

CRYPTO

How to Record Quantum Queries, and Applications to Quantum Indifferentiability
📺 Abstract

The quantum random oracle model (QROM) has become the standard model in which to prove the post-quantum security of random-oracle-based constructions. Unfortunately, none of the known proof techniques allow the reduction to record information about the adversary’s queries, a crucial feature of many classical ROM proofs, including all proofs of indifferentiability for hash function domain extension.In this work, we give a new QROM proof technique that overcomes this “recording barrier”. We do so by giving a new “compressed oracle” which allows for efficient on-the-fly simulation of random oracles, roughly analogous to the usual classical simulation. We then use this new technique to give the first proof of quantum indifferentiability for the Merkle-Damgård domain extender for hash functions. We also give a proof of security for the Fujisaki-Okamoto transformation; previous proofs required modifying the scheme to include an additional hash term. Given the threat posed by quantum computers and the push toward quantum-resistant cryptosystems, our work represents an important tool for efficient post-quantum cryptosystems.

2019

CRYPTO

Quantum Security Proofs Using Semi-classical Oracles
📺 Abstract

We present an improved version of the one-way to hiding (O2H) Theorem by Unruh, J ACM 2015. Our new O2H Theorem gives higher flexibility (arbitrary joint distributions of oracles and inputs, multiple reprogrammed points) as well as tighter bounds (removing square-root factors, taking parallelism into account). The improved O2H Theorem makes use of a new variant of quantum oracles, semi-classical oracles, where queries are partially measured. The new O2H Theorem allows us to get better security bounds in several public-key encryption schemes.

2019

CRYPTO

Quantum Indistinguishability of Random Sponges
📺 Abstract

In this work we show that the sponge construction can be used to construct quantum-secure pseudorandom functions. As our main result we prove that random sponges are quantum indistinguishable from random functions. In this setting the adversary is given superposition access to the input-output behavior of the construction but not to the internal function. Our proofs hold under the assumption that the internal function is a random function or permutation. We then use this result to obtain a quantum-security version of a result by Andreeva, Daemen, Mennink, and Van Assche (FSE’15) which shows that a sponge that uses a secure PRP or PRF as internal function is a secure PRF. This result also proves that the recent attacks against CBC-MAC in the quantum-access model by Kaplan, Leurent, Leverrier, and Naya-Plasencia (Crypto’16) and Santoli, and Schaffner (QIC’16) can be prevented by introducing a state with a non-trivial inner part.The proof of our main result is derived by analyzing the joint distribution of any q input-output pairs. Our method analyzes the statistical behavior of the considered construction in great detail. The used techniques might prove useful in future analysis of different cryptographic primitives considering quantum adversaries. Using Zhandry’s PRF/PRP switching lemma we then obtain that quantum indistinguishability also holds if the internal block function is a random permutation.

2019

CRYPTO

Revisiting Post-quantum Fiat-Shamir
📺 Abstract

The Fiat-Shamir transformation is a useful approach to building non-interactive arguments (of knowledge) in the random oracle model. Unfortunately, existing proof techniques are incapable of proving the security of Fiat-Shamir in the quantum setting. The problem stems from (1) the difficulty of quantum rewinding, and (2) the inability of current techniques to adaptively program random oracles in the quantum setting. In this work, we show how to overcome the limitations above in many settings. In particular, we give mild conditions under which Fiat-Shamir is secure in the quantum setting. As an application, we show that existing lattice signatures based on Fiat-Shamir are secure without any modifications.

2019

CRYPTO

Security of the Fiat-Shamir Transformation in the Quantum Random-Oracle Model
📺 Abstract

The famous Fiat-Shamir transformation turns any public-coin three-round interactive proof, i.e., any so-called
$$\Sigma {\text {-protocol}}$$
, into a non-interactive proof in the random-oracle model. We study this transformation in the setting of a quantum adversary that in particular may query the random oracle in quantum superposition.Our main result is a generic reduction that transforms any quantum dishonest prover attacking the Fiat-Shamir transformation in the quantum random-oracle model into a similarly successful quantum dishonest prover attacking the underlying
$$\Sigma {\text {-protocol}}$$
(in the standard model). Applied to the standard soundness and proof-of-knowledge definitions, our reduction implies that both these security properties, in both the computational and the statistical variant, are preserved under the Fiat-Shamir transformation even when allowing quantum attacks. Our result improves and completes the partial results that have been known so far, but it also proves wrong certain claims made in the literature.In the context of post-quantum secure signature schemes, our results imply that for any
$$\Sigma {\text {-protocol}}$$
that is a proof-of-knowledge against quantum dishonest provers (and that satisfies some additional natural properties), the corresponding Fiat-Shamir signature scheme is secure in the quantum random-oracle model. For example, we can conclude that the non-optimized version of Fish, which is the bare Fiat-Shamir variant of the NIST candidate Picnic, is secure in the quantum random-oracle model.

2019

CRYPTO

Unconditionally Secure Computation Against Low-Complexity Leakage
📺 Abstract

We consider the problem of constructing leakage-resilient circuit compilers that are secure against global leakage functions with bounded output length. By global, we mean that the leakage can depend on all circuit wires and output a low-complexity function (represented as a multi-output Boolean circuit) applied on these wires. In this work, we design compilers both in the stateless (a.k.a. single-shot leakage) setting and the stateful (a.k.a. continuous leakage) setting that are unconditionally secure against $$\mathsf {AC}^0$$ leakage and similar low-complexity classes.In the stateless case, we show that the original private circuits construction of Ishai, Sahai, and Wagner (Crypto 2003) is actually secure against $$\mathsf {AC}^0$$ leakage. In the stateful case, we modify the construction of Rothblum (Crypto 2012), obtaining a simple construction with unconditional security. Prior works that designed leakage-resilient circuit compilers against $$\mathsf {AC}^0$$ leakage had to rely either on secure hardware components (Faust et al., Eurocrypt 2010, Miles-Viola, STOC 2013) or on (unproven) complexity-theoretic assumptions (Rothblum, Crypto 2012).

2019

CRYPTO

Tight Leakage-Resilient CCA-Security from Quasi-Adaptive Hash Proof System
📺 Abstract

We propose the concept of quasi-adaptive hash proof system (QAHPS), where the projection key is allowed to depend on the specific language for which hash values are computed. We formalize leakage-resilient(LR)-ardency for QAHPS by defining two statistical properties, including LR-$$\langle \mathscr {L}_0, \mathscr {L}_1 \rangle $$-universal and LR-$$\langle \mathscr {L}_0, \mathscr {L}_1 \rangle $$-key-switching.We provide a generic approach to tightly leakage-resilient CCA (LR-CCA) secure public-key encryption (PKE) from LR-ardent QAHPS. Our approach is reminiscent of the seminal work of Cramer and Shoup (Eurocrypt’02), and employ three QAHPS schemes, one for generating a uniform string to hide the plaintext, and the other two for proving the well-formedness of the ciphertext. The LR-ardency of QAHPS makes possible the tight LR-CCA security. We give instantiations based on the standard k-Linear (k-LIN) assumptions over asymmetric and symmetric pairing groups, respectively, and obtain fully compact PKE with tight LR-CCA security. The security loss is $${{O}}(\log {Q_{{e}}})$$ where $${Q_{{e}}}$$ denotes the number of encryption queries. Specifically, our tightly LR-CCA secure PKE instantiation from SXDH has only 4 group elements in the public key and 7 group elements in the ciphertext, thus is the most efficient one.

2019

CRYPTO

Non-malleable Secret Sharing in the Computational Setting: Adaptive Tampering, Noisy-Leakage Resilience, and Improved Rate
📺 Abstract

We revisit the concept of non-malleable secret sharing (Goyal and Kumar, STOC 2018) in the computational setting. In particular, under the assumption of one-to-one one-way functions, we exhibit a computationally private, threshold secret sharing scheme satisfying all of the following properties.
Continuous non-malleability: No computationally-bounded adversary tampering independently with all the shares can produce mauled shares that reconstruct to a value related to the original secret. This holds even in case the adversary can tamper continuously, for an unbounded polynomial number of times, with the same target secret sharing, where the next sequence of tampering functions, as well as the subset of shares used for reconstruction, can be chosen adaptively based on the outcome of previous reconstructions.Resilience to noisy leakage: Non-malleability holds even if the adversary can additionally leak information independently from all the shares. There is no bound on the length of leaked information, as long as the overall leakage does not decrease the min-entropy of each share by too much.Improved rate: The information rate of our final scheme, defined as the ratio between the size of the message and the maximal size of a share, asymptotically approaches 1 when the message length goes to infinity.
Previous constructions achieved information-theoretic security, sometimes even for arbitrary access structures, at the price of at least one of the following limitations: (i) Non-malleability only holds against one-time tampering attacks; (ii) Non-malleability holds against a bounded number of tampering attacks, but both the choice of the tampering functions and of the sets used for reconstruction is non-adaptive; (iii) Information rate asymptotically approaching zero; (iv) No security guarantee in the presence of leakage.

2019

CRYPTO

Leakage Resilient Secret Sharing and Applications
📺 Abstract

A secret sharing scheme allows a dealer to share a secret among a set of n parties such that any authorized subset of the parties can recover the secret, while any unauthorized subset learns no information about the secret. A leakage-resilient secret sharing scheme (introduced in independent works by Goyal and Kumar, STOC ’18 and Benhamouda, Degwekar, Ishai and Rabin, CRYPTO ’18) additionally requires the secrecy to hold against every unauthorized set of parties even if they obtain some bounded leakage from every other share. The leakage is said to be local if it is computed independently for each share. So far, the only known constructions of local leakage resilient secret sharing schemes are for threshold access structures for very low (O(1)) or very high (
$$n -o(\log n)$$
) thresholds.In this work, we give a compiler that takes a secret sharing scheme for any monotone access structure and produces a local leakage resilient secret sharing scheme for the same access structure, with only a constant-factor asymptotic blow-up in the sizes of the shares. Furthermore, the resultant secret sharing scheme has optimal leakage-resilience rate, i.e., the ratio between the leakage tolerated and the size of each share can be made arbitrarily close to 1. Using this secret sharing scheme as the main building block, we obtain the following results:Rate Preserving Non-Malleable Secret Sharing. We give a compiler that takes any secret sharing scheme for a 4-monotone access structure (A 4-monotone access structure has the property that any authorized set has size at least 4.) with rate R and converts it into a non-malleable secret sharing scheme for the same access structure with rate
$$\varOmega (R)$$
. The previous such non-zero rate construction (Badrinarayanan and Srinivasan, EUROCRYPT ’19) achieved a rate of
$$\varTheta (R/{t_{\max }\log ^2 n})$$
, where
$$t_{\max }$$
is the maximum size of any minimal set in the access structure. As a special case, for any threshold
$$t \ge 4$$
and an arbitrary
$$n \ge t$$
, we get the first constant-rate construction of t-out-of-n non-malleable secret sharing.Leakage-Tolerant Multiparty Computation for General Interaction Patterns. For any function f, we give a reduction from constructing a leakage-tolerant secure multi-party computation protocol for computing f that obeys any given interaction pattern to constructing a secure (but not necessarily leakage-tolerant) protocol for a related function that obeys the star interaction pattern. Together with the known results for the star interaction pattern, this gives leakage tolerant MPC for any interaction pattern with statistical/computational security. This improves upon the result of (Halevi et al., ITCS 2016), who presented such a reduction in a leak-free environment.

2019

CRYPTO

Stronger Leakage-Resilient and Non-Malleable Secret Sharing Schemes for General Access Structures
📺 Abstract

In this work we present a collection of compilers that take secret sharing schemes for an arbitrary access structure as input and produce either leakage-resilient or non-malleable secret sharing schemes for the same access structure. A leakage-resilient secret sharing scheme hides the secret from an adversary, who has access to an unqualified set of shares, even if the adversary additionally obtains some size-bounded leakage from all other secret shares. A non-malleable secret sharing scheme guarantees that a secret that is reconstructed from a set of tampered shares is either equal to the original secret or completely unrelated. To the best of our knowledge we present the first generic compiler for leakage-resilient secret sharing for general access structures. In the case of non-malleable secret sharing, we strengthen previous definitions, provide separations between them, and construct a non-malleable secret sharing scheme for general access structures that fulfills the strongest definition with respect to independent share tampering functions. More precisely, our scheme is secure against concurrent tampering: The adversary is allowed to (non-adaptively) tamper the shares multiple times, and in each tampering attempt can freely choose the qualified set of shares to be used by the reconstruction algorithm to reconstruct the tampered secret. This is a strong analogue of the multiple-tampering setting for split-state non-malleable codes and extractors.We show how to use leakage-resilient and non-malleable secret sharing schemes to construct leakage-resilient and non-malleable threshold signatures. Classical threshold signatures allow to distribute the secret key of a signature scheme among a set of parties, such that certain qualified subsets can sign messages. We construct threshold signature schemes that remain secure even if an adversary leaks from or tampers with all secret shares.

2019

CRYPTO

Memory-Hard Functions from Cryptographic Primitives
📺 Abstract

Memory-hard functions (MHFs) are moderately-hard functions which enforce evaluation costs both in terms of time and memory (often, in form of a trade-off). They are used e.g. for password protection, password-based key-derivation, and within cryptocurrencies, and have received a considerable amount of theoretical scrutiny over the last few years. However, analyses see MHFs as modes of operation of some underlying hash function $$\mathcal {H}$$, modeled as a monolithic random oracle. This is however a very strong assumption, as such hash functions are built from much simpler primitives, following somewhat ad-hoc design paradigms.This paper initiates the study of how to securely instantiate $$\mathcal {H}$$ within MHF designs using common cryptographic primitives like block ciphers, compression functions, and permutations. Security here will be in a model in which the adversary has parallel access to an idealized version of the underlying primitive. We will provide provably memory-hard constructions from all the aforementioned primitives. Our results are generic, in that we will rely on hard-to-pebble graphs designed in prior works to obtain our constructions.One particular challenge we encounter is that $$\mathcal {H}$$ is usually required to have large outputs (to increase memory hardness without changing the description size of MHFs), whereas the underlying primitives generally have small output sizes.

2019

CRYPTO

Data-Independent Memory Hard Functions: New Attacks and Stronger Constructions
📺 Abstract

Memory-hard functions (MHFs) are a key cryptographic primitive underlying the design of moderately expensive password hashing algorithms and egalitarian proofs of work. Over the past few years several increasingly stringent goals for an MHF have been proposed including the requirement that the MHF have high sequential space-time (ST) complexity, parallel space-time complexity, amortized area-time (aAT) complexity and sustained space complexity. Data-Independent Memory Hard Functions (iMHFs) are of special interest in the context of password hashing as they naturally resist side-channel attacks. iMHFs can be specified using a directed acyclic graph (DAG) G with
$$N=2^n$$
nodes and low indegree and the complexity of the iMHF can be analyzed using a pebbling game. Recently, Alwen et al. [ABH17] constructed a DAG called DRSample that has aAT complexity at least
$$\varOmega \!\left( N^2/{\text {log}} N\right) $$
. Asymptotically DRSample outperformed all prior iMHF constructions including Argon2i, winner of the password hashing competition (aAT cost
$${\mathcal {O}} \!\left( N^{1.767}\right) $$
), though the constants in these bounds are poorly understood. We show that the greedy pebbling strategy of Boneh et al. [BCS16] is particularly effective against DRSample e.g., the aAT cost is
$${\mathcal {O}} (N^2/{\text {log}} N)$$
. In fact, our empirical analysis reverses the prior conclusion of Alwen et al. that DRSample provides stronger resistance to known pebbling attacks for practical values of
$$N \le 2^{24}$$
. We construct a new iMHF candidate (DRSample+BRG) by using the bit-reversal graph to extend DRSample. We then prove that the construction is asymptotically optimal under every MHF criteria, and we empirically demonstrate that our iMHF provides the best resistance to known pebbling attacks. For example, we show that any parallel pebbling attack either has aAT cost
$$\omega (N^2)$$
or requires at least
$$\varOmega (N)$$
steps with
$$\varOmega (N/{\text {log}} N)$$
pebbles on the DAG. This makes our construction the first practical iMHF with a strong sustained space-complexity guarantee and immediately implies that any parallel pebbling has aAT complexity
$$\varOmega (N^2/{\text {log}} N)$$
. We also prove that any sequential pebbling (including the greedy pebbling attack) has aAT cost
$$\varOmega \!\left( N^2\right) $$
and, if a plausible conjecture holds, any parallel pebbling has aAT cost
$$\varOmega (N^2 \log \log N/{\text {log}} N)$$
—the best possible bound for an iMHF. We implement our new iMHF and demonstrate that it is just as fast as Argon2. Along the way we propose a simple modification to the Argon2 round function that increases an attacker’s aAT cost by nearly an order of magnitude without increasing running time on a CPU. Finally, we give a pebbling reduction that proves that in the parallel random oracle model (PROM) the cost of evaluating an iMHF like Argon2i or DRSample+BRG is given by the pebbling cost of the underlying DAG. Prior pebbling reductions assumed that the iMHF round function concatenates input labels before hashing and did not apply to practical iMHFs such as Argon2i, DRSample or DRSample+BRG where input labels are instead XORed together.

2019

CRYPTO

Simultaneous Amplification: The Case of Non-interactive Zero-Knowledge
📺 Abstract

In this work, we explore the question of simultaneous privacy and soundness amplification for non-interactive zero-knowledge argument systems (NIZK). We show that any $$\delta _s-$$sound and $$\delta _z-$$zero-knowledge NIZK candidate satisfying $$\delta _s+\delta _z=1-\epsilon $$, for any constant $$\epsilon >0$$, can be turned into a computationally sound and zero-knowledge candidate with the only extra assumption of a subexponentially secure public-key encryption.We develop novel techniques to leverage the use of leakage simulation lemma (Jetchev-Peitzrak TCC 2014) to argue amplification. A crucial component of our result is a new notion for secret sharing $$\mathsf {NP}$$ instances. We believe that this may be of independent interest.To achieve this result we analyze following two transformations:Parallel Repetition: We show that using parallel repetition any $$\delta _s-$$sound and $$\delta _z-$$zero-knowledge $$\mathsf {NIZK}$$ candidate can be turned into (roughly) $$\delta ^n_s-$$sound and $$1-(1-\delta _{z})^n-$$zero-knowledge candidate. Here n is the repetition parameter.MPC based Repetition: We propose a new transformation that amplifies zero-knowledge in the same way that parallel repetition amplifies soundness. We show that using this any $$\delta _s-$$sound and $$\delta _z-$$zero-knowledge $$\mathsf {NIZK}$$ candidate can be turned into (roughly) $$1-(1-\delta _s)^n-$$sound and $$2\cdot \delta ^n_{z}-$$zero-knowledge candidate.
Then we show that using these transformations in a zig-zag fashion we can obtain our result. Finally, we also present a simple transformation which directly turns any $$\mathsf {NIZK}$$ candidate satisfying $$\delta _s,\delta _z<1/3 -1/\mathsf {poly}(\lambda )$$ to a secure one.

2019

CRYPTO

The Privacy Blanket of the Shuffle Model
📺 Abstract

This work studies differential privacy in the context of the recently proposed shuffle model. Unlike in the local model, where the server collecting privatized data from users can track back an input to a specific user, in the shuffle model users submit their privatized inputs to a server anonymously. This setup yields a trust model which sits in between the classical curator and local models for differential privacy. The shuffle model is the core idea in the Encode, Shuffle, Analyze (ESA) model introduced by Bittau et al. (SOPS 2017). Recent work by Cheu et al. (EUROCRYPT 2019) analyzes the differential privacy properties of the shuffle model and shows that in some cases shuffled protocols provide strictly better accuracy than local protocols. Additionally, Erlingsson et al. (SODA 2019) provide a privacy amplification bound quantifying the level of curator differential privacy achieved by the shuffle model in terms of the local differential privacy of the randomizer used by each user.In this context, we make three contributions. First, we provide an optimal single message protocol for summation of real numbers in the shuffle model. Our protocol is very simple and has better accuracy and communication than the protocols for this same problem proposed by Cheu et al. Optimality of this protocol follows from our second contribution, a new lower bound for the accuracy of private protocols for summation of real numbers in the shuffle model. The third contribution is a new amplification bound for analyzing the privacy of protocols in the shuffle model in terms of the privacy provided by the corresponding local randomizer. Our amplification bound generalizes the results by Erlingsson et al. to a wider range of parameters, and provides a whole family of methods to analyze privacy amplification in the shuffle model.

2019

CRYPTO

Realizing Chosen Ciphertext Security Generically in Attribute-Based Encryption and Predicate Encryption
📺 Abstract

We provide generic and black box transformations from any chosen plaintext secure Attribute-Based Encryption (ABE) or One-sided Predicate Encryption system into a chosen ciphertext secure system. Our transformation requires only the IND-CPA security of the original ABE scheme coupled with a pseudorandom generator (PRG) with a special security property.In particular, we consider a PRG with an n bit input $$s \in \{0,1\}^n$$ and $$n \cdot \ell $$ bit output $$y_1, \ldots , y_n$$ where each $$y_i$$ is an $$\ell $$ bit string. Then for a randomly chosen s the following two distributions should be computationally indistinguishable. In the first distribution $$r_{s_i, i} = y_i$$ and $$r_{\bar{s}_i, i}$$ is chosen randomly for $$i \in [n]$$. In the second distribution all $$r_{b, i}$$ are chosen randomly for $$i \in [n], b \in \{0,1\}$$.We show that such PRGs can be built from either the computational Diffie-Hellman assumption (in non-bilinear groups) or the Learning with Errors (LWE) assumption (and potentially other assumptions). Thus, one can transform any IND-CPA secure system into a chosen ciphertext secure one by adding either assumption. (Or by simply assuming an existing PRG is hinting secure.) In addition, our work provides a new approach and perspective for obtaining chosen ciphertext security in the basic case of public key encryption.

2019

CRYPTO

Match Me if You Can: Matchmaking Encryption and Its Applications
📺 Abstract

We introduce a new form of encryption that we name matchmaking encryption (ME). Using ME, sender S and receiver R (each with its own attributes) can both specify policies the other party must satisfy in order for the message to be revealed. The main security guarantee is that of privacy-preserving policy matching: During decryption nothing is leaked beyond the fact that a match occurred/did not occur.ME opens up new ways of secretly communicating, and enables several new applications where both participants can specify fine-grained access policies to encrypted data. For instance, in social matchmaking, S can encrypt a file containing his/her personal details and specify a policy so that the file can be decrypted only by his/her ideal partner. On the other end, a receiver R will be able to decrypt the file only if S corresponds to his/her ideal partner defined through a policy.On the theoretical side, we define security for ME, as well as provide generic frameworks for constructing ME from functional encryption.These constructions need to face the technical challenge of simultaneously checking the policies chosen by S and R, to avoid any leakage.On the practical side, we construct an efficient identity-based scheme for equality policies, with provable security in the random oracle model under the standard BDH assumption. We implement and evaluate our scheme and provide experimental evidence that our construction is practical. We also apply identity-based ME to a concrete use case, in particular for creating an anonymous bulletin board over a Tor network.

2019

CRYPTO

ABE for DFA from k-Lin
📺 Abstract

We present the first attribute-based encryption (ABE) scheme for deterministic finite automaton (DFA) based on static assumptions in bilinear groups; this resolves an open problem posed by Waters (CRYPTO 2012). Our main construction achieves selective security against unbounded collusions under the standard k-linear assumption in prime-order bilinear groups, whereas previous constructions all rely on q-type assumptions.

2019

CRYPTO

Attribute Based Encryption (and more) for Nondeterministic Finite Automata from LWE
📺 Abstract

Constructing Attribute Based Encryption (ABE) [56] for uniform models of computation from standard assumptions, is an important problem, about which very little is known. The only known ABE schemes in this setting that (i) avoid reliance on multilinear maps or indistinguishability obfuscation, (ii) support unbounded length inputs and (iii) permit unbounded key requests to the adversary in the security game, are by Waters from Crypto, 2012 [57] and its variants. Waters provided the first ABE for Deterministic Finite Automata (DFA) satisfying the above properties, from a parametrized or “q-type” assumption over bilinear maps. Generalizing this construction to Nondeterministic Finite Automata (NFA) was left as an explicit open problem in the same work, and has seen no progress to date. Constructions from other assumptions such as more standard pairing based assumptions, or lattice based assumptions has also proved elusive.In this work, we construct the first symmetric key attribute based encryption scheme for nondeterministic finite automata (NFA) from the learning with errors (LWE) assumption. Our scheme supports unbounded length inputs as well as unbounded length machines. In more detail, secret keys in our construction are associated with an NFA M of unbounded length, ciphertexts are associated with a tuple $$(\mathbf {x}, m)$$ where $$\mathbf {x}$$ is a public attribute of unbounded length and m is a secret message bit, and decryption recovers m if and only if $$M(\mathbf {x})=1$$.Further, we leverage our ABE to achieve (restricted notions of) attribute hiding analogous to the circuit setting, obtaining the first predicate encryption and bounded key functional encryption schemes for NFA from LWE. We achieve machine hiding in the single/bounded key setting to obtain the first reusable garbled NFA from standard assumptions. In terms of lower bounds, we show that secret key functional encryption even for DFAs, with security against unbounded key requests implies indistinguishability obfuscation ($$\mathsf {iO}$$) for circuits; this suggests a barrier in achieving full fledged functional encryption for NFA.

2019

CRYPTO

The Distinction Between Fixed and Random Generators in Group-Based Assumptions
📺 Abstract

There is surprisingly little consensus on the precise role of the generator g in group-based assumptions such as DDH. Some works consider g to be a fixed part of the group description, while others take it to be random. We study this subtle distinction from a number of angles.
In the generic group model, we demonstrate the plausibility of groups in which random-generator DDH (resp. CDH) is hard but fixed-generator DDH (resp. CDH) is easy. We observe that such groups have interesting cryptographic applications.We find that seemingly tight generic lower bounds for the Discrete-Log and CDH problems with preprocessing (Corrigan-Gibbs and Kogan, Eurocrypt 2018) are not tight in the sub-constant success probability regime if the generator is random. We resolve this by proving tight lower bounds for the random generator variants; our results formalize the intuition that using a random generator will reduce the effectiveness of preprocessing attacks.We observe that DDH-like assumptions in which exponents are drawn from low-entropy distributions are particularly sensitive to the fixed- vs. random-generator distinction. Most notably, we discover that the Strong Power DDH assumption of Komargodski and Yogev (Komargodski and Yogev, Eurocrypt 2018) used for non-malleable point obfuscation is in fact false precisely because it requires a fixed generator. In response, we formulate an alternative fixed-generator assumption that suffices for a new construction of non-malleable point obfuscation, and we prove the assumption holds in the generic group model. We also give a generic group proof for the security of fixed-generator, low-entropy DDH (Canetti, Crypto 1997).

2019

CRYPTO

Unifying Computational Entropies via Kullback–Leibler Divergence
📺 Abstract

We introduce hardness in relative entropy, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible entropy, two forms of computational entropy used in recent constructions of pseudorandom generators and statistically hiding commitment schemes, respectively. Thus, hardness in relative entropy unifies the latter two notions of computational entropy and sheds light on the apparent “duality” between them. Additionally, it yields a more modular and illuminating proof that one-way functions imply next-block inaccessible entropy, similar in structure to the proof that one-way functions imply next-block pseudoentropy (Vadhan and Zheng, STOC ‘12).

2019

CRYPTO

Trapdoor Hash Functions and Their Applications
📺 Abstract

We introduce a new primitive, called trapdoor hash functions (TDH), which are hash functions $$\mathsf {H}: \{0,1\}^n \rightarrow \{0,1\}^\lambda $$ with additional trapdoor function-like properties. Specifically, given an index $$i\in [n]$$, TDHs allow for sampling an encoding key $$\mathsf {ek}$$ (that hides i) along with a corresponding trapdoor. Furthermore, given $$\mathsf {H}(x)$$, a hint value $$\mathsf {E}(\mathsf {ek},x)$$, and the trapdoor corresponding to $$\mathsf {ek}$$, the $$i^{th}$$ bit of x can be efficiently recovered. In this setting, one of our main questions is: How small can the hint value $$\mathsf {E}(\mathsf {ek},x)$$ be? We obtain constructions where the hint is only one bit long based on DDH, QR, DCR, or LWE.This primitive opens a floodgate of applications for low-communication secure computation. We mainly focus on two-message protocols between a receiver and a sender, with private inputs x and y, resp., where the receiver should learn f(x, y). We wish to optimize the (download) rate of such protocols, namely the asymptotic ratio between the size of the output and the sender’s message. Using TDHs, we obtain:1.The first protocols for (two-message) rate-1 string OT based on DDH, QR, or LWE. This has several useful consequences, such as:(a)The first constructions of PIR with communication cost poly-logarithmic in the database size based on DDH or QR. These protocols are in fact rate-1 when considering block PIR.(b)The first constructions of a semi-compact homomorphic encryption scheme for branching programs, where the encrypted output grows only with the program length, based on DDH or QR.(c)The first constructions of lossy trapdoor functions with input to output ratio approaching 1 based on DDH, QR or LWE.(d)The first constant-rate LWE-based construction of a 2-message “statistically sender-private” OT protocol in the plain model.2.The first rate-1 protocols (under any assumption) for n parallel OTs and matrix-vector products from DDH, QR or LWE.
We further consider the setting where f evaluates a RAM program y with running time $$T\ll |x|$$ on x. We obtain the first protocols with communication sublinear in the size of x, namely $$T\cdot \sqrt{|x|}$$ or $$T\cdot \root 3 \of {|x|}$$, based on DDH or, resp., pairings (and correlated-input secure hash functions).

2019

CRYPTO

CCA Security and Trapdoor Functions via Key-Dependent-Message Security
📺 Abstract

We study the relationship among public-key encryption (PKE) satisfying indistinguishability against chosen plaintext attacks (IND-CPA security), that against chosen ciphertext attacks (IND-CCA security), and trapdoor functions (TDF). Specifically, we aim at finding a unified approach and some additional requirement to realize IND-CCA secure PKE and TDF based on IND-CPA secure PKE, and show the following two main results.As the first main result, we show how to achieve IND-CCA security via a weak form of key-dependent-message (KDM) security. More specifically, we construct an IND-CCA secure PKE scheme based on an IND-CPA secure PKE scheme and a secret-key encryption (SKE) scheme satisfying one-time KDM security with respect to projection functions (projection-KDM security). Projection functions are very simple functions with respect to which KDM security has been widely studied. Since the existence of projection-KDM secure PKE implies that of the above two building blocks, as a corollary of this result, we see that the existence of IND-CCA secure PKE is implied by that of projection-KDM secure PKE.As the second main result, we extend the above construction of IND-CCA secure PKE into that of TDF by additionally requiring a mild requirement for each building block. Our TDF satisfies adaptive one-wayness. We can instantiate our TDF based on a wide variety of computational assumptions. Especially, we obtain the first TDF (with adaptive one-wayness) based on the sub-exponential hardness of the constant-noise learning-parity-with-noise (LPN) problem.

2019

CRYPTO

Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs
📺 Abstract

We introduce and study the notion of fully linear probabilistically checkable proof systems. In such a proof system, the verifier can make a small number of linear queries that apply jointly to the input and a proof vector.Our new type of proof system is motivated by applications in which the input statement is not fully available to any single verifier, but can still be efficiently accessed via linear queries. This situation arises in scenarios where the input is partitioned or secret-shared between two or more parties, or alternatively is encoded using an additively homomorphic encryption or commitment scheme. This setting appears in the context of secure messaging platforms, verifiable outsourced computation, PIR writing, private computation of aggregate statistics, and secure multiparty computation (MPC). In all these applications, there is a need for fully linear proof systems with short proofs.While several efficient constructions of fully linear proof systems are implicit in the interactive proofs literature, many questions about their complexity are open. We present several new constructions of fully linear zero-knowledge proof systems with sublinear proof size for “simple” or “structured” languages. For example, in the non-interactive setting of fully linear PCPs, we show how to prove that an input vector $$x\in {\mathbb {F}}^n$$, for a finite field $${\mathbb {F}}$$, satisfies a single degree-2 equation with a proof of size $$O(\sqrt{n})$$ and $$O(\sqrt{n})$$ linear queries, which we show to be optimal. More generally, for languages that can be recognized by systems of constant-degree equations, we can reduce the proof size to $$O(\log n)$$ at the cost of $$O(\log n)$$ rounds of interaction.We use our new proof systems to construct new short zero-knowledge proofs on distributed and secret-shared data. These proofs can be used to improve the performance of the example systems mentioned above.Finally, we observe that zero-knowledge proofs on distributed data provide a general-purpose tool for protecting MPC protocols against malicious parties. Applying our short fully linear PCPs to “natural” MPC protocols in the honest-majority setting, we can achieve unconditional protection against malicious parties with sublinear additive communication cost. We use this to improve the communication complexity of recent honest-majority MPC protocols. For instance, using any pseudorandom generator, we obtain a 3-party protocol for Boolean circuits in which the amortized communication cost is only one bit per AND gate per party (compared to 10 bits in the best previous protocol), matching the best known protocols for semi-honest parties.

2019

CRYPTO

Non-Uniformly Sound Certificates with Applications to Concurrent Zero-Knowledge
📺 Abstract

We introduce the notion of non-uniformly sound certificates: succinct single-message (unidirectional) argument systems that satisfy a “best-possible security” against non-uniform polynomial-time attackers. In particular, no polynomial-time attacker with s bits of non-uniform advice can find significantly more than s accepting proofs for false statements. Our first result is a construction of non-uniformly sound certificates for all $$\mathbf{NP }$$ in the random oracle model, where the attacker’s advice can depend arbitrarily on the random oracle.We next show that the existence of non-uniformly sound certificates for $$\mathbf{P }$$ (and collision resistant hash functions) yields a public-coin constant-round fully concurrent zero-knowledge argument for $$\mathbf{NP } $$.

2019

CRYPTO

On Round Optimal Statistical Zero Knowledge Arguments
📺 Abstract

We construct the first three message statistical zero knowledge arguments for all of NP, matching the known lower bound. We do so based on keyless multi-collision resistant hash functions and the Learning with Errors assumption—the same assumptions used to obtain round optimal computational zero knowledge.The main component in our construction is a statistically witness indistinguishable argument of knowledge based on a new notion of statistically hiding commitments with subset opening.

2019

CRYPTO

It Wasn’t Me!
📺 Abstract

Ring signatures, introduced by [RST01], are a variant of digital signatures which certify that one among a particular set of parties has endorsed a message while hiding which party in the set was the signer. Ring signatures are designed to allow anyone to attach anyone else’s name to a signature, as long as the signer’s own name is also attached. But what guarantee do ring signatures provide if a purported signatory wishes to denounce a signed message—or alternatively, if a signatory wishes to later come forward and claim ownership of a signature? Prior security definitions for ring signatures do not give a conclusive answer to this question: under most existing definitions, the guarantees could go either way. That is, it is consistent with some standard definitions that a non-signer might be able to repudiate a signature that he did not produce, or that this might be impossible. Similarly, a signer might be able to later convincingly claim that a signature he produced is indeed his own, or not. Any of these guarantees might be desirable. For instance, a whistleblower might have reason to want to later claim an anonymously released signature, or a person falsely implicated in a crime associated with a ring signature might wish to denounce the signature that is framing them and damaging their reputation. In other circumstances, it might be desirable that even under duress, a member of a ring cannot produce proof that he did or did not sign a particular signature. In any case, a guarantee one way or the other seems highly desirable.In this work, we formalize definitions and give constructions of the new notions of repudiable, unrepudiable, claimable, and unclaimable ring signatures. Our repudiable construction is based on VRFs, which are implied by several number-theoretic assumptions (including strong RSA or bilinear maps); our claimable construction is a black-box transformation from any standard ring signature scheme to a claimable one; and our unclaimable construction is derived from the lattice-based ring signatures of [BK10], which rely on hardness of SIS. Our repudiable construction also provides a new construction of standard ring signatures.

2019

CRYPTO

Two-Party ECDSA from Hash Proof Systems and Efficient Instantiations
📺 Abstract

ECDSA is a widely adopted digital signature standard. Unfortunately, efficient distributed variants of this primitive are notoriously hard to achieve and known solutions often require expensive zero knowledge proofs to deal with malicious adversaries. For the two party case, Lindell [Lin17] recently managed to get an efficient solution which, to achieve simulation-based security, relies on an interactive, non standard, assumption on Paillier’s cryptosystem. In this paper we generalize Lindell’s solution using hash proof systems. The main advantage of our generic method is that it results in a simulation-based security proof without resorting to non-standard interactive assumptions.Moving to concrete constructions, we show how to instantiate our framework using class groups of imaginary quadratic fields. Our implementations show that the practical impact of dropping such interactive assumptions is minimal. Indeed, while for 128-bit security our scheme is marginally slower than Lindell’s, for 256-bit security it turns out to be better both in key generation and signing time. Moreover, in terms of communication cost, our implementation significantly reduces both the number of rounds and the transmitted bits without exception.

2019

CRYPTO

Asymmetric Message Franking: Content Moderation for Metadata-Private End-to-End Encryption
📺 Abstract

Content moderation is crucial for stopping abusive and harassing messages in online platforms. Existing moderation mechanisms, such as message franking, require platform providers to be able to associate user identifiers to encrypted messages. These mechanisms fail in metadata-private messaging systems, such as Signal, where users can hide their identities from platform providers. The key technical challenge preventing moderation is achieving cryptographic accountability while preserving deniability.In this work, we resolve this tension with a new cryptographic primitive: asymmetric message franking (AMF) schemes. We define strong security notions for AMF schemes, including the first formal treatment of deniability in moderation settings. We then construct, analyze, and implement an AMF scheme that is fast enough to use for content moderation of metadata-private messaging.

2019

CRYPTO

Statistical Zeroizing Attack: Cryptanalysis of Candidates of BP Obfuscation over GGH15 Multilinear Map
📺 Abstract

We present a new cryptanalytic algorithm on obfuscations based on GGH15 multilinear map. Our algorithm, statistical zeroizing attack, directly distinguishes two distributions from obfuscation while it follows the zeroizing attack paradigm, that is, it uses evaluations of zeros of obfuscated programs.Our attack breaks the recent indistinguishability obfuscation candidate suggested by Chen et al. (CRYPTO’18) for the optimal parameter settings. More precisely, we show that there are two functionally equivalent branching programs whose CVW obfuscations can be efficiently distinguished by computing the sample variance of evaluations.This statistical attack gives a new perspective on the security of the indistinguishability obfuscations: we should consider the shape of the distributions of evaluation of obfuscation to ensure security.In other words, while most of the previous (weak) security proofs have been studied with respect to algebraic attack model or ideal model, our attack shows that this algebraic security is not enough to achieve indistinguishability obfuscation. In particular, we show that the obfuscation scheme suggested by Bartusek et al. (TCC’18) does not achieve the desired security in a certain parameter regime, in which their algebraic security proof still holds.The correctness of statistical zeroizing attacks holds under a mild assumption on the preimage sampling algorithm with a lattice trapdoor. We experimentally verify this assumption for implemented obfuscation by Halevi et al. (ACM CCS’17).

2019

CRYPTO

Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification
📺 Abstract

The existence of secure indistinguishability obfuscators (
$$i\mathcal {O}$$
) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to constructing
$$i\mathcal {O}$$
rely on d-linear maps. While secure bilinear maps are well established in cryptographic literature, the security of candidates for
$$d>2$$
is poorly understood.We propose a new approach to constructing
$$i\mathcal {O}$$
for general circuits. Unlike all previously known realizations of
$$i\mathcal {O}$$
, we avoid the use of d-linear maps of degree
$$d \ge 3$$
.At the heart of our approach is the assumption that a new weak pseudorandom object exists. We consider two related variants of these objects, which we call perturbation resilient generator (
$$\varDelta $$
RG) and pseudo flawed-smudging generator (
$$\mathrm {PFG}$$
), respectively. At a high level, both objects are polynomially expanding functions whose outputs partially hide (or smudge) small noise vectors when added to them. We further require that they are computable by a family of degree-3 polynomials over
$$\mathbb {Z}$$
. We show how they can be used to construct functional encryption schemes with weak security guarantees. Finally, we use novel amplification techniques to obtain full security.As a result, we obtain
$$i\mathcal {O}$$
for general circuits assuming:Subexponentially secure LWEBilinear Maps
$$\mathrm {poly}(\lambda )$$
-secure 3-block-local PRGs
$$\varDelta $$
RGs or
$$\mathrm {PFG}$$
s

2019

CRYPTO

Watermarking PRFs from Lattices: Stronger Security via Extractable PRFs
📺 Abstract

A software watermarking scheme enables one to embed a “mark” (i.e., a message) within a program while preserving the program’s functionality. Moreover, there is an extraction algorithm that recovers an embedded message from a program. The main security goal is that it should be difficult to remove the watermark without destroying the functionality of the program. Existing constructions of watermarking focus on watermarking cryptographic functions like pseudorandom functions (PRFs); even in this setting, realizing watermarking from standard assumptions remains difficult. The first lattice-based construction of secret-key watermarking due to Kim and Wu (CRYPTO 2017) only ensures mark-unremovability against an adversary who does not have access to the mark-extraction oracle. The construction of Quach et al. (TCC 2018) achieves the stronger notion of mark-unremovability even if the adversary can make extraction queries, but has the drawback that the watermarking authority (who holds the watermarking secret key) can break pseudorandomness of all PRF keys in the family (including unmarked keys).In this work, we construct new lattice-based secret-key watermarking schemes for PRFs that both provide unremovability against adversaries that have access to the mark-extraction oracle and offer a strong and meaningful notion of pseudorandomness even against the watermarking authority (i.e., the outputs of unmarked keys are pseudorandom almost everywhere). Moreover, security of several of our schemes can be based on the hardness of computing nearly polynomial approximations to worst-case lattice problems. This is a qualitatively weaker assumption than that needed for existing lattice-based constructions of watermarking (that support message-embedding), all of which require quasi-polynomial approximation factors. Our constructions rely on a new cryptographic primitive called an extractable PRF, which may be of independent interest.

2019

CRYPTO

Watermarking Public-Key Cryptographic Primitives
📺 Abstract

A software watermarking scheme enables users to embed a message or mark within a program while preserving its functionality. Moreover, it is difficult for an adversary to remove a watermark from a marked program without corrupting its behavior. Existing constructions of software watermarking from standard assumptions have focused exclusively on watermarking pseudorandom functions (PRFs).In this work, we study watermarking public-key primitives such as the signing key of a digital signature scheme or the decryption key of a public-key (predicate) encryption scheme. While watermarking public-key primitives might intuitively seem more challenging than watermarking PRFs, our constructions only rely on simple assumptions. Our watermarkable signature scheme can be built from the minimal assumption of one-way functions while our watermarkable public-key encryption scheme can be built from most standard algebraic assumptions that imply public-key encryption (e.g., factoring, discrete log, or lattice assumptions). Our schemes also satisfy a number of appealing properties: public marking, public mark-extraction, and collusion resistance. Our schemes are the first to simultaneously achieve all of these properties.The key enabler of our new constructions is a relaxed notion of functionality-preserving. While traditionally, we require that a marked program (approximately) preserve the input/output behavior of the original program, in the public-key setting, preserving the “functionality” does not necessarily require preserving the exact input/output behavior. For instance, if we want to mark a signing algorithm, it suffices that the marked algorithm still output valid signatures (even if those signatures might be different from the ones output by the unmarked algorithm). Similarly, if we want to mark a decryption algorithm, it suffices that the marked algorithm correctly decrypt all valid ciphertexts (but may behave differently from the unmarked algorithm on invalid or malformed ciphertexts). Our relaxed notion of functionality-preserving captures the essence of watermarking and still supports the traditional applications, but provides additional flexibility to enable new and simple realizations of this powerful cryptographic notion.

2019

CRYPTO

SpOT-Light: Lightweight Private Set Intersection from Sparse OT Extension
📺 Abstract

We describe a novel approach for two-party private set intersection (PSI) with semi-honest security. Compared to existing PSI protocols, ours has a more favorable balance between communication and computation. Specifically, our protocol has the lowest monetary cost of any known PSI protocol, when run over the Internet using cloud-based computing services (taking into account current rates for CPU + data). On slow networks (e.g., 10 Mbps) our protocol is actually the fastest.Our novel underlying technique is a variant of oblivious transfer (OT) extension that we call sparse OT extension. Conceptually it can be thought of as a communication-efficient multipoint oblivious PRF evaluation. Our sparse OT technique relies heavily on manipulating high-degree polynomials over large finite fields (i.e. elements whose representation requires hundreds of bits). We introduce extensive algorithmic and engineering improvements for interpolation and multi-point evaluation of such polynomials, which we believe will be of independent interest.Finally, we present an extensive empirical comparison of state-of-the-art PSI protocols in several application scenarios and along several dimensions of measurement: running time, communication, peak memory consumption, and—arguably the most relevant metric for practice—monetary cost.

2019

CRYPTO

Universally Composable Secure Computation with Corrupted Tokens
📺 Abstract

We introduce the corrupted token model. This model generalizes the tamper-proof token model proposed by Katz (EUROCRYPT ’07) relaxing the trust assumption on the honest behavior of tokens. Our model is motivated by the real-world practice of outsourcing hardware production to possibly corrupted manufacturers. We capture the malicious behavior of token manufacturers by allowing the adversary to corrupt the tokens of honest players at the time of their creation.We show that under minimal complexity assumptions, i.e., the existence of one-way functions, it is possible to UC-securely realize (a variant of) the tamper-proof token functionality of Katz in the corrupted token model with n stateless tokens assuming that the adversary corrupts at most $$n-1$$ of them (for any $$n>0$$). We apply this result to existing multi-party protocols in Katz’s model to achieve UC-secure MPC in the corrupted token model assuming only the existence of one-way functions. Finally, we show how to obtain the above results using tokens of small size that take only short inputs. The technique in this result can also be used to improve the assumption of UC-secure hardware obfuscation recently proposed by Nayak et al. (NDSS ’17). While their construction requires the existence of collision-resistant hash functions, we can obtain the same result from only one-way functions. Moreover using our main result we can improve the trust assumption on the tokens as well.

2019

CRYPTO

Reusable Non-Interactive Secure Computation
📺 Abstract

We consider the problem of Non-Interactive Two-Party Secure Computation (NISC), where Rachel wishes to publish an encryption of her input x, in such a way that any other party, who holds an input y, can send her a single message which conveys to her the value f(x, y), and nothing more. We demand security against malicious parties. While such protocols are easy to construct using garbled circuits and general non-interactive zero-knowledge proofs, this approach inherently makes a non-black-box use of the underlying cryptographic primitives and is infeasible in practice.Ishai et al. (Eurocrypt 2011) showed how to construct NISC protocols that only use parallel calls to an ideal oblivious transfer (OT) oracle, and additionally make only a black-box use of any pseudorandom generator. Combined with the efficient 2-message OT protocol of Peikert et al. (Crypto 2008), this leads to a practical approach to NISC that has been implemented in subsequent works. However, a major limitation of all known OT-based NISC protocols is that they are subject to selective failure attacks that allows a malicious sender to entirely compromise the security of the protocol when the receiver’s first message is reused.Motivated by the failure of the OT-based approach, we consider the problem of basing reusable NISC on parallel invocations of a standard arithmetic generalization of OT known as oblivious linear-function evaluation (OLE). We obtain the following results:We construct an information-theoretically secure reusable NISC protocol for arithmetic branching programs and general zero-knowledge functionalities in the OLE-hybrid model. Our zero-knowledge protocol only makes an absolute constant number of OLE calls per gate in an arithmetic circuit whose satisfiability is being proved. We also get reusable NISC in the OLE-hybrid model for general Boolean circuits using any one-way function.We complement this by a negative result, showing that reusable NISC is impossible to achieve in the OT-hybrid model. This provides a formal justification for the need to replace OT by OLE.We build a universally composable 2-message reusable OLE protocol in the CRS model that can be based on the security of Paillier encryption and requires only a constant number of modular exponentiations. This provides the first arithmetic analogue of the 2-message OT protocols of Peikert et al. (Crypto 2008).By combining our NISC protocol in the OLE-hybrid model and the 2-message OLE protocol, we get protocols with new attractive asymptotic and concrete efficiency features. In particular, we get the first (designated-verifier) NIZK protocols for NP where following a statement-independent preprocessing, both proving and verifying are entirely “non-cryptographic” and involve only a constant computational overhead. Furthermore, we get the first statistical designated-verifier NIZK argument for NP under an assumption related to factoring.

2019

CRYPTO

Efficient Pseudorandom Correlation Generators: Silent OT Extension and More
📺 Abstract

Secure multiparty computation (MPC) often relies on correlated randomness for better efficiency and simplicity. This is particularly useful for MPC with no honest majority, where input-independent correlated randomness enables a lightweight “non-cryptographic” online phase once the inputs are known. However, since the amount of randomness typically scales with the circuit size of the function being computed, securely generating correlated randomness forms an efficiency bottleneck, involving a large amount of communication and storage.A natural tool for addressing the above limitations is a pseudorandom correlation generator (PCG). A PCG allows two or more parties to securely generate long sources of useful correlated randomness via a local expansion of correlated short seeds and no interaction. PCGs enable MPC with silent preprocessing, where a small amount of interaction used for securely sampling the seeds is followed by silent local generation of correlated pseudorandomness.A concretely efficient PCG for Vector-OLE correlations was recently obtained by Boyle et al. (CCS 2018) based on variants of the learning parity with noise (LPN) assumption over large fields. In this work, we initiate a systematic study of PCGs and present concretely efficient constructions for several types of useful MPC correlations. We obtain the following main contributions:PCG foundations. We give a general security definition for PCGs. Our definition suffices for any MPC protocol satisfying a stronger security requirement that is met by existing protocols. We prove that a stronger security requirement is indeed necessary, and justify our PCG definition by ruling out a stronger and more natural definition.Silent OT extension. We present the first concretely efficient PCG for oblivious transfer correlations. Its security is based on a variant of the binary LPN assumption and any correlation-robust hash function. We expect it to provide a faster alternative to the IKNP OT extension protocol (Crypto 2003) when communication is the bottleneck. We present several applications, including protocols for non-interactive zero-knowledge with bounded-reusable preprocessing from binary LPN, and concretely efficient related-key oblivious pseudorandom functions.PCGs for simple 2-party correlations. We obtain PCGs for several other types of useful 2-party correlations, including (authenticated) one-time truth-tables and Beaver triples. While the latter PCGs are slower than our PCG for OT, they are still practically feasible. These PCGs are based on a host of assumptions and techniques, including specialized homomorphic secret sharing schemes and pseudorandom generators tailored to their structure.Multiparty correlations. We obtain PCGs for multiparty correlations that can be used to make the (input-dependent) online communication of MPC protocols scale linearly with the number of parties, instead of quadratically.

2019

CRYPTO

Non-interactive Non-malleability from Quantum Supremacy
📺 Abstract

We construct non-interactive non-malleable commitments without setup in the plain model, under well-studied assumptions.First, we construct non-interactive non-malleable commitments w.r.t. commitment for $$\epsilon \log \log n$$ tags for a small constant $$\epsilon > 0$$, under the following assumptions:1.Sub-exponential hardness of factoring or discrete log.2.Quantum sub-exponential hardness of learning with errors (LWE).
Second, as our key technical contribution, we introduce a new tag amplification technique. We show how to convert any non-interactive non-malleable commitment w.r.t. commitment for $$\epsilon \log \log n$$ tags (for any constant $$\epsilon >0$$) into a non-interactive non-malleable commitment w.r.t. replacement for $$2^n$$ tags. This part only assumes the existence of sub-exponentially secure non-interactive witness indistinguishable (NIWI) proofs, which can be based on sub-exponential security of the decisional linear assumption.Interestingly, for the tag amplification technique, we crucially rely on the leakage lemma due to Gentry and Wichs (STOC 2011). For the construction of non-malleable commitments for $$\epsilon \log \log n$$ tags, we rely on quantum supremacy. This use of quantum supremacy in classical cryptography is novel, and we believe it will have future applications. We provide one such application to two-message witness indistinguishable (WI) arguments from (quantum) polynomial hardness assumptions.

2019

CRYPTO

Cryptographic Sensing
📺 Abstract

Is it possible to measure a physical object in a way that makes the measurement signals unintelligible to an external observer? Alternatively, can one learn a natural concept by using a contrived training set that makes the labeled examples useless without the line of thought that has led to their choice? We initiate a study of “cryptographic sensing” problems of this type, presenting definitions, positive and negative results, and directions for further research.

2019

CRYPTO

Public-Key Cryptography in the Fine-Grained Setting
📺 Abstract

Cryptography is largely based on unproven assumptions, which, while believable, might fail. Notably if $$P = NP$$, or if we live in Pessiland, then all current cryptographic assumptions will be broken. A compelling question is if any interesting cryptography might exist in Pessiland.A natural approach to tackle this question is to base cryptography on an assumption from fine-grained complexity. Ball, Rosen, Sabin, and Vasudevan [BRSV’17] attempted this, starting from popular hardness assumptions, such as the Orthogonal Vectors (OV) Conjecture. They obtained problems that are hard on average, assuming that OV and other problems are hard in the worst case. They obtained proofs of work, and hoped to use their average-case hard problems to build a fine-grained one-way function. Unfortunately, they proved that constructing one using their approach would violate a popular hardness hypothesis. This motivates the search for other fine-grained average-case hard problems.The main goal of this paper is to identify sufficient properties for a fine-grained average-case assumption that imply cryptographic primitives such as fine-grained public key cryptography (PKC). Our main contribution is a novel construction of a cryptographic key exchange, together with the definition of a small number of relatively weak structural properties, such that if a computational problem satisfies them, our key exchange has provable fine-grained security guarantees, based on the hardness of this problem. We then show that a natural and plausible average-case assumption for the key problem Zero-k-Clique from fine-grained complexity satisfies our properties. We also develop fine-grained one-way functions and hardcore bits even under these weaker assumptions.Where previous works had to assume random oracles or the existence of strong one-way functions to get a key-exchange computable in O(n) time secure against $$O(n^2)$$ adversaries (see [Merkle’78] and [BGI’08]), our assumptions seem much weaker. Our key exchange has a similar gap between the computation of the honest party and the adversary as prior work, while being non-interactive, implying fine-grained PKC.

2019

CRYPTO

Exploring Constructions of Compact NIZKs from Various Assumptions
📺 Abstract

A non-interactive zero-knowledge (NIZK) protocol allows a prover to non-interactively convince a verifier of the truth of the statement without leaking any other information. In this study, we explore shorter NIZK proofs for all $$\mathbf{NP }$$ languages. Our primary interest is NIZK proofs from falsifiable pairing/pairing-free group-based assumptions. Thus far, NIZKs in the common reference string model (CRS-NIZKs) for $$\mathbf{NP }$$ based on falsifiable pairing-based assumptions all require a proof size at least as large as $$O(|C| \kappa )$$, where C is a circuit computing the $$\mathbf{NP }$$ relation and $$\kappa $$ is the security parameter. This holds true even for the weaker designated-verifier NIZKs (DV-NIZKs). Notably, constructing a (CRS, DV)-NIZK with proof size achieving an additive-overhead $$O(|C|) + \mathsf {poly}(\kappa )$$, rather than a multiplicative-overhead $$|C| \cdot \mathsf {poly}(\kappa )$$, based on any falsifiable pairing-based assumptions is an open problem.In this work, we present various techniques for constructing NIZKs with compact proofs, i.e., proofs smaller than $$O(|C|) + \mathsf {poly}(\kappa )$$, and make progress regarding the above situation. Our result is summarized below.
We construct CRS-NIZK for all $$\mathbf{NP }$$ with proof size $$|C| +\mathsf {poly}(\kappa )$$ from a (non-static) falsifiable Diffie-Hellman (DH) type assumption over pairing groups. This is the first CRS-NIZK to achieve a compact proof without relying on either lattice-based assumptions or non-falsifiable assumptions. Moreover, a variant of our CRS-NIZK satisfies universal composability (UC) in the erasure-free adaptive setting. Although it is limited to $$\mathbf{NP }$$ relations in $$\mathbf{NC }^1$$, the proof size is $$|w| \cdot \mathsf {poly}(\kappa )$$ where w is the witness, and in particular, it matches the state-of-the-art UC-NIZK proposed by Cohen, shelat, and Wichs (CRYPTO’19) based on lattices.We construct (multi-theorem) DV-NIZKs for $$\mathbf{NP }$$ with proof size $$|C|+\mathsf {poly}(\kappa )$$ from the computational DH assumption over pairing-free groups. This is the first DV-NIZK that achieves a compact proof from a standard DH type assumption. Moreover, if we further assume the $$\mathbf{NP }$$ relation to be computable in $$\mathbf{NC }^1$$ and assume hardness of a (non-static) falsifiable DH type assumption over pairing-free groups, the proof size can be made as small as $$|w| + \mathsf {poly}(\kappa )$$.
Another related but independent issue is that all (CRS, DV)-NIZKs require the running time of the prover to be at least $$|C|\cdot \mathsf {poly}(\kappa )$$. Considering that there exists NIZKs with efficient verifiers whose running time is strictly smaller than |C|, it is an interesting problem whether we can construct prover-efficient NIZKs. To this end, we construct prover-efficient CRS-NIZKs for $$\mathbf{NP }$$ with compact proof through a generic construction using laconic functional evaluation schemes (Quach, Wee, and Wichs (FOCS’18)). This is the first NIZK in any model where the running time of the prover is strictly smaller than the time it takes to compute the circuit C computing the $$\mathbf{NP }$$ relation.Finally, perhaps of an independent interest, we formalize the notion of homomorphic equivocal commitments, which we use as building blocks to obtain the first result, and show how to construct them from pairing-based assumptions.

2019

CRYPTO

New Constructions of Reusable Designated-Verifier NIZKs
📺 Abstract

Non-interactive zero-knowledge arguments (NIZKs) for $$\mathsf {NP}$$ are an important cryptographic primitive, but we currently only have instantiations under a few specific assumptions. Notably, we are missing constructions from the learning with errors (LWE) assumption, the Diffie-Hellman (CDH/DDH) assumption, and the learning parity with noise (LPN) assumption.In this paper, we study a relaxation of NIZKs to the designated-verifier setting (DV-NIZK), where a trusted setup generates a common reference string together with a secret key for the verifier. We want reusable schemes, which allow the verifier to reuse the secret key to verify many different proofs, and soundness should hold even if the malicious prover learns whether various proofs are accepted or rejected. Such reusable DV-NIZKs were recently constructed under the CDH assumption, but it was open whether they can also be constructed under LWE or LPN.We also consider an extension of reusable DV-NIZKs to the malicious designated-verifier setting (MDV-NIZK). In this setting, the only trusted setup consists of a common random string. However, there is also an additional untrusted setup in which the verifier chooses a public/secret key needed to generate/verify proofs, respectively. We require that zero-knowledge holds even if the public key is chosen maliciously by the verifier. Such reusable MDV-NIZKs were recently constructed under the “one-more CDH” assumption, but constructions under CDH/LWE/LPN remained open.In this work, we give new constructions of (reusable) DV-NIZKs and MDV-NIZKs using generic primitives that can be instantiated under CDH, LWE, or LPN.

2019

CRYPTO

Scalable Zero Knowledge with No Trusted Setup
📺 Abstract

One of the approaches to constructing zero knowledge (ZK) arguments relies on “PCP techniques” that date back to influential works from the early 1990’s [Babai et al., Arora et al. 1991-2]. These techniques require only minimal cryptographic assumptions, namely, the existence of a family of collision-resistant hash functions [Kilian, STOC 1992], and achieve two remarkable properties: (i) all messages generated by the verifier are public random coins, and (ii) total verification time is merely poly-logarithmic in the time needed to naïvely execute the computation being verified [Babai et al., STOC 1991].Those early constructions were never realized in code, mostly because proving time was too large. To address this, the model of interactive oracle proofs (IOPs), which generalizes the PCP model, was recently suggested. Proving time for ZK-IOPs was reduced to quasi-linear, even for problems that require nondeterministic exponential time to decide [Ben-Sasson et al., TCC 2016, ICALP 2017].Despite these recent advances it was still not clear whether ZK-IOP systems can lead to concretely efficient succinct argument systems. Our main claim is that this is indeed the case. We present a new construction of an IOP of knowledge (which we call a zk-STIK) that improves, asymptotically, on the state of art: for log-space computations of length T it is the first to $$O(T \log T)$$ arithmetic prover complexity and $$O(\log T)$$ verifier arithmetic complexity. Prior IOPs had additional $$\mathsf{poly} \log T$$ factors in both prover and verifier. Additionally, we report a C++ realization of this system (which we call libSTARK). Compared to prevailing ZK realizations, it has the fastest proving and (total) verification time for sufficiently large sequential computations.

2019

CRYPTO

Libra: Succinct Zero-Knowledge Proofs with Optimal Prover Computation
📺 Abstract

We present Libra, the first zero-knowledge proof system that has both optimal prover time and succinct proof size/verification time. In particular, if C is the size of the circuit being proved (i) the prover time is O(C) irrespective of the circuit type; (ii) the proof size and verification time are both $$O(d\log C)$$ for d-depth log-space uniform circuits (such as RAM programs). In addition Libra features an one-time trusted setup that depends only on the size of the input to the circuit and not on the circuit logic. Underlying Libra is a new linear-time algorithm for the prover of the interactive proof protocol by Goldwasser, Kalai and Rothblum (also known as GKR protocol), as well as an efficient approach to turn the GKR protocol to zero-knowledge using small masking polynomials. Not only does Libra have excellent asymptotics, but it is also efficient in practice. For example, our implementation shows that it takes 200 s to generate a proof for constructing a SHA2-based Merkle tree root on 256 leaves, outperforming all existing zero-knowledge proof systems. Proof size and verification time of Libra are also competitive.

2019

CRYPTO

Highly Efficient Key Exchange Protocols with Optimal Tightness
📺 Abstract

In this paper we give nearly-tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols, which are extremely simple and efficient. Unlike previous approaches, the combination of nearly-tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner.Our reductions have only a linear loss in the number of users, implying that our protocols are more efficient than the state of the art when instantiated with theoretically sound parameters. We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions.

2019

CRYPTO

Strong Asymmetric PAKE Based on Trapdoor CKEM
📺 Abstract

Password-Authenticated Key Exchange (PAKE) protocols allow two parties that share a password to establish a shared key in a way that is immune to offline attacks. Asymmetric PAKE (aPAKE) [20] adapts this notion to the common client-server setting, where the server stores a one-way hash of the password instead of the password itself, and server compromise allows the adversary to recover the password only via the (inevitable) offline dictionary attack. Most aPAKE protocols, however, allow an attacker to pre-compute a dictionary of hashed passwords, thus instantly learning the password on server compromise. Recently, Jarecki, Krawczyk, and Xu formalized a Universally Composable strong aPAKE (saPAKE) [23], which requires the password hash to be salted so that the dictionary attack can only start after the server compromise leaks the salt and the salted hash. The UC saPAKE protocol shown in [23], called OPAQUE, uses 3 protocol flows, 3–4 exponentiations per party, and relies on the One-More Diffie-Hellman assumption in ROM.We propose an alternative UC saPAKE construction based on a novel use of the encryption+SPHF paradigm for UC PAKE design [19, 26]. Compared to OPAQUE, our protocol uses only 2 flows, has comparable costs, avoids hashing onto a group, and relies on different assumptions, namely Decisional Diffie-Hellman (DDH), Strong Diffie-Hellman (SDH), and an assumption that the Boneh-Boyen function $$f_ s (x)=g^{1/( s +x)}$$ [9] is a Salted Tight One-Way Function (STOWF). We formalize a UC model for STOWF and analyze the Boneh-Boyen function as UC STOWF in the generic group model and ROM.Our saPAKE protocol employs a new form of Conditional Key Encapsulation Mechanism (CKEM), a generalization of SPHF, which we call an implicit-statement CKEM. This strengthening of SPHF allows for a UC (sa)PAKE design where only the client commits to its password, and only the server performs an SPHF, compared to the standard UC PAKE design paradigm where the encrypt+SPHF subroutine is used symmetrically by both parties.

2019

CRYPTO

Broadcast and Trace with
$N^{\varepsilon }$
Ciphertext Size from Standard Assumptions
📺 Abstract

We construct a broadcast and trace scheme (also known as trace and revoke or broadcast, trace and revoke) with N users, where the ciphertext size can be made as low as
$$O(N^\varepsilon )$$
, for any arbitrarily small constant
$$\varepsilon >0$$
. This improves on the prior best construction of broadcast and trace under standard assumptions by Boneh and Waters (CCS ‘06), which had ciphertext size
$$O(N^{1/2})$$
. While that construction relied on bilinear maps, ours uses a combination of the learning with errors (LWE) assumption and bilinear maps.Recall that, in both broadcast encryption and traitor-tracing schemes, there is a collection of N users, each of which gets a different secret key
$${\mathsf {sk}}_i$$
. In broadcast encryption, it is possible to create ciphertexts targeted to a subset
$$S \subseteq [N]$$
of the users such that only those users can decrypt it correctly. In a traitor tracing scheme, if a subset of users gets together and creates a decoder box D that is capable of decrypting ciphertexts, then it is possible to trace at least one of the users responsible for creating D. A broadcast and trace scheme intertwines the two properties, in a way that results in more than just their union. In particular, it ensures that if a decoder D is able to decrypt ciphertexts targeted toward a set S of users, then it should be possible to trace one of the users in the set S responsible for creating D, even if other users outside of S also participated. As of recently, we have essentially optimal broadcast encryption (Boneh, Gentry, Waters CRYPTO ’05) under bilinear maps and traitor tracing (Goyal, Koppula, Waters STOC ’18) under LWE, where the ciphertext size is at most poly-logarithmic in N. The main contribution of our paper is to carefully combine LWE and bilinear-map based components, and get them to interact with each other, to achieve broadcast and trace.

2019

EUROCRYPT

Lower Bounds for Differentially Private RAMs
📺 Abstract

In this work, we study privacy-preserving storage primitives that are suitable for use in data analysis on outsourced databases within the differential privacy framework. The goal in differentially private data analysis is to disclose global properties of a group without compromising any individual’s privacy. Typically, differentially private adversaries only ever learn global properties. For the case of outsourced databases, the adversary also views the patterns of access to data. Oblivious RAM (ORAM) can be used to hide access patterns but ORAM might be excessive as in some settings it could be sufficient to be compatible with differential privacy and only protect the privacy of individual accesses.We consider $$(\epsilon ,\delta )$$(ϵ,δ)-Differentially Private RAM, a weakening of ORAM that only protects individual operations and seems better suited for use in data analysis on outsourced databases. As differentially private RAM has weaker security than ORAM, there is hope that we can bypass the $$\varOmega (\log (nb/c))$$Ω(log(nb/c)) bandwidth lower bounds for ORAM by Larsen and Nielsen [CRYPTO ’18] for storing an array of nb-bit entries and a client with c bits of memory. We answer in the negative and present an $$\varOmega (\log (nb/c))$$Ω(log(nb/c)) bandwidth lower bound for privacy budgets of $$\epsilon = O(1)$$ϵ=O(1) and $$\delta \le 1/3$$δ≤1/3.The information transfer technique used for ORAM lower bounds does not seem adaptable for use with the weaker security guarantees of differential privacy. Instead, we prove our lower bounds by adapting the chronogram technique to our setting. To our knowledge, this is the first work that uses the chronogram technique for lower bounds on privacy-preserving storage primitives.

2019

EUROCRYPT

Beyond Birthday Bound Secure MAC in Faulty Nonce Model
📺 Abstract

Encrypt-then-MAC (EtM) is a popular mode for authenticated encryption (AE). Unfortunately, almost all designs following the EtM paradigm, including the AE suites for TLS, are vulnerable against nonce misuse. A single repetition of the nonce value reveals the hash key, leading to a universal forgery attack. There are only two authenticated encryption schemes following the EtM paradigm which can resist nonce misuse attacks, the GCM-RUP (CRYPTO-17) and the $$\mathsf {GCM/2}^{+} $$ (INSCRYPT-12). However, they are secure only up to the birthday bound in the nonce respecting setting, resulting in a restriction on the data limit for a single key. In this paper we show that nEHtM, a nonce-based variant of EHtM (FSE-10) constructed using a block cipher, has a beyond birthday bound (BBB) unforgeable security that gracefully degrades under nonce misuse. We combine nEHtM with the CENC (FSE-06) mode of encryption using the EtM paradigm to realize a nonce-based AE, CWC+. CWC+ is very close (requiring only a few more xor operations) to the CWC AE scheme (FSE-04) and it not only provides BBB security but also gracefully degrading security on nonce misuse.

2019

EUROCRYPT

Tight Time-Memory Trade-Offs for Symmetric Encryption
📺 Abstract

Concrete security proofs give upper bounds on the attacker’s advantage as a function of its time/query complexity. Cryptanalysis suggests however that other resource limitations – most notably, the attacker’s memory – could make the achievable advantage smaller, and thus these proven bounds too pessimistic. Yet, handling memory limitations has eluded existing security proofs.This paper initiates the study of time-memory trade-offs for basic symmetric cryptography. We show that schemes like counter-mode encryption, which are affected by the Birthday Bound, become more secure (in terms of time complexity) as the attacker’s memory is reduced.One key step of this work is a generalization of the Switching Lemma: For adversaries with S bits of memory issuing q distinct queries, we prove an n-to-n bit random function indistinguishable from a permutation as long as $$S \times q \ll 2^n$$S×q≪2n. This result assumes a combinatorial conjecture, which we discuss, and implies right away trade-offs for deterministic, stateful versions of CTR and OFB encryption.We also show an unconditional time-memory trade-off for the security of randomized CTR based on a secure PRF. Via the aforementioned conjecture, we extend the result to assuming a PRP instead, assuming only one-block messages are encrypted.Our results solely rely on standard PRF/PRP security of an underlying block cipher. We frame the core of our proofs within a general framework of indistinguishability for streaming algorithms which may be of independent interest.

2019

EUROCRYPT

Non-Malleable Codes Against Bounded Polynomial Time Tampering
📺 Abstract

We construct efficient non-malleable codes (NMC) that are (computationally) secure against tampering by functions computable in any fixed polynomial time. Our construction is in the plain (no-CRS) model and requires the assumptions that (1) $$\mathbf {E}$$E is hard for $$\mathbf {NP}$$NP circuits of some exponential $$2^{\beta n}$$2βn ($$\beta >0$$β>0) size (widely used in the derandomization literature), (2) sub-exponential trapdoor permutations exist, and (3) $$\mathbf {P}$$P-certificates with sub-exponential soundness exist.While it is impossible to construct NMC secure against arbitrary polynomial-time tampering (Dziembowski, Pietrzak, Wichs, ICS ’10), the existence of NMC secure against $$O(n^c)$$O(nc)-time tampering functions (for any fixedc), was shown (Cheraghchi and Guruswami, ITCS ’14) via a probabilistic construction. An explicit construction was given (Faust, Mukherjee, Venturi, Wichs, Eurocrypt ’14) assuming an untamperable CRS with length longer than the runtime of the tampering function. In this work, we show that under computational assumptions, we can bypass these limitations. Specifically, under the assumptions listed above, we obtain non-malleable codes in the plain model against $$O(n^c)$$O(nc)-time tampering functions (for any fixed c), with codeword length independent of the tampering time bound.Our new construction of NMC draws a connection with non-interactive non-malleable commitments. In fact, we show that in the NMC setting, it suffices to have a much weaker notion called quasi non-malleable commitments—these are non-interactive, non-malleable commitments in the plain model, in which the adversary runs in $$O(n^c)$$O(nc)-time, whereas the honest parties may run in longer (polynomial) time. We then construct a 4-tag quasi non-malleable commitment from any sub-exponential OWF and the assumption that $$\mathbf {E}$$E is hard for some exponential size $$\mathbf {NP}$$NP-circuits, and use tag amplification techniques to support an exponential number of tags.

2019

EUROCRYPT

Continuous Non-Malleable Codes in the 8-Split-State Model
📺 Abstract

Non-malleable codes (NMCs), introduced by Dziembowski, Pietrzak and Wichs [20], provide a useful message integrity guarantee in situations where traditional error-correction (and even error-detection) is impossible; for example, when the attacker can completely overwrite the encoded message. NMCs have emerged as a fundamental object at the intersection of coding theory and cryptography. In particular, progress in the study of non-malleable codes and the related notion of non-malleable extractors has led to new insights and progress on even more fundamental problems like the construction of multi-source randomness extractors. A large body of the recent work has focused on various constructions of non-malleable codes in the split-state model. Many variants of NMCs have been introduced in the literature, e.g., strong NMCs, super strong NMCs and continuous NMCs. The most general, and hence also the most useful notion among these is that of continuous non-malleable codes, that allows for continuous tampering by the adversary. We present the first efficient information-theoretically secure continuously non-malleable code in the constant split-state model. We believe that our main technical result could be of independent interest and some of the ideas could in future be used to make progress on other related questions.

2019

EUROCRYPT

Correlated-Source Extractors and Cryptography with Correlated-Random Tapes
📺 Abstract

In this paper, we consider the setting where a party uses correlated random tapes across multiple executions of a cryptographic algorithm. We ask if the security properties could still be preserved in such a setting. As examples, we introduce the notion of correlated-tape zero knowledge, and, correlated-tape multi-party computation, where, the zero-knowledge property, and, the ideal/real model security must still be preserved even if a party uses correlated random tapes in multiple executions.Our constructions are based on a new type of randomness extractor which we call correlated-source extractors. Correlated-source extractors can be seen as a dual of non-malleable extractors, and, allow an adversary to choose several tampering functions which are applied to the randomness source. Correlated-source extractors guarantee that even given the output of the extractor on the tampered sources, the output on the original source is still uniformly random. Given (seeded) correlated-source extractors, and, resettably-secure computation protocols, we show how to directly get a positive result for both correlated-tape zero-knowledge and correlated-tape multi-party computation in the CRS model. This is tight considering the known impossibility results on cryptography with imperfect randomness.Our main technical contribution is an explicit construction of a correlated-source extractor where the length of the seed is independent of the number of tamperings. Additionally, we also provide a (non-explicit) existential result for correlated source extractors with almost optimal parameters.

2019

EUROCRYPT

Revisiting Non-Malleable Secret Sharing
📺 Abstract

A threshold secret sharing scheme (with threshold t) allows a dealer to share a secret among a set of parties such that any group of t or more parties can recover the secret and no group of at most
$$t-1$$
t-1 parties learn any information about the secret. A non-malleable threshold secret sharing scheme, introduced in the recent work of Goyal and Kumar (STOC’18), additionally protects a threshold secret sharing scheme when its shares are subject to tampering attacks. Specifically, it guarantees that the reconstructed secret from the tampered shares is either the original secret or something that is unrelated to the original secret.In this work, we continue the study of threshold non-malleable secret sharing against the class of tampering functions that tamper each share independently. We focus on achieving greater efficiency and guaranteeing a stronger security property. We obtain the following results:Rate Improvement. We give the first construction of a threshold non-malleable secret sharing scheme that has rate
$$> 0$$
>0. Specifically, for every
$$n,t \ge 4$$
n,t≥4, we give a construction of a t-out-of-n non-malleable secret sharing scheme with rate
$$\varTheta (\frac{1}{t\log ^2 n})$$
Θ(1tlog2n). In the prior constructions, the rate was
$$\varTheta (\frac{1}{n\log m})$$
Θ(1nlogm) where m is the length of the secret and thus, the rate tends to 0 as
$$m \rightarrow \infty $$
m→∞. Furthermore, we also optimize the parameters of our construction and give a concretely efficient scheme.Multiple Tampering. We give the first construction of a threshold non-malleable secret sharing scheme secure in the stronger setting of bounded tampering wherein the shares are tampered by multiple (but bounded in number) possibly different tampering functions. The rate of such a scheme is
$$\varTheta (\frac{1}{k^3t\log ^2 n})$$
Θ(1k3tlog2n) where k is an apriori bound on the number of tamperings. We complement this positive result by proving that it is impossible to have a threshold non-malleable secret sharing scheme that is secure in the presence of an apriori unbounded number of tamperings.General Access Structures. We extend our results beyond threshold secret sharing and give constructions of rate-efficient, non-malleable secret sharing schemes for more general monotone access structures that are secure against multiple (bounded) tampering attacks.

2019

EUROCRYPT

Multi-party Virtual State Channels
📺 Abstract

Smart contracts are self-executing agreements written in program code and are envisioned to be one of the main applications of blockchain technology. While they are supported by prominent cryptocurrencies such as Ethereum, their further adoption is hindered by fundamental scalability challenges. For instance, in Ethereum contract execution suffers from a latency of more than 15 s, and the total number of contracts that can be executed per second is very limited. State channel networks are one of the core primitives aiming to address these challenges. They form a second layer over the slow and expensive blockchain, thereby enabling instantaneous contract processing at negligible costs.In this work we present the first complete description of a state channel network that exhibits the following key features. First, it supports virtual multi-party state channels, i.e. state channels that can be created and closed without blockchain interaction and that allow contracts with any number of parties. Second, the worst case time complexity of our protocol is constant for arbitrary complex channels. This is in contrast to the existing virtual state channel construction that has worst case time complexity linear in the number of involved parties. In addition to our new construction, we provide a comprehensive model for the modular design and security analysis of our construction.

2019

EUROCRYPT

Aggregate Cash Systems: A Cryptographic Investigation of Mimblewimble
📺 Abstract

Mimblewimble is an electronic cash system proposed by an anonymous author in 2016. It combines several privacy-enhancing techniques initially envisioned for Bitcoin, such as Confidential Transactions (Maxwell, 2015), non-interactive merging of transactions (Saxena, Misra, Dhar, 2014), and cut-through of transaction inputs and outputs (Maxwell, 2013). As a remarkable consequence, coins can be deleted once they have been spent while maintaining public verifiability of the ledger, which is not possible in Bitcoin. This results in tremendous space savings for the ledger and efficiency gains for new users, who must verify their view of the system.In this paper, we provide a provable-security analysis for Mimblewimble. We give a precise syntax and formal security definitions for an abstraction of Mimblewimble that we call an aggregate cash system. We then formally prove the security of Mimblewimble in this definitional framework. Our results imply in particular that two natural instantiations (with Pedersen commitments and Schnorr or BLS signatures) are provably secure against inflation and coin theft under standard assumptions.

2019

EUROCRYPT

Consensus Through Herding
📺 Abstract

State Machine Replication (SMR) is an important abstraction for a set of nodes to agree on an ever-growing, linearly-ordered log of transactions. In decentralized cryptocurrency applications, we would like to design SMR protocols that (1) resist adaptive corruptions; and (2) achieve small bandwidth and small confirmation time. All past approaches towards constructing SMR fail to achieve either small confirmation time or small bandwidth under adaptive corruptions (without resorting to strong assumptions such as the erasure model or proof-of-work).We propose a novel paradigm for reaching consensus that departs significantly from classical approaches. Our protocol is inspired by a social phenomenon called herding, where people tend to make choices considered as the social norm. In our consensus protocol, leader election and voting are coalesced into a single (randomized) process: in every round, every node tries to cast a vote for what it views as the most popular item so far: such a voting attempt is not always successful, but rather, successful with a certain probability. Importantly, the probability that the node is elected to vote for v is independent from the probability it is elected to vote for $$v' \ne v$$v′≠v. We will show how to realize such a distributed, randomized election process using appropriate, adaptively secure cryptographic building blocks.We show that amazingly, not only can this new paradigm achieve consensus (e.g., on a batch of unconfirmed transactions in a cryptocurrency system), but it also allows us to derive the first SMR protocol which, even under adaptive corruptions, requires only polylogarithmically many rounds and polylogarithmically many honest messages to be multicast to confirm each batch of transactions; and importantly, we attain these guarantees under standard cryptographic assumptions.

2019

EUROCRYPT

Homomorphic Secret Sharing from Lattices Without FHE
📺 Abstract

Homomorphic secret sharing (HSS) is an analog of somewhat- or fully homomorphic encryption (S/FHE) to the setting of secret sharing, with applications including succinct secure computation, private manipulation of remote databases, and more. While HSS can be viewed as a relaxation of S/FHE, the only constructions from lattice-based assumptions to date build atop specific forms of threshold or multi-key S/FHE. In this work, we present new techniques directly yielding efficient 2-party HSS for polynomial-size branching programs from a range of lattice-based encryption schemes, without S/FHE. More concretely, we avoid the costly key-switching and modulus-reduction steps used in S/FHE ciphertext multiplication, replacing them with a new distributed decryption procedure for performing “restricted” multiplications of an input with a partial computation value. Doing so requires new methods for handling the blowup of “noise” in ciphertexts in a distributed setting, and leverages several properties of lattice-based encryption schemes together with new tricks in share conversion.The resulting schemes support a superpolynomial-size plaintext space and negligible correctness error, with share sizes comparable to SHE ciphertexts, but cost of homomorphic multiplication roughly one order of magnitude faster. Over certain rings, our HSS can further support some level of packed SIMD homomorphic operations. We demonstrate the practical efficiency of our schemes within two application settings, where we compare favorably with current best approaches: 2-server private database pattern-match queries, and secure 2-party computation of low-degree polynomials.

2019

EUROCRYPT

Improved Bootstrapping for Approximate Homomorphic Encryption
📺 Abstract

Since Cheon et al. introduced a homomorphic encryption scheme for approximate arithmetic (Asiacrypt ’17), it has been recognized as suitable for important real-life usecases of homomorphic encryption, including training of machine learning models over encrypted data. A follow up work by Cheon et al. (Eurocrypt ’18) described an approximate bootstrapping procedure for the scheme. In this work, we improve upon the previous bootstrapping result. We improve the amortized bootstrapping time per plaintext slot by two orders of magnitude, from $$\sim $$∼1 s to $$\sim $$∼0.01 s. To achieve this result, we adopt a smart level-collapsing technique for evaluating DFT-like linear transforms on a ciphertext. Also, we replace the Taylor approximation of the sine function with a more accurate and numerically stable Chebyshev approximation, and design a modified version of the Paterson-Stockmeyer algorithm for fast evaluation of Chebyshev polynomials over encrypted data.

2019

EUROCRYPT

Minicrypt Primitives with Algebraic Structure and Applications
📺 Abstract

Algebraic structure lies at the heart of Cryptomania as we know it. An interesting question is the following: instead of building (Cryptomania) primitives from concrete assumptions, can we build them from simple Minicrypt primitives endowed with some additional algebraic structure? In this work, we affirmatively answer this question by adding algebraic structure to the following Minicrypt primitives:One-Way Function (OWF)Weak Unpredictable Function (wUF)Weak Pseudorandom Function (wPRF)
The algebraic structure that we consider is group homomorphism over the input/output spaces of these primitives. We also consider a “bounded” notion of homomorphism where the primitive only supports an a priori bounded number of homomorphic operations in order to capture lattice-based and other “noisy” assumptions. We show that these structured primitives can be used to construct many cryptographic protocols. In particular, we prove that: (Bounded) Homomorphic OWFs (HOWFs) imply collision-resistant hash functions, Schnorr-style signatures and chameleon hash functions.(Bounded) Input-Homomorphic weak UFs (IHwUFs) imply CPA-secure PKE, non-interactive key exchange, trapdoor functions, blind batch encryption (which implies anonymous IBE, KDM-secure and leakage-resilient PKE), CCA2 deterministic PKE, and hinting PRGs (which in turn imply transformation of CPA to CCA security for ABE/1-sided PE).(Bounded) Input-Homomorphic weak PRFs (IHwPRFs) imply PIR, lossy trapdoor functions, OT and MPC (in the plain model).
In addition, we show how to realize any CDH/DDH-based protocol with certain properties in a generic manner using IHwUFs/IHwPRFs, and how to instantiate such a protocol from many concrete assumptions.We also consider primitives with substantially richer structure, namely Ring IHwPRFs and L-composable IHwPRFs. In particular, we show the following:
Ring IHwPRFs with certain properties imply FHE.2-composable IHwPRFs imply (black-box) IBE, and L-composable IHwPRFs imply non-interactive
$$(L+1)$$
(L+1)-party key exchange.
Our framework allows us to categorize many cryptographic protocols based on which structured Minicrypt primitive implies them. In addition, it potentially makes showing the existence of many cryptosystems from novel assumptions substantially easier in the future.

2019

EUROCRYPT

Attacks only Get Better: How to Break FF3 on Large Domains
📺 Abstract

We improve the attack of Durak and Vaudenay (CRYPTO’17) on NIST Format-Preserving Encryption standard FF3, reducing the running time from $$O(N^5)$$O(N5) to $$O(N^{17/6})$$O(N17/6) for domain $$\mathbb {Z}_N \times \mathbb {Z}_N$$ZN×ZN. Concretely, DV’s attack needs about $$2^{50}$$250 operations to recover encrypted 6-digit PINs, whereas ours only spends about $$2^{30}$$230 operations. In realizing this goal, we provide a pedagogical example of how to use distinguishing attacks to speed up slide attacks. In addition, we improve the running time of DV’s known-plaintext attack on 4-round Feistel of domain $$\mathbb {Z}_N \times \mathbb {Z}_N$$ZN×ZN from $$O(N^3)$$O(N3) time to just $$O(N^{5/3})$$O(N5/3) time. We also generalize our attacks to a general domain $$\mathbb {Z}_M \times \mathbb {Z}_N$$ZM×ZN, allowing one to recover encrypted SSNs using about $$2^{50}$$250 operations. Finally, we provide some proof-of-concept implementations to empirically validate our results.

2019

EUROCRYPT

Session Resumption Protocols and Efficient Forward Security for TLS 1.3 0-RTT
📺 Abstract

The TLS 1.3 0-RTT mode enables a client reconnecting to a server to send encrypted application-layer data in “0-RTT” (“zero round-trip time”), without the need for a prior interactive handshake. This fundamentally requires the server to reconstruct the previous session’s encryption secrets upon receipt of the client’s first message. The standard techniques to achieve this are Session Caches or, alternatively, Session Tickets. The former provides forward security and resistance against replay attacks, but requires a large amount of server-side storage. The latter requires negligible storage, but provides no forward security and is known to be vulnerable to replay attacks.In this paper, we first formally define session resumption protocols as an abstract perspective on mechanisms like Session Caches and Session Tickets. We give a new generic construction that provably provides forward security and replay resilience, based on puncturable pseudorandom functions (PPRFs). This construction can immediately be used in TLS 1.3 0-RTT and deployed unilaterally by servers, without requiring any changes to clients or the protocol.We then describe two new constructions of PPRFs, which are particularly suitable for use for forward-secure and replay-resilient session resumption in TLS 1.3. The first construction is based on the strong RSA assumption. Compared to standard Session Caches, for “128-bit security” it reduces the required server storage by a factor of almost 20, when instantiated in a way such that key derivation and puncturing together are cheaper on average than one full exponentiation in an RSA group. Hence, a 1 GB Session Cache can be replaced with only about 51 MBs of storage, which significantly reduces the amount of secure memory required. For larger security parameters or in exchange for more expensive computations, even larger storage reductions are achieved. The second construction combines a standard binary tree PPRF with a new “domain extension” technique. For a reasonable choice of parameters, this reduces the required storage by a factor of up to 5 compared to a standard Session Cache. It employs only symmetric cryptography, is suitable for high-traffic scenarios, and can serve thousands of tickets per second.

2019

EUROCRYPT

An Analysis of NIST SP 800-90A
📺 Abstract

We investigate the security properties of the three deterministic random bit generator (DRBG) mechanisms in NIST SP 800-90A [2]. The standard received considerable negative attention due to the controversy surrounding the now retracted $$\mathsf{{DualEC\text {-}DRBG}}$$DualEC-DRBG, which appeared in earlier versions. Perhaps because of the attention paid to the DualEC, the other algorithms in the standard have received surprisingly patchy analysis to date, despite widespread deployment. This paper addresses a number of these gaps in analysis, with a particular focus on $$\mathsf{{HASH\text {-}DRBG}}$$HASH-DRBG and $$\mathsf{{HMAC\text {-}DRBG}}$$HMAC-DRBG. We uncover a mix of positive and less positive results. On the positive side, we prove (with a caveat) the robustness [13] of $$\mathsf{{HASH\text {-}DRBG}}$$HASH-DRBG and $$\mathsf{{HMAC\text {-}DRBG}}$$HMAC-DRBG in the random oracle model (ROM). Regarding the caveat, we show that if an optional input is omitted, then – contrary to claims in the standard—$$\mathsf{{HMAC\text {-}DRBG}}$$HMAC-DRBG does not even achieve the (weaker) property of forward security. We then conduct a more informal and practice-oriented exploration of flexibility in the standard. Specifically, we argue that these DRBGs have the property that partial state leakage may lead security to break down in unexpected ways. We highlight implementation choices allowed by the overly flexible standard that exacerbate both the likelihood, and impact, of such attacks. While our attacks are theoretical, an analysis of two open source implementations of $$\mathsf{{CTR\text {-}DRBG}}$$CTR-DRBG shows that these potentially problematic implementation choices are made in the real world.

2019

EUROCRYPT

Computationally Volume-Hiding Structured Encryption
📺 Abstract

We initiate the study of structured encryption schemes with computationally-secure leakage. Specifically, we focus on the design of volume-hiding encrypted multi-maps; that is, of encrypted multi-maps that hide the response length to computationally-bounded adversaries. We describe the first volume-hiding STE schemes that do not rely on naïve padding; that is, padding all tuples to the same length. Our first construction has efficient query complexity and storage but can be lossy. We show, however, that the information loss can be bounded with overwhelming probability for a large class of multi-maps (i.e., with lengths distributed according to a Zipf distribution). Our second construction is not lossy and can achieve storage overhead that is asymptotically better than naïve padding for Zipf-distributed multi-maps. We also show how to further improve the storage when the multi-map is highly concentrated in the sense that it has a large number of tuples with a large intersection. We achieve these results by leveraging computational assumptions; not just for encryption but, more interestingly, to hide the volumes themselves. Our first construction achieves this using a pseudo-random function whereas our second construction achieves this by relying on the conjectured hardness of the planted densest subgraph problem which is a planted variant of the well-studied densest subgraph problem. This assumption was previously used to design public-key encryptions schemes (Applebaum et al., STOC ’10) and to study the computational complexity of financial products (Arora et al., ICS ’10).

2019

EUROCRYPT

Locality-Preserving Oblivious RAM
📺 Abstract

Oblivious RAMs, introduced by Goldreich and Ostrovsky [JACM’96], compile any RAM program into one that is “memory oblivious”, i.e., the access pattern to the memory is independent of the input. All previous ORAM schemes, however, completely break the locality of data accesses (for instance, by shuffling the data to pseudorandom positions in memory).In this work, we initiate the study of locality-preserving ORAMs—ORAMs that preserve locality of the accessed memory regions, while leaking only the lengths of contiguous memory regions accessed. Our main results demonstrate the existence of a locality-preserving ORAM with poly-logarithmic overhead both in terms of bandwidth and locality. We also study the tradeoff between locality, bandwidth and leakage, and show that any scheme that preserves locality and does not leak the lengths of the contiguous memory regions accessed, suffers from prohibitive bandwidth.To the best of our knowledge, before our work, the only works combining locality and obliviousness were for symmetric searchable encryption [e.g., Cash and Tessaro (EUROCRYPT’14), Asharov et al. (STOC’16)]. Symmetric search encryption ensures obliviousness if each keyword is searched only once, whereas ORAM provides obliviousness to any input program. Thus, our work generalizes that line of work to the much more challenging task of preserving locality in ORAMs.

2019

EUROCRYPT

Private Anonymous Data Access
📺 Abstract

We consider a scenario where a server holds a huge database that it wants to make accessible to a large group of clients. After an initial setup phase, clients should be able to read arbitrary locations in the database while maintaining privacy (the server does not learn which locations are being read) and anonymity (the server does not learn which client is performing each read). This should hold even if the server colludes with a subset of the clients. Moreover, the run-time of both the server and the client during each read operation should be low, ideally only poly-logarithmic in the size of the database and the number of clients. We call this notion Private Anonymous Data Access (PANDA). PANDA simultaneously combines aspects of Private Information Retrieval (PIR) and Oblivious RAM (ORAM). PIR has no initial setup, and allows anybody to privately and anonymously access a public database, but the server’s run-time is linear in the data size. On the other hand, ORAM achieves poly-logarithmic server run-time, but requires an initial setup after which only a single client with a secret key can access the database. The goal of PANDA is to get the best of both worlds: allow many clients to privately and anonymously access the database as in PIR, while having an efficient server as in ORAM.In this work, we construct bounded-collusion PANDA schemes, where the efficiency scales linearly with a bound on the number of corrupted clients that can collude with the server, but is otherwise poly-logarithmic in the data size and the total number of clients. Our solution relies on standard assumptions, namely the existence of fully homomorphic encryption, and combines techniques from both PIR and ORAM. We also extend PANDA to settings where clients can write to the database.

2019

EUROCRYPT

Reversible Proofs of Sequential Work
📺 Abstract

Proofs of sequential work (PoSW) are proof systems where a prover, upon receiving a statement
$$\chi $$
and a time parameter T computes a proof
$$\phi (\chi ,T)$$
which is efficiently and publicly verifiable. The proof can be computed in T sequential steps, but not much less, even by a malicious party having large parallelism. A PoSW thus serves as a proof that T units of time have passed since
$$\chi $$
was received.PoSW were introduced by Mahmoody, Moran and Vadhan [MMV11], a simple and practical construction was only recently proposed by Cohen and Pietrzak [CP18].In this work we construct a new simple PoSW in the random permutation model which is almost as simple and efficient as [CP18] but conceptually very different. Whereas the structure underlying [CP18] is a hash tree, our construction is based on skip lists and has the interesting property that computing the PoSW is a reversible computation.The fact that the construction is reversible can potentially be used for new applications like constructing proofs of replication. We also show how to “embed” the sloth function of Lenstra and Weselowski [LW17] into our PoSW to get a PoSW where one additionally can verify correctness of the output much more efficiently than recomputing it (though recent constructions of “verifiable delay functions” subsume most of the applications this construction was aiming at).

2019

EUROCRYPT

Incremental Proofs of Sequential Work
📺 Abstract

A proof of sequential work allows a prover to convince a verifier that a certain amount of sequential steps have been computed. In this work we introduce the notion of incremental proofs of sequential work where a prover can carry on the computation done by the previous prover incrementally, without affecting the resources of the individual provers or the size of the proofs.To date, the most efficient instance of proofs of sequential work [Cohen and Pietrzak, Eurocrypt 2018] for N steps require the prover to have $$\sqrt{N}$$N memory and to run for $$N + \sqrt{N}$$N+N steps. Using incremental proofs of sequential work we can bring down the prover’s storage complexity to $$\log N$$logN and its running time to N.We propose two different constructions of incremental proofs of sequential work: Our first scheme requires a single processor and introduces a poly-logarithmic factor in the proof size when compared with the proposals of Cohen and Pietrzak. Our second scheme assumes $$\log N$$logN parallel processors but brings down the overhead of the proof size to a factor of 9. Both schemes are simple to implement and only rely on hash functions (modelled as random oracles).

2019

EUROCRYPT

Tight Proofs of Space and Replication
📺 Abstract

We construct a concretely practical proof-of-space (PoS) with arbitrarily tight security based on stacked depth robust graphs and constant-degree expander graphs. A proof-of-space (PoS) is an interactive proof system where a prover demonstrates that it is persistently using space to store information. A PoS is arbitrarily tight if the honest prover uses exactly N space and for any $$\epsilon > 0$$ϵ>0 the construction can be tuned such that no adversary can pass verification using less than $$(1-\epsilon ) N$$(1-ϵ)N space. Most notably, the degree of the graphs in our construction are independent of $$\epsilon $$ϵ, and the number of layers is only $$O(\log (1/\epsilon ))$$O(log(1/ϵ)). The proof size is $$O(d/\epsilon )$$O(d/ϵ). The degree d depends on the depth robust graphs, which are only required to maintain $$\varOmega (N)$$Ω(N) depth in subgraphs on 80% of the nodes. Our tight PoS is also secure against parallel attacks.Tight proofs of space are necessary for proof-of-replication (PoRep), which is a publicly verifiable proof that the prover is dedicating unique resources to storing one or more retrievable replicas of a specified file. Our main PoS construction can be used as a PoRep, but data extraction is as inefficient as replica generation. We present a second variant of our construction called ZigZag PoRep that has fast/parallelizable data extraction compared to replica generation and maintains the same space tightness while only increasing the number of levels by roughly a factor two.

2019

EUROCRYPT

Founding Secure Computation on Blockchains
📺 Abstract

We study the foundations of secure computation in the blockchain-hybrid model, where a blockchain – modeled as a global functionality – is available as an Oracle to all the participants of a cryptographic protocol. We demonstrate both destructive and constructive applications of blockchains:We show that classical rewinding-based simulation techniques used in many security proofs fail against blockchain-active adversaries that have read and post access to a global blockchain. In particular, we show that zero-knowledge (ZK) proofs with black-box simulation are impossible against blockchain-active adversaries.Nevertheless, we show that achieving security against blockchain-active adversaries is possible if the honest parties are also blockchain active. We construct an $$\omega (1)$$-round ZK protocol with black-box simulation. We show that this result is tight by proving the impossibility of constant-round ZK with black-box simulation.Finally, we demonstrate a novel application of blockchains to overcome the known impossibility results for concurrent secure computation in the plain model. We construct a concurrent self-composable secure computation protocol for general functionalities in the blockchain-hybrid model based on standard cryptographic assumptions.
We develop a suite of techniques for constructing secure protocols in the blockchain-hybrid model that we hope will find applications to future research in this area.

2019

EUROCRYPT

Uncovering Algebraic Structures in the MPC Landscape
📺 Abstract

A fundamental problem in the theory of secure multi-party computation (MPC) is to characterize functions with more than 2 parties which admit MPC protocols with information-theoretic security against passive corruption. This question has seen little progress since the work of Chor and Ishai (1996), which demonstrated difficulties in resolving it. In this work, we make significant progress towards resolving this question in the important case of aggregating functionalities, in which m parties
$$P_1,\dots ,P_m$$
P1,⋯,Pm hold inputs
$$x_1,\dots ,x_m$$
x1,⋯,xm and an aggregating party
$$P_0$$
P0 must learn
$$f(x_1,\dots ,x_m)$$
f(x1,⋯,xm).We uncover a rich class of algebraic structures that are closely related to secure computability, namely, “Commuting Permutations Systems” (CPS) and its variants. We present an extensive set of results relating these algebraic structures among themselves and to MPC, including new protocols, impossibility results and separations. Our results include a necessary algebraic condition and slightly stronger sufficient algebraic condition for a function to admit information-theoretically secure MPC protocols.We also introduce and study new models of minimally interactive MPC (called UNIMPC and
), which not only help in understanding our positive and negative results better, but also open up new avenues for studying the cryptographic complexity landscape of multi-party functionalities. Our positive results include novel protocols in these models, which may be of independent practical interest.Finally, we extend our results to a definition that requires UC security as well as semi-honest security (which we term strong security). In this model we are able to carry out the characterization of all computable functions, except for a gap in the case of aggregating functionalities.

2019

EUROCRYPT

Quantum Circuits for the CSIDH: Optimizing Quantum Evaluation of Isogenies
📺 Abstract

Choosing safe post-quantum parameters for the new CSIDH isogeny-based key-exchange system requires concrete analysis of the cost of quantum attacks. The two main contributions to attack cost are the number of queries in hidden-shift algorithms and the cost of each query. This paper analyzes algorithms for each query, introducing several new speedups while showing that some previous claims were too optimistic for the attacker. This paper includes a full computer-verified simulation of its main algorithm down to the bit-operation level.

2019

EUROCRYPT

A Quantum-Proof Non-malleable Extractor
📺 Abstract

In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret X in order to establish a shared private key K by exchanging messages over an insecure communication channel. If the channel is authenticated the task can be solved in a single round of communication using a strong randomness extractor; choosing a quantum-proof extractor allows one to establish security against quantum adversaries.In the case that the channel is not authenticated, this simple solution is no longer secure. Nevertheless, Dodis and Wichs (STOC’09) showed that the problem can be solved in two rounds of communication using a non-malleable extractor, a stronger pseudo-random construction than a strong extractor.We give the first construction of a non-malleable extractor that is secure against quantum adversaries. The extractor is based on a construction by Li (FOCS’12), and is able to extract from source of min-entropy rates larger than 1 / 2. Combining this construction with a quantum-proof variant of the reduction of Dodis and Wichs, due to Cohen and Vidick (unpublished) we obtain the first privacy amplification protocol secure against active quantum adversaries.

2019

EUROCRYPT

A Note on the Communication Complexity of Multiparty Computation in the Correlated Randomness Model
📺 Abstract

Secure multiparty computation (
$$\mathsf {MPC}$$
MPC) addresses the challenge of evaluating functions on secret inputs without compromising their privacy. A central question in multiparty computation is to understand the amount of communication needed to securely evaluate a circuit of size s. In this work, we revisit this fundamental question in the setting of information-theoretically secure
$$\mathsf {MPC}$$
MPC in the correlated randomness model, where a trusted dealer distributes correlated random coins, independent of the inputs, to all parties before the start of the protocol. This setting is of strong theoretical interest, and has led to the most practically efficient
$$\mathsf {MPC}$$
MPC protocols known to date.While it is known that protocols with optimal communication (proportional to input plus output size) can be obtained from the LWE assumption, and that protocols with sublinear communication o(s) can be obtained from the DDH assumption, the question of constructing protocols with o(s) communication remains wide open for the important case of information-theoretic
$$\mathsf {MPC}$$
MPC in the correlated randomness model; all known protocols in this model require O(s) communication in the online phase.In this work, we exhibit the first generic multiparty computation protocol in the correlated randomness model with communication sublinear in the circuit size, for a large class of circuits. More precisely, we show the following: any size-slayered circuit (whose nodes can be partitioned into layers so that any edge connects adjacent layers) can be evaluated with
$$O(s/\log \log s)$$
O(s/loglogs) communication. Our results holds for both boolean and arithmetic circuits, in the honest-but-curious setting, and do not assume honest majority. For boolean circuits, we extend our results to handle malicious corruption.

2019

EUROCRYPT

Degree 2 is Complete for the Round-Complexity of Malicious MPC
📺 Abstract

We show, via a non-interactive reduction, that the existence of a secure multi-party computation (MPC) protocol for degree-2 functions implies the existence of a protocol with the same round complexity for general functions. Thus showing that when considering the round complexity of MPC, it is sufficient to consider very simple functions.Our completeness theorem applies in various settings: information theoretic and computational, fully malicious and malicious with various types of aborts. In fact, we give a master theorem from which all individual settings follow as direct corollaries. Our basic transformation does not require any additional assumptions and incurs communication and computation blow-up which is polynomial in the number of players and in $$S,2^D$$S,2D, where S, D are the circuit size and depth of the function to be computed. Using one-way functions as an additional assumption, the exponential dependence on the depth can be removed.As a consequence, we are able to push the envelope on the state of the art in various settings of MPC, including the following cases.
3-round perfectly-secure protocol (with guaranteed output delivery) against an active adversary that corrupts less than 1/4 of the parties.2-round statistically-secure protocol that achieves security with “selective abort” against an active adversary that corrupts less than half of the parties.Assuming one-way functions, 2-round computationally-secure protocol that achieves security with (standard) abort against an active adversary that corrupts less than half of the parties. This gives a new and conceptually simpler proof to the recent result of Ananth et al. (Crypto 2018).
Technically, our non-interactive reduction draws from the encoding method of Applebaum, Brakerski and Tsabary (TCC 2018). We extend these methods to ones that can be meaningfully analyzed even in the presence of malicious adversaries.

2019

EUROCRYPT

Two Round Information-Theoretic MPC with Malicious Security
📺 Abstract

We provide the first constructions of two round information-theoretic (IT) secure multiparty computation (MPC) protocols in the plain model that tolerate any $$t<n/2$$t<n/2 malicious corruptions. Our protocols satisfy the strongest achievable standard notions of security in two rounds in different communication models.Previously, IT-MPC protocols in the plain model either required a larger number of rounds, or a smaller minority of corruptions.

2019

EUROCRYPT

Designated-Verifier Pseudorandom Generators, and Their Applications
📺 Abstract

We provide a generic construction of non-interactive zero-knowledge (NIZK) schemes. Our construction is a refinement of Dwork and Naor’s (FOCS 2000) implementation of the hidden bits model using verifiable pseudorandom generators (VPRGs). Our refinement simplifies their construction and relaxes the necessary assumptions considerably.As a result of this conceptual improvement, we obtain interesting new instantiations:A designated-verifier NIZK (with unbounded soundness) based on the computational Diffie-Hellman (CDH) problem. If a pairing is available, this NIZK becomes publicly verifiable. This constitutes the first fully secure CDH-based designated-verifier NIZKs (and more generally, the first fully secure designated-verifier NIZK from a non-generic assumption which does not already imply publicly-verifiable NIZKs), and it answers an open problem recently raised by Kim and Wu (CRYPTO 2018).A NIZK based on the learning with errors (LWE) assumption, and assuming a non-interactive witness-indistinguishable (NIWI) proof system for bounded distance decoding (BDD). This simplifies and improves upon a recent NIZK from LWE that assumes a NIZK for BDD (Rothblum et al., PKC 2019).

2019

EUROCRYPT

Reusable Designated-Verifier NIZKs for all NP from CDH
📺 Abstract

Non-interactive zero-knowledge proofs (NIZKs) are a fundamental cryptographic primitive. Despite a long history of research, we only know how to construct NIZKs under a few select assumptions, such as the hardness of factoring or using bilinear maps. Notably, there are no known constructions based on either the computational or decisional Diffie-Hellman (CDH/DDH) assumption without relying on a bilinear map.In this paper, we study a relaxation of NIZKs in the designated verifier setting (DV-NIZK), in which the public common-reference string is generated together with a secret key that is given to the verifier in order to verify proofs. In this setting, we distinguish between one-time and reusable schemes, depending on whether they can be used to prove only a single statement or arbitrarily many statements. For reusable schemes, the main difficulty is to ensure that soundness continues to hold even when the malicious prover learns whether various proofs are accepted or rejected by the verifier. One-time DV-NIZKs are known to exist for general NP statements assuming only public-key encryption. However, prior to this work, we did not have any construction of reusable DV-NIZKs for general NP statements from any assumption under which we didn’t already also have standard NIZKs.In this work, we construct reusable DV-NIZKs for general NP statements under the CDH assumption, without requiring a bilinear map. Our construction is based on the hidden-bits paradigm, which was previously used to construct standard NIZKs. We define a cryptographic primitive called a hidden-bits generator (HBG), along with a designated-verifier variant (DV-HBG), which modularly abstract out how to use this paradigm to get both standard NIZKs and reusable DV-NIZKs. We construct a DV-HBG scheme under the CDH assumption by relying on techniques from the Cramer-Shoup hash-proof system, and this yields our reusable DV-NIZK for general NP statements under CDH.We also consider a strengthening of DV-NIZKs to the malicious designated-verifier setting (MDV-NIZK) where the setup consists of an honestly generated common random string and the verifier then gets to choose his own (potentially malicious) public/secret key pair to generate/verify proofs. We construct MDV-NIZKs under the “one-more CDH” assumption without relying on bilinear maps.

2019

EUROCRYPT

Designated Verifier/Prover and Preprocessing NIZKs from Diffie-Hellman Assumptions
📺 Abstract

In a non-interactive zero-knowledge (NIZK) proof, a prover can non-interactively convince a verifier of a statement without revealing any additional information. Thus far, numerous constructions of NIZKs have been provided in the common reference string (CRS) model (CRS-NIZK) from various assumptions, however, it still remains a long standing open problem to construct them from tools such as pairing-free groups or lattices. Recently, Kim and Wu (CRYPTO’18) made great progress regarding this problem and constructed the first lattice-based NIZK in a relaxed model called NIZKs in the preprocessing model (PP-NIZKs). In this model, there is a trusted statement-independent preprocessing phase where secret information are generated for the prover and verifier. Depending on whether those secret information can be made public, PP-NIZK captures CRS-NIZK, designated-verifier NIZK (DV-NIZK), and designated-prover NIZK (DP-NIZK) as special cases. It was left as an open problem by Kim and Wu whether we can construct such NIZKs from weak paring-free group assumptions such as DDH. As a further matter, all constructions of NIZKs from Diffie-Hellman (DH) type assumptions (regardless of whether it is over a paring-free or paring group) require the proof size to have a multiplicative-overhead $$|C| \cdot \mathsf {poly}(\kappa )$$|C|·poly(κ), where |C| is the size of the circuit that computes the $$\mathbf {NP}$$NP relation.In this work, we make progress of constructing (DV, DP, PP)-NIZKs with varying flavors from DH-type assumptions. Our results are summarized as follows:DV-NIZKs for $$\mathbf {NP}$$NP from the CDH assumption over pairing-free groups. This is the first construction of such NIZKs on pairing-free groups and resolves the open problem posed by Kim and Wu (CRYPTO’18).DP-NIZKs for $$\mathbf {NP}$$NP with short proof size from a DH-type assumption over pairing groups. Here, the proof size has an additive-overhead $$|C|+\mathsf {poly}(\kappa )$$|C|+poly(κ) rather then an multiplicative-overhead $$|C| \cdot \mathsf {poly}(\kappa )$$|C|·poly(κ). This is the first construction of such NIZKs (including CRS-NIZKs) that does not rely on the LWE assumption, fully-homomorphic encryption, indistinguishability obfuscation, or non-falsifiable assumptions.PP-NIZK for $$\mathbf {NP}$$NP with short proof size from the DDH assumption over pairing-free groups. This is the first PP-NIZK that achieves a short proof size from a weak and static DH-type assumption such as DDH. Similarly to the above DP-NIZK, the proof size is $$|C|+\mathsf {poly}(\kappa )$$|C|+poly(κ). This too serves as a solution to the open problem posed by Kim and Wu (CRYPTO’18).
Along the way, we construct two new homomorphic authentication (HomAuth) schemes which may be of independent interest.

2019

EUROCRYPT

Building an Efficient Lattice Gadget Toolkit: Subgaussian Sampling and More
📺 Abstract

Many advanced lattice cryptography applications require efficient algorithms for inverting the so-called “gadget” matrices, which are used to formally describe a digit decomposition problem that produces an output with specific (statistical) properties. The common gadget inversion problems are the classical (often binary) digit decomposition, subgaussian decomposition, Learning with Errors (LWE) decoding, and discrete Gaussian sampling. In this work, we build and implement an efficient lattice gadget toolkit that provides a general treatment of gadget matrices and algorithms for their inversion/sampling. The main contribution of our work is a set of new gadget matrices and algorithms for efficient subgaussian sampling that have a number of major theoretical and practical advantages over previously known algorithms. Another contribution deals with efficient algorithms for LWE decoding and discrete Gaussian sampling in the Residue Number System (RNS) representation.We implement the gadget toolkit in PALISADE and evaluate the performance of our algorithms both in terms of runtime and noise growth. We illustrate the improvements due to our algorithms by implementing a concrete complex application, key-policy attribute-based encryption (KP-ABE), which was previously considered impractical for CPU systems (except for a very small number of attributes). Our runtime improvements for the main bottleneck operation based on subgaussian sampling range from 18x (for 2 attributes) to 289x (for 16 attributes; the maximum number supported by a previous implementation). Our results are applicable to a wide range of other advanced applications in lattice cryptography, such as GSW-based homomorphic encryption schemes, leveled fully homomorphic signatures, other forms of ABE, some program obfuscation constructions, and more.

2019

EUROCRYPT

Approx-SVP in Ideal Lattices with Pre-processing
📺 Abstract

We describe an algorithm to solve the approximate Shortest Vector Problem for lattices corresponding to ideals of the ring of integers of an arbitrary number field K. This algorithm has a pre-processing phase, whose run-time is exponential in
$$\log |\varDelta |$$
log|Δ| with
$$\varDelta $$
Δ the discriminant of K. Importantly, this pre-processing phase depends only on K. The pre-processing phase outputs an “advice”, whose bit-size is no more than the run-time of the query phase. Given this advice, the query phase of the algorithm takes as input any ideal I of the ring of integers, and outputs an element of I which is at most
$$\exp (\widetilde{O}((\log |\varDelta |)^{\alpha +1}/n))$$
exp(O~((log|Δ|)α+1/n)) times longer than a shortest non-zero element of I (with respect to the Euclidean norm of its canonical embedding). This query phase runs in time and space
$$\exp (\widetilde{O}( (\log |\varDelta |)^{\max (2/3, 1-2\alpha )}))$$
exp(O~((log|Δ|)max(2/3,1-2α))) in the classical setting, and
$$\exp (\widetilde{O}((\log |\varDelta |)^{1-2\alpha }))$$
exp(O~((log|Δ|)1-2α)) in the quantum setting. The parameter
$$\alpha $$
α can be chosen arbitrarily in [0, 1 / 2]. Both correctness and cost analyses rely on heuristic assumptions, whose validity is consistent with experiments.The algorithm builds upon the algorithms from Cramer et al. [EUROCRYPT 2016] and Cramer et al. [EUROCRYPT 2017]. It relies on the framework from Buchmann [Séminaire de théorie des nombres 1990], which allows to merge them and to extend their applicability from prime-power cyclotomic fields to all number fields. The cost improvements are obtained by allowing precomputations that depend on the field only.

2019

EUROCRYPT

The General Sieve Kernel and New Records in Lattice Reduction
📺 Abstract

We propose the General Sieve Kernel (G6K, pronounced /
e.si.ka/), an abstract stateful machine supporting a wide variety of lattice reduction strategies based on sieving algorithms. Using the basic instruction set of this abstract stateful machine, we first give concise formulations of previous sieving strategies from the literature and then propose new ones. We then also give a light variant of BKZ exploiting the features of our abstract stateful machine. This encapsulates several recent suggestions (Ducas at Eurocrypt 2018; Laarhoven and Mariano at PQCrypto 2018) to move beyond treating sieving as a blackbox SVP oracle and to utilise strong lattice reduction as preprocessing for sieving. Furthermore, we propose new tricks to minimise the sieving computation required for a given reduction quality with mechanisms such as recycling vectors between sieves, on-the-fly lifting and flexible insertions akin to Deep LLL and recent variants of Random Sampling Reduction.Moreover, we provide a highly optimised, multi-threaded and tweakable implementation of this machine which we make open-source. We then illustrate the performance of this implementation of our sieving strategies by applying G6K to various lattice challenges. In particular, our approach allows us to solve previously unsolved instances of the Darmstadt SVP (151, 153, 155) and LWE (e.g. (75, 0.005)) challenges. Our solution for the SVP-151 challenge was found 400 times faster than the time reported for the SVP-150 challenge, the previous record. For exact-SVP, we observe a performance crossover between G6K and FPLLL’s state of the art implementation of enumeration at dimension 70.

2019

EUROCRYPT

Misuse Attacks on Post-quantum Cryptosystems
📺 Abstract

Many post-quantum cryptosystems which have been proposed in the National Institute of Standards and Technology (NIST) standardization process follow the same meta-algorithm, but in different algebras or different encoding methods. They usually propose two constructions, one being weaker and the other requiring a random oracle. We focus on the weak version of nine submissions to NIST. Submitters claim no security when the secret key is used several times. In this paper, we analyze how easy it is to run a key recovery under multiple key reuse. We mount a classical key recovery under plaintext checking attacks (i.e., with a plaintext checking oracle saying if a given ciphertext decrypts well to a given plaintext) and a quantum key recovery under chosen ciphertext attacks. In the latter case, we assume quantum access to the decryption oracle.

2019

EUROCRYPT

On ELFs, Deterministic Encryption, and Correlated-Input Security
📺 Abstract

We construct deterministic public key encryption secure for any constant number of arbitrarily correlated computationally unpredictable messages. Prior works required either random oracles or non-standard knowledge assumptions. In contrast, our constructions are based on the exponential hardness of DDH, which is plausible in elliptic curve groups. Our central tool is a new trapdoored extremely lossy function, which modifies extremely lossy functions by adding a trapdoor.

2019

EUROCRYPT

New Techniques for Efficient Trapdoor Functions and Applications
📺 Abstract

We develop techniques for constructing trapdoor functions (TDFs) with short image size and advanced security properties. Our approach builds on the recent framework of Garg and Hajiabadi [CRYPTO 2018]. As applications of our techniques, we obtainThe first construction of deterministic-encryption schemes for block-source inputs (both for the CPA and CCA cases) based on the Computational Diffie-Hellman (CDH) assumption. Moreover, by applying our efficiency-enhancing techniques, we obtain CDH-based schemes with ciphertext size linear in plaintext size.The first construction of lossy TDFs based on the Decisional Diffie-Hellman (DDH) assumption with image size linear in input size, while retaining the lossiness rate of [Peikert-Waters STOC 2008].
Prior to our work, all constructions of deterministic encryption based even on the stronger DDH assumption incurred a quadratic gap between the ciphertext and plaintext sizes. Moreover, all DDH-based constructions of lossy TDFs had image size quadratic in the input size.At a high level, we break the previous quadratic barriers by introducing a novel technique for encoding input bits via hardcore output bits with the use of erasure-resilient codes. All previous schemes used group elements for encoding input bits, resulting in quadratic expansions.

2019

EUROCRYPT

Symbolic Encryption with Pseudorandom Keys
📺 Abstract

We give an efficient decision procedure that, on input two (acyclic) expressions making arbitrary use of common cryptographic primitives (namely, encryption and pseudorandom generators), determines (in polynomial time) if the two expressions produce computationally indistinguishable distributions for any cryptographic instantiation satisfying the standard security notions of pseudorandomness and indistinguishability under chosen plaintext attack. The procedure works by mapping each expression to a symbolic pattern that captures, in a fully abstract way, the information revealed by the expression to a computationally bounded observer. Our main result shows that if two expressions are mapped to different symbolic patterns, then there are secure pseudorandom generators and encryption schemes for which the two distributions can be distinguished with overwhelming advantage. At the same time if any two (acyclic) expressions are mapped to the same pattern, then the associated distributions are indistinguishable.

2019

EUROCRYPT

Efficient Circuit-Based PSI with Linear Communication
📺 Abstract

We present a new protocol for computing a circuit which implements the private set intersection functionality (PSI). Using circuits for this task is advantageous over the usage of specific protocols for PSI, since many applications of PSI do not need to compute the intersection itself but rather functions based on the items in the intersection.Our protocol is the first circuit-based PSI protocol to achieve linear communication complexity. It is also concretely more efficient than all previous circuit-based PSI protocols. For example, for sets of size
$$2^{20}$$
it improves the communication of the recent work of Pinkas et al. (EUROCRYPT’18) by more than 10 times, and improves the run time by a factor of 2.8x in the LAN setting, and by a factor of 5.8x in the WAN setting.Our protocol is based on the usage of a protocol for computing oblivious programmable pseudo-random functions (OPPRF), and more specifically on our technique to amortize the cost of batching together multiple invocations of OPPRF.

2019

EUROCRYPT

An Algebraic Approach to Maliciously Secure Private Set Intersection
📺 Abstract

Private set intersection (PSI) is an important area of research and has been the focus of many works over the past decades. It describes the problem of finding an intersection between the input sets of at least two parties without revealing anything about the input sets apart from their intersection.In this paper, we present a new approach to compute the intersection between sets based on a primitive called Oblivious Linear Function Evaluation (OLE). On an abstract level, we use this primitive to efficiently add two polynomials in a randomized way while preserving the roots of the added polynomials. Setting the roots of the input polynomials to be the elements of the input sets, this directly yields an intersection protocol with optimal asymptotic communication complexity $$O(m\kappa )$$. We highlight that the protocol is information-theoretically secure against a malicious adversary assuming OLE.We also present a natural generalization of the 2-party protocol for the fully malicious multi-party case. Our protocol does away with expensive (homomorphic) threshold encryption and zero-knowledge proofs. Instead, we use simple combinatorial techniques to ensure the security. As a result we get a UC-secure protocol with asymptotically optimal communication complexity $$O((n^2+nm)\kappa )$$, where n is the number of parties, m is the set size and $$\kappa $$ is the security parameter. Apart from yielding an asymptotic improvement over previous works, our protocols are also conceptually simple and require only simple field arithmetic. Along the way we develop techniques that might be of independent interest.

2019

EUROCRYPT

On Finding Quantum Multi-collisions
📺 Abstract

A k-collision for a compressing hash function H is a set of k distinct inputs that all map to the same output. In this work, we show that for any constant k,
$$\varTheta \left( N^{\frac{1}{2}(1-\frac{1}{2^k-1})}\right) $$
quantum queries are both necessary and sufficient to achieve a k-collision with constant probability. This improves on both the best prior upper bound (Hosoyamada et al., ASIACRYPT 2017) and provides the first non-trivial lower bound, completely resolving the problem.

2019

EUROCRYPT

On Quantum Advantage in Information Theoretic Single-Server PIR
📺 Abstract

In (single-server) Private Information Retrieval (PIR), a server holds a large database
$${\mathtt {DB}}$$
of size n, and a client holds an index
$$i \in [n]$$
and wishes to retrieve
$${\mathtt {DB}}[i]$$
without revealing i to the server. It is well known that information theoretic privacy even against an “honest but curious” server requires
$$\varOmega (n)$$
communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (“input purification attack”).Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity
$$O(\sqrt{n})$$
, and a protocol by Kerenidis et al. (QIC 2016) with communication complexity
$$O(\log (n))$$
, and O(n) shared entanglement.We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called anchored privacy, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries.Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).

2019

EUROCRYPT

Verifier-on-a-Leash: New Schemes for Verifiable Delegated Quantum Computation, with Quasilinear Resources
📺 Abstract

The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits required of the honest provers, scaling as
$$O(g\log g)$$
for delegating a circuit of size g. This is in contrast to previous protocols, whose overhead in terms of resources employed, while polynomial, is far beyond what is feasible in practice. Our first protocol requires a number of rounds that is linear in the depth of the circuit being delegated, and is blind, meaning neither prover can learn the circuit or its input. The second protocol is not blind, but requires only a constant number of rounds of interaction.Our main technical innovation is an efficient rigidity theorem which allows a verifier to test that two entangled provers perform measurements specified by an arbitrary m-qubit tensor product of single-qubit Clifford observables on their respective halves of m shared EPR pairs, with a robustness that is independent of m. Our two-prover classical-verifier delegation protocols are obtained by combining this rigidity theorem with a single-prover quantum-verifier protocol for the verifiable delegation of a quantum computation, introduced by Broadbent.

2019

EUROCRYPT

Ring Signatures: Logarithmic-Size, No Setup—from Standard Assumptions
📺 Abstract

Ring signatures allow for creating signatures on behalf of an ad hoc group of signers, hiding the true identity of the signer among the group. A natural goal is to construct a ring signature scheme for which the signature size is short in the number of ring members. Moreover, such a construction should not rely on a trusted setup and be proven secure under falsifiable standard assumptions. Despite many years of research this question is still open.In this paper, we present the first construction of size-optimal ring signatures which do not rely on a trusted setup or the random oracle heuristic. Specifically, our scheme can be instantiated from standard assumptions and the size of signatures grows only logarithmically in the number of ring members.We also extend our techniques to the setting of linkable ring signatures, where signatures created using the same signing key can be linked.

2019

EUROCRYPT

A Modular Treatment of Blind Signatures from Identification Schemes
📺 Abstract

We propose a modular security treatment of blind signatures derived from linear identification schemes in the random oracle model. To this end, we present a general framework that captures several well known schemes from the literature and allows to prove their security. Our modular security reduction introduces a new security notion for identification schemes called One-More-Man In the Middle Security which we show equivalent to the classical One-More-Unforgeability notion for blind signatures.We also propose a generalized version of the Forking Lemma due to Bellare and Neven (CCS 2006) and show how it can be used to greatly improve the understandability of the classical security proofs for blind signatures schemes by Pointcheval and Stern (Journal of Cryptology 2000).

2019

EUROCRYPT

Efficient Verifiable Delay Functions
📺 Abstract

★ Best Young Researcher Paper

We construct a verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of trustworthy public randomness in a trustless environment, or resource-efficient blockchains. To construct our VDF, we actually build a trapdoor VDF. A trapdoor VDF is essentially a VDF which can be evaluated efficiently by parties who know a secret (the trapdoor). By setting up this scheme in a way that the trapdoor is unknown (not even by the party running the setup, so that there is no need for a trusted setup environment), we obtain a simple VDF. Our construction is based on groups of unknown order such as an RSA group, or the class group of an imaginary quadratic field. The output of our construction is very short (the result and the proof of correctness are each a single element of the group), and the verification of correctness is very efficient.

2019

EUROCRYPT

Quantum Lightning Never Strikes the Same State Twice
📺 Abstract

★ Best Paper

Public key quantum money can be seen as a version of the quantum no-cloning theorem that holds even when the quantum states can be verified by the adversary. In this work, we investigate quantum lightning where no-cloning holds even when the adversary herself generates the quantum state to be cloned. We then study quantum money and quantum lightning, showing the following results:We demonstrate the usefulness of quantum lightning beyond quantum money by showing several potential applications, such as generating random strings with a proof of entropy, to completely decentralized cryptocurrency without a block-chain, where transactions is instant and local.We give Either/Or results for quantum money/lightning, showing that either signatures/hash functions/commitment schemes meet very strong recently proposed notions of security, or they yield quantum money or lightning. Given the difficulty in constructing public key quantum money, this suggests that natural schemes do attain strong security guarantees.We show that instantiating the quantum money scheme of Aaronson and Christiano [STOC’12] with indistinguishability obfuscation that is secure against quantum computers yields a secure quantum money scheme. This construction can be seen as an instance of our Either/Or result for signatures, giving the first separation between two security notions for signatures from the literature.Finally, we give a plausible construction for quantum lightning, which we prove secure under an assumption related to the multi-collision resistance of degree-2 hash functions. Our construction is inspired by our Either/Or result for hash functions, and yields the first plausible standard model instantiation of a non-collapsing collision resistant hash function. This improves on a result of Unruh [Eurocrypt’16] which is relative to a quantum oracle.

2019

EUROCRYPT

Secret-Sharing Schemes for General and Uniform Access Structures
📺 Abstract

A secret-sharing scheme allows some authorized sets of parties to reconstruct a secret; the collection of authorized sets is called the access structure. For over 30 years, it was known that any (monotone) collection of authorized sets can be realized by a secret-sharing scheme whose shares are of size $$2^{n-o(n)}$$ and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) have reduced the share size to $$O(2^{0.994n})$$. Our first contribution is improving the exponent of secret sharing down to 0.892. For the special case of linear secret-sharing schemes, we get an exponent of 0.942 (compared to 0.999 of Liu and Vaikuntanathan).Motivated by the construction of Liu and Vaikuntanathan, we study secret-sharing schemes for uniform access structures. An access structure is k-uniform if all sets of size larger than k are authorized, all sets of size smaller than k are unauthorized, and each set of size k can be either authorized or unauthorized. The construction of Liu and Vaikuntanathan starts from protocols for conditional disclosure of secrets, constructs secret-sharing schemes for uniform access structures from them, and combines these schemes in order to obtain secret-sharing schemes for general access structures. Our second contribution in this paper is constructions of secret-sharing schemes for uniform access structures. We achieve the following results:A secret-sharing scheme for k-uniform access structures for large secrets in which the share size is $$O(k^2)$$ times the size of the secret.A linear secret-sharing scheme for k-uniform access structures for a binary secret in which the share size is $$\tilde{O}(2^{h(k/n)n/2})$$ (where h is the binary entropy function). By counting arguments, this construction is optimal (up to polynomial factors).A secret-sharing scheme for k-uniform access structures for a binary secret in which the share size is $$2^{\tilde{O}(\sqrt{k \log n})}$$.
Our third contribution is a construction of ad-hoc PSM protocols, i.e., PSM protocols in which only a subset of the parties will compute a function on their inputs. This result is based on ideas we used in the construction of secret-sharing schemes for k-uniform access structures for a binary secret.

2019

EUROCRYPT

Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary
📺 Abstract

Robust secret sharing enables the reconstruction of a secret-shared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when $$n = 2t+1$$, which is the largest t for which the task is still possible, up to a small error probability $$2^{-\kappa }$$ and with some overhead in the share size.Recently, Bishop, Pastro, Rajaraman and Wichs [3] proposed a scheme with an (almost) optimal overhead of $$\widetilde{O}(\kappa )$$. This seems to answer the open question posed by Cevallos et al. [6] who proposed a scheme with overhead of $$\widetilde{O}(n+\kappa )$$ and asked whether the linear dependency on n was necessary or not. However, a subtle issue with Bishop et al.’s solution is that it (implicitly) assumes a non-rushing adversary, and thus it satisfies a weaker notion of security compared to the scheme by Cevallos et al. [6], or to the classical scheme by Rabin and BenOr [13].In this work, we almost close this gap. We propose a new robust secret sharing scheme that offers full security against a rushing adversary, and that has an overhead of $$O(\kappa n^\varepsilon )$$, where $$\varepsilon > 0$$ is arbitrary but fixed. This $$n^\varepsilon $$-factor is obviously worse than the $$\mathrm {polylog}(n)$$-factor hidden in the $$\widetilde{O}$$ notation of the scheme of Bishop et al. [3], but it greatly improves on the linear dependency on n of the best known scheme that features security against a rushing adversary (when $$\kappa $$ is substantially smaller than n).A small variation of our scheme has the same $$\widetilde{O}(\kappa )$$ overhead as the scheme of Bishop et al. and achieves security against a rushing adversary, but suffers from a (slightly) superpolynomial reconstruction complexity.

2019

EUROCRYPT

Simple Schemes in the Bounded Storage Model
📺 Abstract

The bounded storage model promises unconditional security proofs against computationally unbounded adversaries, so long as the adversary’s space is bounded. In this work, we develop simple new constructions of two-party key agreement, bit commitment, and oblivious transfer in this model. In addition to simplicity, our constructions have several advantages over prior work, including an improved number of rounds and enhanced correctness. Our schemes are based on Raz’s lower bound for learning parities.

2019

EUROCRYPT

From Collisions to Chosen-Prefix Collisions Application to Full SHA-1
📺 Abstract

A chosen-prefix collision attack is a stronger variant of a collision attack, where an arbitrary pair of challenge prefixes are turned into a collision. Chosen-prefix collisions are usually significantly harder to produce than (identical-prefix) collisions, but the practical impact of such an attack is much larger. While many cryptographic constructions rely on collision-resistance for their security proofs, collision attacks are hard to turn into break of concrete protocols, because the adversary has a limited control over the colliding messages. On the other hand, chosen-prefix collisions have been shown to break certificates (by creating a rogue CA) and many internet protocols (TLS, SSH, IPsec).In this article, we propose new techniques to turn collision attacks into chosen-prefix collision attacks. Our strategy is composed of two phases: first a birthday search that aims at taking the random chaining variable difference (due to the chosen-prefix model) to a set of pre-defined target differences. Then, using a multi-block approach, carefully analysing the clustering effect, we map this new chaining variable difference to a colliding pair of states using techniques developed for collision attacks.We apply those techniques to MD5 and SHA-1, and obtain improved attacks. In particular, we have a chosen-prefix collision attack against SHA-1 with complexity between $$2^{66.9}$$ and $$2^{69.4}$$ (depending on assumptions about the cost of finding near-collision blocks), while the best-known attack has complexity $$2^{77.1}$$. This is within a small factor of the complexity of the classical collision attack on SHA-1 (estimated as $$2^{64.7}$$). This represents yet another warning that industries and users have to move away from using SHA-1 as soon as possible.

2019

EUROCRYPT

Preimage Attacks on Round-Reduced Keccak-224/256 via an Allocating Approach
📺 Abstract

We present new preimage attacks on standard Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. An allocating approach is used in the attacks, and the whole complexity is allocated to two stages, such that fewer constraints are considered and the complexity is lowered in each stage. Specifically, we are trying to find a 2-block preimage, instead of a 1-block one, for a given hash value, and the first and second message blocks are found in two stages, respectively. Both the message blocks are constrained by a set of newly proposed conditions on the middle state, which are weaker than those brought by the initial values and the hash values. Thus, the complexities in the two stages are both lower than that of finding a 1-block preimage directly. Together with the basic allocating approach, an improved method is given to balance the complexities of two stages, and hence, obtains the optimal attacks. As a result, we present the best theoretical preimage attacks on Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. Moreover, we practically found a (second) preimage for 3-round Keccak-224 with a complexity of $$2^{39.39}$$.

2019

EUROCRYPT

bison Instantiating the Whitened Swap-Or-Not Construction
📺 Abstract

We give the first practical instance – bison – of the Whitened Swap-Or-Not construction. After clarifying inherent limitations of the construction, we point out that this way of building block ciphers allows easy and very strong arguments against differential attacks.

2019

EUROCRYPT

Worst-Case Hardness for LPN and Cryptographic Hashing via Code Smoothing
📺 Abstract

We present a worst case decoding problem whose hardness reduces to that of solving the Learning Parity with Noise (LPN) problem, in some parameter regime. Prior to this work, no worst case hardness result was known for LPN (as opposed to syntactically similar problems such as Learning with Errors). The caveat is that this worst case problem is only mildly hard and in particular admits a quasi-polynomial time algorithm, whereas the LPN variant used in the reduction requires extremely high noise rate of
$$1/2-1/\mathrm{poly}(n)$$
. Thus we can only show that “very hard” LPN is harder than some “very mildly hard” worst case problem. We note that LPN with noise
$$1/2-1/\mathrm{poly}(n)$$
already implies symmetric cryptography.Specifically, we consider the (n, m, w)-nearest codeword problem ((n, m, w)-NCP) which takes as input a generating matrix for a binary linear code in m dimensions and rank n, and a target vector which is very close to the code (Hamming distance at most w), and asks to find the codeword nearest to the target vector. We show that for balanced (unbiased) codes and for relative error
$$w/m \approx {\log ^2 n}/{n}$$
, (n, m, w)-NCP can be solved given oracle access to an LPN distinguisher with noise ratio
$$1/2-1/\mathrm{poly}(n)$$
.Our proof relies on a smoothing lemma for codes which we show to have further implications: We show that (n, m, w)-NCP with the aforementioned parameters lies in the complexity class
$$\mathrm {{Search}\hbox {-}\mathcal {BPP}}^\mathcal {SZK}$$
(i.e. reducible to a problem that has a statistical zero knowledge protocol) implying that it is unlikely to be
$$\mathcal {NP}$$
-hard. We then show that the hardness of LPN with very low noise rate
$$\log ^2(n)/n$$
implies the existence of collision resistant hash functions (our aforementioned result implies that in this parameter regime LPN is also in
$$\mathcal {BPP}^\mathcal {SZK}$$
).

2019

EUROCRYPT

New Techniques for Obfuscating Conjunctions
📺 Abstract

A conjunction is a function $$f(x_1,\dots ,x_n) = \bigwedge _{i \in S} l_i$$ where $$S \subseteq [n]$$ and each $$l_i$$ is $$x_i$$ or $$\lnot x_i$$. Bishop et al. (CRYPTO 2018) recently proposed obfuscating conjunctions by embedding them in the error positions of a noisy Reed-Solomon codeword and placing the codeword in a group exponent. They prove distributional virtual black box (VBB) security in the generic group model for random conjunctions where $$|S| \ge 0.226n$$. While conjunction obfuscation is known from LWE [31, 47], these constructions rely on substantial technical machinery.In this work, we conduct an extensive study of simple conjunction obfuscation techniques.
We abstract the Bishop et al. scheme to obtain an equivalent yet more efficient “dual” scheme that can handle conjunctions over exponential size alphabets. This scheme admits a straightforward proof of generic group security, which we combine with a novel combinatorial argument to obtain distributional VBB security for |S| of any size.If we replace the Reed-Solomon code with a random binary linear code, we can prove security from standard LPN and avoid encoding in a group. This addresses an open problem posed by Bishop et al. to prove security of this simple approach in the standard model.We give a new construction that achieves information theoretic distributional VBB security and weak functionality preservation for $$|S| \ge n - n^\delta $$ and $$\delta < 1$$. Assuming discrete log and $$\delta < 1/2$$, we satisfy a stronger notion of functionality preservation for computationally bounded adversaries while still achieving information theoretic security.

2019

EUROCRYPT

Distributional Collision Resistance Beyond One-Way Functions
📺 Abstract

Distributional collision resistance is a relaxation of collision resistance that only requires that it is hard to sample a collision (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. The notion lies between one-wayness and collision resistance, but its exact power is still not well-understood. On one hand, distributional collision resistant hash functions cannot be built from one-way functions in a black-box way, which may suggest that they are stronger. On the other hand, so far, they have not yielded any applications beyond one-way functions.Assuming distributional collision resistant hash functions, we construct constant-round statistically hiding commitment scheme. Such commitments are not known based on one-way functions, and are impossible to obtain from one-way functions in a black-box way. Our construction relies on the reduction from inaccessible entropy generators to statistically hiding commitments by Haitner et al. (STOC ’09). In the converse direction, we show that two-message statistically hiding commitments imply distributional collision resistance, thereby establishing a loose equivalence between the two notions.A corollary of the first result is that constant-round statistically hiding commitments are implied by average-case hardness in the class $${\textsf {SZK}}$$ (which is known to imply distributional collision resistance). This implication seems to be folklore, but to the best of our knowledge has not been proven explicitly. We provide yet another proof of this implication, which is arguably more direct than the one going through distributional collision resistance.

2019

EUROCRYPT

Multi-target Attacks on the Picnic Signature Scheme and Related Protocols
📺 Abstract

Picnic is a signature scheme that was presented at ACM CCS 2017 by Chase et al. and submitted to NIST’s post-quantum standardization project. Among all submissions to NIST’s project, Picnic is one of the most innovative, making use of recent progress in construction of practically efficient zero-knowledge (ZK) protocols for general circuits.In this paper, we devise multi-target attacks on Picnic and its underlying ZK protocol, ZKB++. Given access to S signatures, produced by a single or by several users, our attack can (information theoretically) recover the $$\kappa $$-bit signing key of a user in complexity of about $$2^{\kappa - 7}/S$$. This is faster than Picnic’s claimed $$2^{\kappa }$$ security against classical (non-quantum) attacks by a factor of $$2^7 \cdot S$$ (as each signature contains about $$2^7$$ attack targets).Whereas in most multi-target attacks, the attacker can easily sort and match the available targets, this is not the case in our attack on Picnic, as different bits of information are available for each target. Consequently, it is challenging to reach the information theoretic complexity in a computational model, and we had to perform cryptanalytic optimizations by carefully analyzing ZKB++ and its underlying circuit. Our best attack for $$\kappa = 128$$ has time complexity of $$T = 2^{77}$$ for $$S = 2^{64}$$. Alternatively, we can reach the information theoretic complexity of $$T = 2^{64}$$ for $$S = 2^{57}$$, given that all signatures are produced with the same signing key.Our attack exploits a weakness in the way that the Picnic signing algorithm uses a pseudo-random generator. The weakness is fixed in the recent Picnic 2.0 version.In addition to our attack on Picnic, we show that a recently proposed improvement of the ZKB++ protocol (due to Katz, Kolesnikov and Wang) is vulnerable to a similar multi-target attack.

2019

EUROCRYPT

Durandal: A Rank Metric Based Signature Scheme
📺 Abstract

We describe a variation of the Schnorr-Lyubashevsky approach to devising signature schemes that is adapted to rank based cryptography. This new approach enables us to obtain a randomization of the signature, which previously seemed difficult to derive for code-based cryptography. We provide a detailed analysis of attacks and an EUF-CMA proof for our scheme. Our scheme relies on the security of the Ideal Rank Support Learning and the Ideal Rank Syndrome problems and a newly introduced problem: Product Spaces Subspaces Indistinguishability, for which we give a detailed analysis. Overall the parameters we propose are efficient and comparable in terms of signature size to the Dilithium lattice-based scheme, with a signature size of 4 kB for a public key of size less than 20 kB.

2019

EUROCRYPT

SeaSign: Compact Isogeny Signatures from Class Group Actions
📺 Abstract

We give a new signature scheme for isogenies that combines the class group actions of CSIDH with the notion of Fiat-Shamir with aborts. Our techniques allow to have signatures of size less than one kilobyte at the 128-bit security level, even with tight security reduction (to a non-standard problem) in the quantum random oracle model. Hence our signatures are potentially shorter than lattice signatures, but signing and verification are currently very expensive.

2019

TCHES

AuCPace: Efficient verifier-based PAKE protocol tailored for the IIoT
📺 Abstract

Increasingly connectivity becomes integrated in products and devices that previously operated in a stand-alone setting. This observation holds for many consumer applications in the so-called "Internet of Things" (IoT) as well as for corresponding industry applications (IIoT), such as industrial process sensors. Often the only practicable means for authentication of human users is a password. The security of password-based authentication schemes frequently forms the weakest point of the security infrastructure. In this paper we first explain why a tailored protocol designed for the IIoT use case is considered necessary. The differences between IIoT and the conventional Internet use-cases result in largely modified threats and require special procedures for allowing both, convenient and secure use in the highly constrained industrial setting. Specifically the use of a verifier-based password-authenticated key-exchange (V-PAKE) protocol as a hedge against public-key-infrastructure (PKI) failures is considered important. Availability concerns for the case of failures of (part of) the communication infrastructure makes local storage of access credentials mandatory. The larger threat of physical attacks makes it important to use memory-hard password hashing. This paper presents a corresponding tailored protocol, AuCPace, together with a security proof within the Universal Composability (UC) framework considering fully adaptive adversaries. We also introduce a new security notion of partially augmented PAKE that provides specific performance advantages and makes them suitable for a larger set of IIoT applications. We also present an actual instantiation of our protocol, AuCPace25519, and present performance results on ARM Cortex-M0 and Cortex-M4 microcontrollers. Our implementation realizes new speed-records for PAKE and X25519 Diffie-Hellman for the ARM Cortex M4 architecture.

2019

TCHES

Best Information is Most Successful
📺 Abstract

Using information-theoretic tools, this paper establishes a mathematical link between the probability of success of a side-channel attack and the minimum number of queries to reach a given success rate, valid for any possible distinguishing rule and with the best possible knowledge on the attacker’s side. This link is a lower bound on the number of queries highly depends on Shannon’s mutual information between the traces and the secret key. This leads us to derive upper bounds on the mutual information that are as tight as possible and can be easily calculated. It turns out that, in the case of an additive white Gaussian noise, the bound on the probability of success of any attack is directly related to the signal to noise ratio. This leads to very easy computations and predictions of the success rate in any leakage model.

2019

TCHES

Secure Data Retrieval on the Cloud: Homomorphic Encryption meets Coresets
📺 Abstract

Secure report is the problem of a client that retrieves all records matching specified attributes from a database table at the server (e.g. cloud), as in SQL SELECT queries, but where the query and the database are encrypted. Here, only the client has the secret key, but still the server is expected to compute and return the encrypted result. Secure report is theoretically possible with Fully Homomorphic Encryption (FHE). However, the current state-of-the-art solutions are realized by a polynomial of degree that is at least linear in the number m of records, which is too slow in practice even for very small databases. We present the first solution that is realized by a polynomial that attains degree independent of the number of records m, as well as the first implementation of an FHE solution to Secure report. This is by suggesting a novel paradigm that forges a link between cryptography and modern data summarization techniques known as coresets (core-sets), and sketches in particular. The key idea is to compute only a coreset of the desired report. Since the coreset is small, the client can quickly decode the desired report that the server computes after decrypting the coreset. We implemented our main reporting system in an open source library. This is the first implemented system that can answer such database queries when processing only FHE encrypted data and queries. As our analysis promises, the experimental results show that we can run Secure report queries on billions records in minutes on an Amazon EC2 server, compared to less than a hundred-thousands in previous FHE based solutions.

2019

TCHES

Non-Profiled Deep Learning-based Side-Channel attacks with Sensitivity Analysis
📺 Abstract

Deep Learning has recently been introduced as a new alternative to perform Side-Channel analysis [MPP16]. Until now, studies have been focused on applying Deep Learning techniques to perform Profiled Side-Channel attacks where an attacker has a full control of a profiling device and is able to collect a large amount of traces for different key values in order to characterize the device leakage prior to the attack. In this paper we introduce a new method to apply Deep Learning techniques in a Non-Profiled context, where an attacker can only collect a limited number of side-channel traces for a fixed unknown key value from a closed device. We show that by combining key guesses with observations of Deep Learning metrics, it is possible to recover information about the secret key. The main interest of this method is that it is possible to use the power of Deep Learning and Neural Networks in a Non-Profiled scenario. We show that it is possible to exploit the translation-invariance property of Convolutional Neural Networks [CDP17] against de-synchronized traces also during Non-Profiled side-channel attacks. In this case, we show that this method can outperform classic Non-Profiled attacks such as Correlation Power Analysis. We also highlight that it is possible to break masked implementations in black-box, without leakages combination pre-preprocessing and with no assumptions nor knowledge about the masking implementation. To carry the attack, we introduce metrics based on Sensitivity Analysis that can reveal both the secret key value as well as points of interest, such as leakages and masks locations in the traces. The results of our experiments demonstrate the interests of this new method and show that this attack can be performed in practice.

2019

TCHES

Deep Learning to Evaluate Secure RSA Implementations
📺 Abstract

This paper presents the results of several successful profiled side-channel attacks against a secure implementation of the RSA algorithm. The implementation was running on a ARM Core SC 100 completed with a certified EAL4+ arithmetic co-processor. The analyses have been conducted by three experts’ teams, each working on a specific attack path and exploiting information extracted either from the electromagnetic emanation or from the power consumption. A particular attention is paid to the description of all the steps that are usually followed during a security evaluation by a laboratory, including the acquisitions and the observations preprocessing which are practical issues usually put aside in the literature. Remarkably, the profiling portability issue is also taken into account and different device samples are involved for the profiling and testing phases. Among other aspects, this paper shows the high potential of deep learning attacks against secure implementations of RSA and raises the need for dedicated countermeasures.

2019

TCHES

Towards Globally Optimized Masking: From Low Randomness to Low Noise Rate
📺 Abstract

We improve the state-of-the-art masking schemes in two important directions. First, we propose a new masked multiplication algorithm that satisfies a recently introduced notion called Probe-Isolating Non-Interference (PINI). It captures a sufficient requirement for designing masked implementations in a trivial way, by combining PINI multiplications and linear operations performed share by share. Our improved algorithm has the best reported randomness complexity for large security orders (while the previous PINI multiplication was best for small orders). Second, we analyze the security of most existing multiplication algorithms in the literature against so-called horizontal attacks, which aim to reduce the noise of the actual leakages measured by an adversary, by combining the information of multiple target intermediate values. For this purpose, we leave the (abstract) probing model and consider a specialization of the (more realistic) noisy leakage / random probing models. Our (still partially heuristic but quantitative) analysis allows confirming the improved security of an algorithm by Battistello et al. from CHES 2016 in this setting. We then use it to propose new improved algorithms, leading to better tradeoffs between randomness complexity and noise rate, and suggesting the possibility to design efficient masked multiplication algorithms with constant noise rate in F2.

2019

TCHES

Shaping the Glitch: Optimizing Voltage Fault Injection Attacks
📺 Abstract

Voltage fault injection is a powerful active side channel attack that modifies the execution-flow of a device by creating disturbances on the power supply line. The attack typically aims at skipping security checks or generating side-channels that gradually leak sensitive data, including the firmware code. In this paper we propose a new voltage fault injection technique that generates fully arbitrary voltage glitch waveforms using off-the-shelf and low cost equipment. To show the effectiveness of our setup, we present new, unpublished firmware extraction attacks on six microcontrollers from three major manufacturers: STMicroelectronics, Texas Instruments and Renesas Electronics that, in 2016 declared a market of $1.5 billion, $800 million and $2.5 billion on units sold, respectively. Among the presented attacks, the most challenging ones exploit multiple vulnerabilities and inject over one million glitches, heavily leveraging on the performance and repeatability of the new proposed technique. We perform a thorough evaluation of arbitrary glitch waveforms by comparing the attack performance against two other major V-FI techniques in the literature. Along a responsible disclosure policy, all the vulnerabilities have been timely reported to the manufacturers.

2019

TCHES

Analysis and Improvement of Differential Computation Attacks against Internally-Encoded White-Box Implementations
📺 Abstract

White-box cryptography is the last security barrier for a cryptographic software implementation deployed in an untrusted environment. The principle of internal encodings is a commonly used white-box technique to protect block cipher implementations. It consists in representing an implementation as a network of look-up tables which are then encoded using randomly generated bijections (the internal encodings). When this approach is implemented based on nibble (i.e. 4-bit wide) encodings, the protected implementation has been shown to be vulnerable to differential computation analysis (DCA). The latter is essentially an adaptation of differential power analysis techniques to computation traces consisting of runtime information, e.g., memory accesses, of the target software. In order to thwart DCA, it has then been suggested to use wider encodings, and in particular byte encodings, at least to protect the outer rounds of the block cipher which are the prime targets of DCA.In this work, we provide an in-depth analysis of when and why DCA works. We pinpoint the properties of the target variables and the encodings that make the attack (in)feasible. In particular, we show that DCA can break encodings wider than 4-bit, such as byte encodings. Additionally, we propose new DCA-like attacks inspired from side-channel analysis techniques. Specifically, we describe a collision attack particularly effective against the internal encoding countermeasure. We also investigate mutual information analysis (MIA) which naturally applies in this context. Compared to the original DCA, these attacks are also passive and they require very limited knowledge of the attacked implementation, but they achieve significant improvements in terms of trace complexity. All the analyses of our work are experimentally backed up with various attack simulation results. We also verified the practicability of our analyses and attack techniques against a publicly available white-box AES implementation protected with byte encodings –which DCA has failed to break before– and against a “masked” white-box AES implementation –which intends to resist DCA.

2019

TCHES

Glitch-Resistant Masking Revisited
📺 Abstract

Implementing the masking countermeasure in hardware is a delicate task. Various solutions have been proposed for this purpose over the last years: we focus on Threshold Implementations (TIs), Domain-Oriented Masking (DOM), the Unified Masking Approach (UMA) and Generic Low Latency Masking (GLM). The latter generally come with innovative ideas to cope with physical defaults such as glitches. Yet, and in contrast to the situation in software-oriented masking, these schemes have not been formally proven at arbitrary security orders and their composability properties were left unclear. So far, only a 2-cycle implementation of the seminal masking scheme by Ishai, Sahai and Wagner has been shown secure and composable in the robust probing model – a variation of the probing model aimed to capture physical defaults such as glitches – for any number of shares.In this paper, we argue that this lack of proofs for TIs, DOM, UMA and GLM makes the interpretation of their security guarantees difficult as the number of shares increases. For this purpose, we first put forward that the higher-order variants of all these schemes are affected by (local or composability) security flaws in the (robust) probing model, due to insufficient refreshing. We then show that composability and robustness against glitches cannot be analyzed independently. We finally detail how these abstract flaws translate into concrete (experimental) attacks, and discuss the additional constraints robust probing security implies on the need of registers. Despite not systematically leading to improved complexities at low security orders, e.g., with respect to the required number of measurements for a successful attack, we argue that these weaknesses provide a case for the need of security proofs in the robust probing model (or a similar abstraction) at higher security orders.

2019

TCHES

Reducing a Masked Implementation’s Effective Security Order with Setup Manipulations
📺 Abstract

Couplings are a type of physical default that can violate the independence assumption needed for the secure implementation of the masking countermeasure. Two recent works by De Cnudde et al. put forward qualitatively that couplings can cause information leakages of lower order than theoretically expected. However, the (quantitative) amplitude of these lower-order leakages (e.g., measured as the amplitude of a detection metric such as Welch’s T statistic) was usually lower than the one of the (theoretically expected) dth order leakages. So the actual security level of these implementations remained unaffected. In addition, in order to make the couplings visible, the authors sometimes needed to amplify them internally (e.g., by tweaking the placement and routing or iterating linear operations on the shares). In this paper, we first show that the amplitude of low-order leakages in masked implementations can be amplified externally, by tweaking side-channel measurement setups in a way that is under control of a power analysis adversary. Our experiments put forward that the “effective security order” of both hardware (FPGA) and software (ARM-32) implementations can be reduced, leading to concrete reductions of their security level. For this purpose, we move from the detection-based analyzes of previous works to attack-based evaluations, allowing to confirm the exploitability of the lower-order leakages that we amplify. We also provide a tentative explanation for these effects based on couplings, and describe a model that can be used to predict them in function of the measurement setup’s external resistor and implementation’s supply voltage. We posit that the effective security orders observed are mainly due to “externally-amplified couplings” that can be systematically exploited by actual adversaries.

2019

TCHES

Multi-Tuple Leakage Detection and the Dependent Signal Issue
📺 Abstract

Leakage detection is a common tool to quickly assess the security of a cryptographic implementation against side-channel attacks. The Test Vector Leakage Assessment (TVLA) methodology using Welch’s t-test, proposed by Cryptography Research, is currently the most popular example of such tools, thanks to its simplicity and good detection speed compared to attack-based evaluations. However, as any statistical test, it is based on certain assumptions about the processed samples and its detection performances strongly depend on parameters like the measurement’s Signal-to-Noise Ratio (SNR), their degree of dependency, and their density, i.e., the ratio between the amount of informative and non-informative points in the traces. In this paper, we argue that the correct interpretation of leakage detection results requires knowledge of these parameters which are a priori unknown to the evaluator, and, therefore, poses a non-trivial challenge to evaluators (especially if restricted to only one test). For this purpose, we first explore the concept of multi-tuple detection, which is able to exploit differences between multiple informative points of a trace more effectively than tests relying on the minimum p-value of concurrent univariate tests. To this end, we map the common Hotelling’s T2-test to the leakage detection setting and, further, propose a specialized instantiation of it which trades computational overheads for a dependency assumption. Our experiments show that there is not one test that is the optimal choice for every leakage scenario. Second, we highlight the importance of the assumption that the samples at each point in time are independent, which is frequently considered in leakage detection, e.g., with Welch’s t-test. Using simulated and practical experiments, we show that (i) this assumption is often violated in practice, and (ii) deviations from it can affect the detection performances, making the correct interpretation of the results more difficult. Finally, we consolidate our findings by providing guidelines on how to use a combination of established and newly-proposed leakage detection tools to infer the measurements parameters. This enables a better interpretation of the tests’ results than the current state-of-the-art (yet still relying on heuristics for the most challenging evaluation scenarios).

2019

TCHES

M&M: Masks and Macs against Physical Attacks
📺 Abstract

Cryptographic implementations on embedded systems need to be protected against physical attacks. Today, this means that apart from incorporating countermeasures against side-channel analysis, implementations must also withstand fault attacks and combined attacks. Recent proposals in this area have shown that there is a big tradeoff between the implementation cost and the strength of the adversary model. In this work, we introduce a new combined countermeasure M&M that combines Masking with information-theoretic MAC tags and infective computation. It works in a stronger adversary model than the existing scheme ParTI, yet is a lot less costly to implement than the provably secure MPC-based scheme CAPA. We demonstrate M&M with a SCA- and DFA-secure implementation of the AES block cipher. We evaluate the side-channel leakage of the second-order secure design with a non-specific t-test and use simulation to validate the fault resistance.

2019

TCHES

Return of the Hidden Number Problem. A Widespread and Novel Key Extraction Attack on ECDSA and DSA
📺 Abstract

Side channels have long been recognized as a threat to the security of cryptographic applications. Implementations can unintentionally leak secret information through many channels, such as microarchitectural state changes in processors, changes in power consumption, or electromagnetic radiation. As a result of these threats, many implementations have been hardened to defend against these attacks. Despite these mitigations, this work presents a novel side-channel attack against ECDSA and DSA. The attack targets a common implementation pattern that is found in many cryptographic libraries. In fact, about half of the libraries that were tested exhibited the vulnerable pattern. This pattern is exploited in a full proof of concept attack against OpenSSL, demonstrating that it is possible to extract a 256-bit ECDSA private key using a simple cache attack after observing only a few thousand signatures. The target of this attack is a previously unexplored part of (EC)DSA signature generation, which explains why mitigations are lacking and the issue is so widespread. Finally, estimates are provided for the minimum number of signatures needed to perform the attack, and countermeasures are suggested to protect against this attack.

2019

TCHES

Error Amplification in Code-based Cryptography
📺 Abstract

Code-based cryptography is one of the main techniques enabling cryptographic primitives in a post-quantum scenario. In particular, the MDPC scheme is a basic scheme from which many other schemes have been derived. These schemes rely on iterative decoding in the decryption process and thus have a certain small probability p of having a decryption (decoding) error.In this paper we show a very fundamental and important property of code-based encryption schemes. Given one initial error pattern that fails to decode, the time needed to generate another message that fails to decode is strictly much less than 1/p. We show this by developing a method for fast generation of undecodable error patterns (error pattern chaining), which additionally proves that a measure of closeness in ciphertext space can be exploited through its strong linkage to the difficulty of decoding these messages. Furthermore, if side-channel information is also available (time to decode), then the initial error pattern no longer needs to be given since one can be easily generated in this case.These observations are fundamentally important because they show that a, say, 128- bit encryption scheme is not inherently safe from reaction attacks even if it employs a decoder with a failure rate of 2−128. In fact, unless explicit protective measures are taken, having a failure rate at all – of any magnitude – can pose a security problem because of the error amplification effect of our method.A key-recovery reaction attack was recently shown on the MDPC scheme as well as similar schemes, taking advantage of decoding errors in order to recover the secret key. It was also shown that knowing the number of iterations in the iterative decoding step, which could be received in a timing attack, would also enable and enhance such an attack. In this paper we apply our error pattern chaining method to show how to improve the performance of such reaction attacks in the CPA case. We show that after identifying a single decoding error (or a decoding step taking more time than expected in a timing attack), we can adaptively create new error patterns that have a much higher decoding error probability than for a random error. This leads to a significant improvement of the attack based on decoding errors in the CPA case and it also gives the strongest known attack on MDPC-like schemes, both with and without using side-channel information.

2019

TCHES

Implementing RLWE-based Schemes Using an RSA Co-Processor
📺 Abstract

We repurpose existing RSA/ECC co-processors for (ideal) lattice-based cryptography by exploiting the availability of fast long integer multiplication. Such co-processors are deployed in smart cards in passports and identity cards, secured microcontrollers and hardware security modules (HSM). In particular, we demonstrate an implementation of a variant of the Module-LWE-based Kyber Key Encapsulation Mechanism (KEM) that is tailored for high performance on a commercially available smart card chip (SLE 78). To benefit from the RSA/ECC co-processor we use Kronecker substitution in combination with schoolbook and Karatsuba polynomial multiplication. Moreover, we speed-up symmetric operations in our Kyber variant using the AES co-processor to implement a PRNG and a SHA-256 co-processor to realise hash functions. This allows us to execute CCA-secure Kyber768 key generation in 79.6 ms, encapsulation in 102.4 ms and decapsulation in 132.7 ms.

2019

TCHES

3-Share Threshold Implementation of AES S-box without Fresh Randomness
📺 Abstract

Threshold implementation is studied as a countermeasure against sidechannel attack. There had been no threshold implementation for the AES and Keccak S-boxes that satisfies an important property called uniformity. In the conventional implementations, intermediate values are remasked to compensate for the lack of uniformity. The remasking consumes thousands of fresh random bits and its implementation cost is a serious concern. Daemen recently proposed a 3-share uniform threshold implementation of the Keccak S-box. This is enabled by a new technique called the changing of the guards which can be applied to any invertible functions. Subsequently, Wegener et al. proposed a 4-share threshold implementation of the AES S-box based on the changing of the guards technique. However, a 3-share threshold implementation of AES S-box remains open. The difficulty stays in 2-input multiplication, used in decomposed S-box representations, which is non-invertible because of different input and output sizes. In this study, this problem is addressed by introducing a certain generalization of the changing of the guards technique. The proposed method provides a generic way to construct a uniform sharing for a target function having different input and output sizes. The key idea is to transform a target function into an invertible one by adding additional inputs and outputs. Based on the proposed technique, the first 3-share threshold implementation of AES S-box without fresh randomness is presented. Performance evaluation and simulation-based leakage assessment of the implementation are also presented.

2019

TCHES

Secure Physical Enclosures from Covers with Tamper-Resistance
📺 Abstract

Ensuring physical security of multiple-chip embedded systems on a PCB is challenging, since the attacker can control the device in a hostile environment. To detect physical intruders as part of a layered approach to security, it is common to create a physical security boundary that is difficult to penetrate or remove, e.g., enclosures created from tamper-respondent envelopes or covers. Their physical integrity is usually checked by active sensing, i.e., a battery-backed circuit continuously monitors the enclosure. However, adoption is often hampered by the disadvantages of a battery and due to specialized equipment which is required to create the enclosure. In contrast, we present a batteryless tamper-resistant cover made from standard flexPCB technology, i.e., a commercially widespread, scalable, and proven technology. The cover comprises a fine mesh of electrodes and an evaluation unit underneath the cover checks their integrity by detecting short and open circuits. Additionally, it measures the capacitances between the electrodes of the mesh. Once its preliminary integrity is confirmed, a cryptographic key is derived from the capacitive measurements representing a PUF, to decrypt and authenticate sensitive data of the enclosed system. We demonstrate the feasibility of our concept, provide details on the layout, electrical properties of the cover, and explain the underlying security architecture. Practical results including statistics over a set of 115 flexPCB covers, physical attacks, and environmental testing support our design rationale. Hence, our work opens up a new direction of counteracting physical tampering without the need of batteries, while aiming at a physical security level comparable to FIPS 140-2 level 3.

2019

TCHES

Practical Evaluation of Protected Residue Number System Scalar Multiplication
📺 Abstract

The Residue Number System (RNS) arithmetic is gaining grounds in public key cryptography, because it offers fast, efficient and secure implementations over large prime fields or rings of integers. In this paper, we propose a generic, thorough and analytic evaluation approach for protected scalar multiplication implementations with RNS and traditional Side Channel Attack (SCA) countermeasures in an effort to assess the SCA resistance of RNS. This paper constitutes the first robust evaluation of RNS software for Elliptic Curve Cryptography against electromagnetic (EM) side-channel attacks. Four different countermeasures, namely scalar and point randomization, random base permutations and random moduli operation sequence, are implemented and evaluated using the Test Vector Leakage Assessment (TVLA) and template attacks. More specifically, variations of RNS-based Montgomery Powering Ladder scalar multiplication algorithms are evaluated on an ARM Cortex A8 processor using an EM probe for acquisition of the traces. We show experimentally and theoretically that new bounds should be put forward when TVLA evaluations on public key algorithms are performed. On the security of RNS, our data and location dependent template attacks show that even protected implementations are vulnerable to these attacks. A combination of RNS-based countermeasures is the best way to protect against side-channel leakage.

2019

TCHES

Improving CEMA using Correlation Optimization
📺 Abstract

Sensitive cryptographic information, e.g. AES secret keys, can be extracted from the electromagnetic (EM) leakages unintentionally emitted by a device using techniques such as Correlation Electromagnetic Analysis (CEMA). In this paper, we introduce Correlation Optimization (CO), a novel approach that improves CEMA attacks by formulating the selection of useful EM leakage samples in a trace as a machine learning optimization problem. To this end, we propose the correlation loss function, which aims to maximize the Pearson correlation between a set of EM traces and the true AES key during training. We show that CO works with high-dimensional and noisy traces, regardless of time-domain trace alignment and without requiring prior knowledge of the power consumption characteristics of the cryptographic hardware. We evaluate our approach using the ASCAD benchmark dataset and a custom dataset of EM leakages from an Arduino Duemilanove, captured with a USRP B200 SDR. Our results indicate that the masked AES implementation used in all three ASCAD datasets can be broken with a shallow Multilayer Perceptron model, whilst requiring only 1,000 test traces on average. A similar methodology was employed to break the unprotected AES implementation from our custom dataset, using 22,000 unaligned and unfiltered test traces.

2019

TCHES

Fully Automated Differential Fault Analysis on Software Implementations of Block Ciphers
📺 Abstract

Differential Fault Analysis (DFA) is considered as the most popular fault analysis method. While there are techniques that provide a fault analysis automation on the cipher level to some degree, it can be shown that when it comes to software implementations, there are new vulnerabilities, which cannot be found by observing the cipher design specification.This work bridges the gap by providing a fully automated way to carry out DFA on assembly implementations of symmetric block ciphers. We use a customized data flow graph to represent the program and develop a novel fault analysis methodology to capture the program behavior under faults. We establish an effective description of DFA as constraints that are passed to an SMT solver. We create a tool that takes assembly code as input, analyzes the dependencies among instructions, automatically attacks vulnerable instructions using SMT solver and outputs the attack details that recover the last round key (and possibly the earlier keys). We support our design with evaluations on lightweight ciphers SIMON, SPECK, and PRIDE, and a current NIST standard, AES. By automated assembly analysis, we were able to find new efficient DFA attacks on SPECK and PRIDE, exploiting implementation specific vulnerabilities, and previously published DFA on SIMON and AES. Moreover, we present a novel DFA on multiplication operation that has never been shown for symmetric block ciphers before. Our experimental evaluation also shows reasonable execution times that are scalable to current cipher designs and can easily outclass the manual analysis. Moreover, we present a method to check the countermeasure-protected implementations in a way that helps implementers to decide how many rounds should be protected. We note that this is the first work that automatically carries out DFA on cipher implementations without any plaintext or ciphertext information and therefore, can be generally applied to any input data to the cipher.

2019

TCHES

The Curse of Class Imbalance and Conflicting Metrics with Machine Learning for Side-channel Evaluations
📺 Abstract

We concentrate on machine learning techniques used for profiled sidechannel analysis in the presence of imbalanced data. Such scenarios are realistic and often occurring, for instance in the Hamming weight or Hamming distance leakage models. In order to deal with the imbalanced data, we use various balancing techniques and we show that most of them help in mounting successful attacks when the data is highly imbalanced. Especially, the results with the SMOTE technique are encouraging, since we observe some scenarios where it reduces the number of necessary measurements more than 8 times. Next, we provide extensive results on comparison of machine learning and side-channel metrics, where we show that machine learning metrics (and especially accuracy as the most often used one) can be extremely deceptive. This finding opens a need to revisit the previous works and their results in order to properly assess the performance of machine learning in side-channel analysis.

2019

TCHES

New Insights to Key Derivation for Tamper-Evident Physical Unclonable Functions
📺 Abstract

Several publications presented tamper-evident Physical Unclonable Functions (PUFs) for secure storage of cryptographic keys and tamper-detection. Unfortunately, previously published PUF-based key derivation schemes do not sufficiently take into account the specifics of the underlying application, i.e., an attacker that tampers with the physical parameters of the PUF outside of an idealized noise error model. This is a notable extension of existing schemes for PUF key derivation, as they are typically concerned about helper data leakage, i.e., by how much the PUF’s entropy is diminished when gaining access to its helper data.To address the specifics of tamper-evident PUFs, we formalize the aspect of tamper-sensitivity, thereby providing a new tool to rate by how much an attacker is allowed to tamper with the PUF. This complements existing criteria such as effective number of secret bits for entropy and failure rate for reliability. As a result, it provides a fair comparison among different schemes and independent of the PUF implementation, as its unit is based on the noise standard deviation of the underlying PUF measurement. To overcome the limitations of previous schemes, we then propose an Error-Correcting Code (ECC) based on the Lee metric, i.e., a distance metric well-suited to describe the distance between q-ary symbols as output from an equidistant quantization, i.e., a higher-order alphabet PUF. This novel approach is required, as the underlying symbols’ bits are not i.i.d. which hinders applying previous state-of-the-art approaches. We present the concept for our scheme and demonstrate its feasibility based on an empirical PUF distribution. The benefits of our approach are an increase by over 21% in effective secret bit compared to previous approaches based on equidistant quantization. At the same time, we improve tamper-sensitivity compared to an equiprobable quantization while ensuring similar reliability and entropy. Hence, this work opens up a new direction of how to interpret the PUF output and details a practically relevant scheme outperforming all previous constructions.

2019

TCHES

Fast, Furious and Insecure: Passive Keyless Entry and Start Systems in Modern Supercars
📺 Abstract

The security of immobiliser and Remote Keyless Entry systems has been extensively studied over many years. Passive Keyless Entry and Start systems, which are currently deployed in luxury vehicles, have not received much attention besides relay attacks. In this work we fully reverse engineer a Passive Keyless Entry and Start system and perform a thorough analysis of its security.Our research reveals several security weaknesses. Specifically, we document the use of an inadequate proprietary cipher using 40-bit keys, the lack of mutual authentication in the challenge-response protocol, no firmware readout protection features enabled and the absence of security partitioning.In order to validate our findings, we implement a full proof of concept attack allowing us to clone a Tesla Model S key fob in a matter of seconds with low cost commercial off the shelf equipment. Our findings most likely apply to other manufacturers of luxury vehicles including McLaren, Karma and Triumph motorcycles as they all use the same system developed by Pektron.

2019

TCHES

Covert Gates: Protecting Integrated Circuits with Undetectable Camouflaging
📺 Abstract

Integrated circuit (IC) camouflaging has emerged as a promising solution for protecting semiconductor intellectual property (IP) against reverse engineering. Existing methods of camouflaging are based on standard cells that can assume one of many Boolean functions, either through variation of transistor threshold voltage or contact configurations. Unfortunately, such methods lead to high area, delay and power overheads, and are vulnerable to invasive as well as non-invasive attacks based on Boolean satisfiability/VLSI testing. In this paper, we propose, fabricate, and demonstrate a new cell camouflaging strategy, termed as ‘covert gate’ that leverages doping and dummy contacts to create camouflaged cells that are indistinguishable from regular standard cells under modern imaging techniques. We perform a comprehensive security analysis of covert gate, and show that it achieves high resiliency against SAT and test-based attacks at very low overheads. We also derive models to characterize the covert cells, and develop measures to incorporate them into a gate-level design. Simulation results of overheads and attacks are presented on benchmark circuits.

2019

TCHES

Consolidating Security Notions in Hardware Masking
📺 Abstract

In this paper, we revisit the security conditions of masked hardware implementations. We describe a new, succinct, information-theoretic condition called d-glitch immunity which is both necessary and sufficient for security in the presence of glitches. We show that this single condition includes, but is not limited to, previous security notions such as those used in higher-order threshold implementations and in abstractions using ideal gates. As opposed to these previously known necessary conditions, our new condition is also sufficient. On the other hand, it excludes avoidable notions such as uniformity. We also treat the notion of (strong) noninterference from an information-theoretic point-of-view in order to unify the different security concepts and pave the way to the verification of composability in the presence of glitches. We conclude the paper by demonstrating how the condition can be used as an efficient and highly generic flaw detection mechanism for a variety of functions and schemes based on different operations.

2019

TCHES

SMT Attack: Next Generation Attack on Obfuscated Circuits with Capabilities and Performance Beyond the SAT Attacks
📺 Abstract

In this paper, we introduce the Satisfiability Modulo Theory (SMT) attack on obfuscated circuits. The proposed attack is the superset of Satisfiability (SAT) attack, with many additional features. It uses one or more theory solvers in addition to its internal SAT solver. For this reason, it is capable of modeling far more complex behaviors and could formulate much stronger attacks. In this paper, we illustrate that the use of theory solvers enables the SMT to carry attacks that are not possible by SAT formulated attacks. As an example of its capabilities, we use the SMT attack to break a recent obfuscation scheme that uses key values to alter delay properties (setup and hold time) of a circuit to remain SAT hard. Considering that the logic delay is not a Boolean logical property, the targeted obfuscation mechanism is not breakable by a SAT attack. However, in this paper, we illustrate that the proposed SMT attack, by deploying a simple graph theory solver, can model and break this obfuscation scheme in few minutes. We describe how the SMT attack could be used in one of four different attack modes: (1) We explain how SMT attack could be reduced to a SAT attack, (2) how the SMT attack could be carried out in Eager, and (3) Lazy approach, and finally (4) we introduce the Accelerated SMT (AccSMT) attack that offers significant speed-up to SAT attack. Additionally, we explain how AccSMT attack could be used as an approximate attack when facing SMT-Hard obfuscation schemes.

2019

TCHES

Make Some Noise. Unleashing the Power of Convolutional Neural Networks for Profiled Side-channel Analysis
📺 Abstract

Profiled side-channel analysis based on deep learning, and more precisely Convolutional Neural Networks, is a paradigm showing significant potential. The results, although scarce for now, suggest that such techniques are even able to break cryptographic implementations protected with countermeasures. In this paper, we start by proposing a new Convolutional Neural Network instance able to reach high performance for a number of considered datasets. We compare our neural network with the one designed for a particular dataset with masking countermeasure and we show that both are good designs but also that neither can be considered as a superior to the other one.Next, we address how the addition of artificial noise to the input signal can be actually beneficial to the performance of the neural network. Such noise addition is equivalent to the regularization term in the objective function. By using this technique, we are able to reduce the number of measurements needed to reveal the secret key by orders of magnitude for both neural networks. Our new convolutional neural network instance with added noise is able to break the implementation protected with the random delay countermeasure by using only 3 traces in the attack phase. To further strengthen our experimental results, we investigate the performance with a varying number of training samples, noise levels, and epochs. Our findings show that adding noise is beneficial throughout all training set sizes and epochs.

2019

TCHES

NTTRU: Truly Fast NTRU Using NTT
📺 Abstract

We present NTTRU – an IND-CCA2 secure NTRU-based key encapsulation scheme that uses the number theoretic transform (NTT) over the cyclotomic ring Z7681[X]/(X768−X384+1) and produces public keys and ciphertexts of approximately 1.25 KB at the 128-bit security level. The number of cycles on a Skylake CPU of our constant-time AVX2 implementation of the scheme for key generation, encapsulation and decapsulation is approximately 6.4K, 6.1K, and 7.9K, which is more than 30X, 5X, and 8X faster than these respective procedures in the NTRU schemes that were submitted to the NIST post-quantum standardization process. These running times are also, by a large margin, smaller than those for all the other schemes in the NIST process as well as the KEMs based on elliptic curve Diffie-Hellman. We additionally give a simple transformation that allows one to provably deal with small decryption errors in OW-CPA encryption schemes (such as NTRU) when using them to construct an IND-CCA2 key encapsulation.

2019

TCHES

Static Power SCA of Sub-100 nm CMOS ASICs and the Insecurity of Masking Schemes in Low-Noise Environments
📺 Abstract

Semiconductor technology scaling faced tough engineering challenges while moving towards and beyond the deep sub-micron range. One of the most demanding issues, limiting the shrinkage process until the present day, is the difficulty to control the leakage currents in nanometer-scaled field-effect transistors. Previous articles have shown that this source of energy dissipation, at least in case of digital CMOS logic, can successfully be exploited as a side-channel to recover the secrets of cryptographic implementations. In this work, we present the first fair technology comparison with respect to static power side-channel measurements on real silicon and demonstrate that the effect of down-scaling on the potency of this security threat is huge. To this end, we designed two ASICs in sub-100nm CMOS nodes (90 nm, 65 nm) and got them fabricated by one of the leading foundries. Our experiments, which we performed at different operating conditions, show consistently that the ASIC technology with the smaller minimum feature size (65 nm) indeed exhibits substantially more informative leakages (factor of ~10) than the 90nm one, even though all targeted instances have been derived from identical RTL code. However, the contribution of this work extends well beyond a mere technology comparison. With respect to the real-world impact of static power attacks, we present the first realistic scenarios that allow to perform a static power side-channel analysis (including noise reduction) without requiring control over the clock signal of the target. Furthermore, as a follow-up to some proof-of-concept work indicating the vulnerability of masking schemes to static powerattacks, we perform a detailed study on how the reduction of the noise level in static leakage measurements affects the security provided by masked implementations. As a result of this study, we do not only find out that the threat for masking schemes is indeed real, but also that common leakage assessment techniques, such as the Welch’s t-test, together with essentially any moment-based analysis of the leakage traces, is simply not sufficient in low-noise contexts. In fact, we are able to show that either a conversion (resp. compression) of the leakage order or the recently proposed X2 test need to be considered in assessment and attack to avoid false negatives.

2019

TCHES

Exploring the Effect of Device Aging on Static Power Analysis Attacks
📺 Abstract

Vulnerability of cryptographic devices to side-channel analysis attacks, and in particular power analysis attacks has been extensively studied in the recent years. Among them, static power analysis attacks have become relevant with moving towards smaller technology nodes for which the static power is comparable to the dynamic power of a chip, or even dominant in future technology generations. The magnitude of the static power of a chip depends on the physical characteristics of transistors (e.g., the dimensions) as well as operating conditions (e.g., the temperature) and the electrical specifications such as the threshold voltage. In fact, the electrical specifications of transistors deviate from their originally intended ones during device lifetime due to aging mechanisms. Although device aging has been extensively investigated from reliability point of view, the impact of aging on the security of devices, and in particular on the vulnerability of devices to power analysis attacks are yet to be considered.This paper fills the gap and investigates how device aging can affect the susceptibility of a chip exposed to static power analysis attacks. To this end, we conduct both, simulation and practical experiments on real silicon. The experimental results are extracted from a realization of the PRESENT cipher fabricated using a 65nm commercial standard cell library. The results show that the amount of exploitable leakage through the static power consumption as a side channel is reduced when the device is aged. This can be considered as a positive development which can (even slightly) harden such static power analysis attacks. Additionally, this result is of great interest to static power side-channel adversaries since state-of-the-art leakage current measurements are conducted over long time periods under increased working temperatures and supply voltages to amplify the exploitable information, which certainly fuels aging-related device degradation.

2019

TCHES

Software Toolkit for HFE-based Multivariate Schemes
📺 Abstract

In 2017, NIST shook the cryptographic world by starting a process for standardizing post-quantum cryptography. Sixty-four submissions have been considered for the first round of the on-going NIST Post-Quantum Cryptography (PQC) process. Multivariate cryptography is a classical post-quantum candidate that turns to be the most represented in the signature category. At this stage of the process, it is of primary importance to investigate efficient implementations of the candidates. This article presents MQsoft, an efficient library which permits to implement HFE-based multivariate schemes submitted to the NIST PQC process such as GeMSS, Gui and DualModeMS. The library is implemented in C targeting Intel 64-bit processors and using avx2 set instructions. We present performance results for our library and its application to GeMSS, Gui and DualModeMS. In particular, we optimize several crucial parts for these schemes. These include root finding for HFE polynomials and evaluation of multivariate quadratic systems in F2. We propose a new method which accelerates root finding for specific HFE polynomials by a factor of two. For GeMSS and Gui, we obtain a speed-up of a factor between 2 and 19 for the keypair generation, between 1.2 and 2.5 for the signature generation, and between 1.6 and 2 for the verifying process. We have also improved the arithmetic in F2n by a factor of 4 compared to the NTL library. Moreover, a large part of our implementation is protected against timing attacks.

2019

TCHES

Leaky Noise: New Side-Channel Attack Vectors in Mixed-Signal IoT Devices
📺 Abstract

Microcontrollers and SoC devices have widely been used in Internet of Things applications. This also brings the question whether they lead to new security threats unseen in traditional computing systems. In fact, almost all modern SoC chips, particularly in the IoT domain, contain both analog and digital components, for various sensing and transmission tasks. Traditional remote-accessible online systems do not have this property, which can potentially become a security vulnerability. In this paper we demonstrate that such mixed-signal components, namely ADCs, expose a new security threat that allows attackers with ADC access to deduce the activity of a CPU in the system. To prove the leakage, we perform leakage assessment on three individual microcontrollers from two different vendors with various ADC settings. After showing a correlation of CPU activity with ADC noise, we continue with a leakage assessment of modular exponentiation and AES. It is shown that for all of these devices, leakage occurs for at least one algorithm and configuration of the ADC. Finally, we show a full key recovery attack on AES that works despite of the limited ADC sampling rate. These results imply that even remotely accessible microcontroller systems should be equipped with proper countermeasures against power analysis attacks, or restrict access to ADC data.

2019

TCHES

Fast constant-time gcd computation and modular inversion
📺 Abstract

This paper introduces streamlined constant-time variants of Euclid’s algorithm, both for polynomial inputs and for integer inputs. As concrete applications, this paper saves time in (1) modular inversion for Curve25519, which was previously believed to be handled much more efficiently by Fermat’s method, and (2) key generation for the ntruhrss701 and sntrup4591761 lattice-based cryptosystems.

2019

TCHES

Security on Plastics: Fake or Real?
📺 Abstract

Electronic devices on plastic foil, also referred to as flexible electronics, are making their way into mainstream applications. In the near future, flexible electronic labels can be embedded in smart blisters, but also used as mainstream technology for flexible medical patches. A key technology for flexible electronics is based on thin-film transistors, which have the potential to be manufactured at low cost, making them an ideal candidate for these applications. Yet, up to now, no-one is taking digital security into account in the design of flexible electronics.In this paper, we present, to our knowledge, the first cryptographic core on plastic foil. Two main research challenges arise. The first challenge is related to the reliability of the circuit, which typically decreases when the circuit area increases. By integrating cryptographic modules, we explore the limits of the technology, since the smallest lightweight block ciphers feature a larger area than the largest digital circuit on flex foil reported up to now. The second challenge is related to key hiding. The relatively large features on the chip and the fact that electronic chips on plastics are used as bare dies, i.e. they are not packaged, make it easy to read out the value of the stored secret key. Because there is no dedicated non-volatile memory technology yet, existing methods for writing data to the flexible chip after fabrication are based on wire cutting with a laser or inkjet printing. With these techniques, however, it is extremely easy to “see” the value of the secret key under a microscope. We propose a novel solution that allows us to invisibly program the key after fabrication.

2019

TCHES

Sapphire: A Configurable Crypto-Processor for Post-Quantum Lattice-based Protocols
📺 Abstract

Public key cryptography protocols, such as RSA and elliptic curve cryptography, will be rendered insecure by Shor’s algorithm when large-scale quantum computers are built. Cryptographers are working on quantum-resistant algorithms, and lattice-based cryptography has emerged as a prime candidate. However, high computational complexity of these algorithms makes it challenging to implement lattice-based protocols on low-power embedded devices. To address this challenge, we present Sapphire – a lattice cryptography processor with configurable parameters. Efficient sampling, with a SHA-3-based PRNG, provides two orders of magnitude energy savings; a single-port RAM-based number theoretic transform memory architecture is proposed, which provides 124k-gate area savings; while a low-power modular arithmetic unit accelerates polynomial computations. Our test chip was fabricated in TSMC 40nm low-power CMOS process, with the Sapphire cryptographic core occupying 0.28 mm2 area consisting of 106k logic gates and 40.25 KB SRAM. Sapphire can be programmed with custom instructions for polynomial arithmetic and sampling, and it is coupled with a low-power RISC-V micro-processor to demonstrate NIST Round 2 lattice-based CCA-secure key encapsulation and signature protocols Frodo, NewHope, qTESLA, CRYSTALS-Kyber and CRYSTALS-Dilithium, achieving up to an order of magnitude improvement in performance and energy-efficiency compared to state-of-the-art hardware implementations. All key building blocks of Sapphire are constant-time and secure against timing and simple power analysis side-channel attacks. We also discuss how masking-based DPA countermeasures can be implemented on the Sapphire core without any changes to the hardware.

2019

TCHES

Electromagnetic Information Extortion from Electronic Devices Using Interceptor and Its Countermeasure
📺 Abstract

The problem of information leakage through electromagnetic waves for various devices has been extensively discussed in literature. Conventionally, devices that are under such a threat suffer from potential electromagnetic information leakage during their operation. Further, the information inside the devices can be obtained by monitoring the electromagnetic waves leaking at the boundaries of the devices. The leakage of electromagnetic waves, however, was not observed for some devices, and such devices were not the target of the threat discussed above. In light of this circumstance, this paper discusses an “interceptor” that forces the leakage of information through electromagnetic waves, even from devices in which potential electromagnetic leakage does not occur. The proposed interceptor is a small circuit consisting of an affordable semiconductor chip and wiring and is powered by electromagnetic waves that irradiate from the outside of a device as its driving energy. The distance at which information is obtained is controlled by increasing the intensity of the irradiated electromagnetic waves. The paper presents the structure of the circuit for implementing the proposed interceptor to be used in major input–output devices and cryptographic modules, mounting a pathway designed on the basis of the construction method onto each device. Moreover, it is shown that it is possible to forcefully cause information leakage through electromagnetic waves. To detect the aforementioned threat, the paper also focuses on the changes in a device itself and the surrounding electromagnetic environment as a result of mounting an interceptor and considers a method of detecting an interceptor by both passive and active monitoring methods.

2019

TCHES

New Circuit Minimization Techniques for Smaller and Faster AES SBoxes
📺 Abstract

In this paper we consider various methods and techniques to find the smallest circuit realizing a given linear transformation on n input signals and m output signals, with a constraint of a maximum depth, maxD, of the circuit. Additional requirements may include that input signals can arrive to the circuit with different delays, and output signals may be requested to be ready at a different depth. We apply these methods and also improve previous results in order to find hardware circuits for forward, inverse, and combined AES SBoxes, and for each of them we provide the fastest and smallest combinatorial circuits. Additionally, we propose a novel technique with “floating multiplexers” to minimize the circuit for the combined SBox, where we have two different linear matrices (forward and inverse) combined with multiplexers. The resulting AES SBox solutions are the fastest and smallest to our knowledge.

2019

TCHES

On-Device Power Analysis Across Hardware Security Domains.
📺 Abstract

Side-channel power analysis is a powerful method of breaking secure cryptographic algorithms, but typically power analysis is considered to require specialized measurement equipment on or near the device. Assuming an attacker first gained the ability to run code on the unsecure side of a device, they could trigger encryptions and use the on-board ADC to capture power traces of that hardware encryption engine.This is demonstrated on a SAML11 which contains a M23 core with a TrustZone-M implementation as the hardware security barrier. This attack requires 160 × 106 traces, or approximately 5 GByte of data. This attack does not use any external measurement equipment, entirely performing the power analysis using the ADC on-board the microcontroller under attack. The attack is demonstrated to work both from the non-secure and secure environment on the chip, being a demonstration of a cross-domain power analysis attack.To understand the effect of noise and sample rate reduction, an attack is mounted on the SAML11 hardware AES peripheral using classic external equipment, and results are compared for various sample rates and hardware setups. A discussion on how users of this device can help prevent such remote attacks is also presented, along with metrics that can be used in evaluating other devices. Complete copies of all recorded power traces and scripts used by the authors are publicly presented.

2019

TCHES

Fast and simple constant-time hashing to the BLS12-381 elliptic curve
📺 Abstract

Pairing-friendly elliptic curves in the Barreto-Lynn-Scott family are seeing a resurgence in popularity because of the recent result of Kim and Barbulescu that improves attacks against other pairing-friendly curve families. One particular Barreto-Lynn-Scott curve, called BLS12-381, is the locus of significant development and deployment effort, especially in blockchain applications. This effort has sparked interest in using the BLS12-381 curve for BLS signatures, which requires hashing to one of the groups of the bilinear pairing defined by BLS12-381.While there is a substantial body of literature on the problem of hashing to elliptic curves, much of this work does not apply to Barreto-Lynn-Scott curves. Moreover, the work that does apply has the unfortunate property that fast implementations are complex, while simple implementations are slow.In this work, we address these issues. First, we show a straightforward way of adapting the “simplified SWU” map of Brier et al. to BLS12-381. Second, we describe optimizations to this map that both simplify its implementation and improve its performance; these optimizations may be of interest in other contexts. Third, we implement and evaluate. We find that our work yields constant-time hash functions that are simple to implement, yet perform within 9% of the fastest, non–constant-time alternatives, which require much more complex implementations.

2019

TCHES

Novel Side-Channel Attacks on Quasi-Cyclic Code-Based Cryptography
📺 Abstract

Chou suggested a constant-time implementation for quasi-cyclic moderatedensity parity-check (QC-MDPC) code-based cryptography to mitigate timing attacks at CHES 2016. This countermeasure was later found to become vulnerable to a differential power analysis (DPA) in private syndrome computation, as described by Rossi et al. at CHES 2017. The proposed DPA, however, still could not completely recover accurate secret indices, requiring further solving linear equations to obtain entire secret information. In this paper, we propose a multiple-trace attack which enables to completely recover accurate secret indices. We further propose a singletrace attack which can even work when using ephemeral keys or applying Rossi et al.’s DPA countermeasures. Our experiments show that the BIKE and LEDAcrypt may become vulnerable to our proposed attacks. The experiments are conducted using power consumption traces measured from ChipWhisperer-Lite XMEGA (8-bit processor) and ChipWhisperer UFO STM32F3 (32-bit processor) target boards.

2019

TCHES

Cache-Timing Attacks on RSA Key Generation
📺 Abstract

During the last decade, constant-time cryptographic software has quickly transitioned from an academic construct to a concrete security requirement for real-world libraries. Most of OpenSSL’s constant-time code paths are driven by cryptosystem implementations enabling a dedicated flag at runtime. This process is perilous, with several examples emerging in the past few years of the flag either not being set or software defects directly mishandling the flag. In this work, we propose a methodology to analyze security-critical software for side-channel insecure code path traversal. Applying our methodology to OpenSSL, we identify three new code paths during RSA key generation that potentially leak critical algorithm state. Exploiting one of these leaks, we design, implement, and mount a single trace cache-timing attack on the GCD computation step. We overcome several hurdles in the process, including but not limited to: (1) granularity issues due to word-size operands to the GCD function; (2) bulk processing of desynchronized trace data; (3) non-trivial error rate during information extraction; and (4) limited high-confidence information on the modulus factors. Formulating lattice problem instances after obtaining and processing this limited information, our attack achieves roughly a 27% success rate for key recovery using the empirical data from 10K trials.

2019

TCHES

The Interpose PUF: Secure PUF Design against State-of-the-art Machine Learning Attacks
📺 Abstract

The design of a silicon Strong Physical Unclonable Function (PUF) that is lightweight and stable, and which possesses a rigorous security argument, has been a fundamental problem in PUF research since its very beginnings in 2002. Various effective PUF modeling attacks, for example at CCS 2010 and CHES 2015, have shown that currently, no existing silicon PUF design can meet these requirements. In this paper, we introduce the novel Interpose PUF (iPUF) design, and rigorously prove its security against all known machine learning (ML) attacks, including any currently known reliability-based strategies that exploit the stability of single CRPs (we are the first to provide a detailed analysis of when the reliability based CMA-ES attack is successful and when it is not applicable). Furthermore, we provide simulations and confirm these in experiments with FPGA implementations of the iPUF, demonstrating its practicality. Our new iPUF architecture so solves the currently open problem of constructing practical, silicon Strong PUFs that are secure against state-of-the-art ML attacks.

2019

TOSC

CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks
📺 Abstract

Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of cryptanalytic security. This picture has been changed by the introduction of PICARO, ZORRO, and FIDES, where efficient protection against Side-Channel Analysis (SCA) attacks has been considered in their design. In this work we present the tweakable block cipher CRAFT: the efficient protection of its implementations against Differential Fault Analysis (DFA) attacks has been one of the main design criteria, while we provide strong bounds for its security in the related-tweak model. Considering the area footprint of round-based hardware implementations, CRAFT outperforms the other lightweight ciphers with the same state and key size. This holds not only for unprotected implementations but also when fault-detection facilities, side-channel protection, and their combination are integrated into the implementation. In addition to supporting a 64-bit tweak, CRAFT has the additional property that the circuit realizing the encryption can support the decryption functionality as well with very little area overhead.

2019

TOSC

libInterMAC: Beyond Confidentiality and Integrity in Practice
📺 Abstract

Boldyreva et al. (Eurocrypt 2012) defined a fine-grained security model capturing ciphertext fragmentation attacks against symmetric encryption schemes. The model was extended by Albrecht et al. (CCS 2016) to include an integrity notion. The extended security model encompasses important security goals of SSH that go beyond confidentiality and integrity to include length hiding and denial-of-service resistance properties. Boldyreva et al. also defined and analysed the InterMAC scheme, while Albrecht et al. showed that InterMAC satisfies stronger security notions than all currently available SSH encryption schemes. In this work, we take the InterMAC scheme and make it fully ready for use in practice. This involves several steps. First, we modify the InterMAC scheme to support encryption of arbitrary length plaintexts and we replace the use of Encrypt-then-MAC in InterMAC with modern noncebased authenticated encryption. Second, we describe a reference implementation of the modified InterMAC scheme in the form of the library libInterMAC. We give a performance analysis of libInterMAC. Third, to test the practical performance of libInterMAC, we implement several InterMAC-based encryption schemes in OpenSSH and carry out a performance analysis for the use-case of file transfer using SCP. We measure the data throughput and the data overhead of using InterMAC-based schemes compared to existing schemes in OpenSSH. Our analysis shows that, for some network set-ups, using InterMAC-based schemes in OpenSSH only moderately affects performance whilst providing stronger security guarantees compared to existing schemes.

2019

TOSC

Constructing Low-latency Involutory MDS Matrices with Lightweight Circuits
📺 Abstract

MDS matrices are important building blocks providing diffusion functionality for the design of many symmetric-key primitives. In recent years, continuous efforts are made on the construction of MDS matrices with small area footprints in the context of lightweight cryptography. Just recently, Duval and Leurent (ToSC 2018/FSE 2019) reported some 32 × 32 binary MDS matrices with branch number 5, which can be implemented with only 67 XOR gates, whereas the previously known lightest ones of the same size cost 72 XOR gates.In this article, we focus on the construction of lightweight involutory MDS matrices, which are even more desirable than ordinary MDS matrices, since the same circuit can be reused when the inverse is required. In particular, we identify some involutory MDS matrices which can be realized with only 78 XOR gates with depth 4, whereas the previously known lightest involutory MDS matrices cost 84 XOR gates with the same depth. Notably, the involutory MDS matrix we find is much smaller than the AES MixColumns operation, which requires 97 XOR gates with depth 8 when implemented as a block of combinatorial logic that can be computed in one clock cycle. However, with respect to latency, the AES MixColumns operation is superior to our 78-XOR involutory matrices, since the AES MixColumns can be implemented with depth 3 by using more XOR gates.We prove that the depth of a 32 × 32 MDS matrix with branch number 5 (e.g., the AES MixColumns operation) is at least 3. Then, we enhance Boyar’s SLP-heuristic algorithm with circuit depth awareness, such that the depth of its output circuit is limited. Along the way, we give a formula for computing the minimum achievable depth of a circuit implementing the summation of a set of signals with given depths, which is of independent interest. We apply the new SLP heuristic to a large set of lightweight involutory MDS matrices, and we identify a depth 3 involutory MDS matrix whose implementation costs 88 XOR gates, which is superior to the AES MixColumns operation with respect to both lightweightness and latency, and enjoys the extra involution property.

2019

TOSC

Boomerang Connectivity Table Revisited. Application to SKINNY and AES
📺 Abstract

The boomerang attack is a variant of differential cryptanalysis which regards a block cipher E as the composition of two sub-ciphers, i.e., E = E1 o E0, and which constructs distinguishers for E with probability p2q2 by combining differential trails for E0 and E1 with probability p and q respectively. However, the validity of this attack relies on the dependency between the two differential trails. Murphy has shown cases where probabilities calculated by p2q2 turn out to be zero, while techniques such as boomerang switches proposed by Biryukov and Khovratovich give rise to probabilities greater than p2q2. To formalize such dependency to obtain a more accurate estimation of the probability of the distinguisher, Dunkelman et al. proposed the sandwich framework that regards E as Ẽ1 o Em o Ẽ0, where the dependency between the two differential trails is handled by a careful analysis of the probability of the middle part Em. Recently, Cid et al. proposed the Boomerang Connectivity Table (BCT) which unifies the previous switch techniques and incompatibility together and evaluates the probability of Em theoretically when Em is composed of a single S-box layer. In this paper, we revisit the BCT and propose a generalized framework which is able to identify the actual boundaries of Em which contains dependency of the two differential trails and systematically evaluate the probability of Em with any number of rounds. To demonstrate the power of this new framework, we apply it to two block ciphers SKINNY and AES. In the application to SKINNY, the probabilities of four boomerang distinguishers are re-evaluated. It turns out that Em involves5 or 6 rounds and the probabilities of the full distinguishers are much higher than previously evaluated. In the application to AES, the new framework is used to exclude incompatibility and find high probability distinguishers of AES-128 under the related-subkey setting. As a result, a 6-round distinguisher with probability 2−109.42 is constructed. Lastly, we discuss the relation between the dependency of two differential trails in boomerang distinguishers and the properties of components of the cipher.

2019

TOSC

Boomerang Switch in Multiple Rounds. Application to AES Variants and Deoxys
📺 Abstract

The boomerang attack is a cryptanalysis technique that allows an attacker to concatenate two short differential characteristics. Several research results (ladder switch, S-box switch, sandwich attack, Boomerang Connectivity Table (BCT), ...) showed that the dependency between these two characteristics at the switching round can have a significant impact on the complexity of the attack, or even potentially invalidate it. In this paper, we revisit the issue of boomerang switching effect, and exploit it in the case where multiple rounds are involved. To support our analysis, we propose a tool called Boomerang Difference Table (BDT), which can be seen as an improvement of the BCT and allows a systematic evaluation of the boomerang switch through multiple rounds. In order to illustrate the power of this technique, we propose a new related-key attack on 10-round AES-256 which requires only 2 simple related-keys and 275 computations. This is a much more realistic scenario than the state-of-the-art 10-round AES-256 attacks, where subkey oracles, or several related-keys and high computational power is needed. Furthermore, we also provide improved attacks against full AES-192 and reduced-round Deoxys.

2019

TOSC

A General Proof Framework for Recent AES Distinguishers
📺 Abstract

In this paper, a new framework is developed for proving and adapting the recently proposed multiple-of-8 property and mixture-differential distinguishers. The above properties are formulated as immediate consequences of an equivalence relation on the input pairs, under which the difference at the output of the round function is invariant. This approach provides a further understanding of these newly developed distinguishers. For example, it clearly shows that the branch number of the linear layer does not influence the validity of the property, on the contrary of what was previously believed. We further provide an extension of the mixture-differential distinguishers and multiple-of-8 property to any SPN and to a larger class of subspaces. These adapted properties can then be exhibited in a systematic way for other ciphers than the AES. We illustrate this with the examples of Midori, Klein, LED and Skinny.

2019

TOSC

Zero-Correlation Attacks on Tweakable Block Ciphers with Linear Tweakey Expansion
📺 Abstract

The design and analysis of dedicated tweakable block ciphers is a quite recent and very active research field that provides an ongoing stream of new insights. For instance, results of Kranz, Leander, and Wiemer from FSE 2017 show that the addition of a tweak using a linear tweak schedule does not introduce new linear characteristics. In this paper, we consider – to the best of our knowledge – for the first time the effect of the tweak on zero-correlation linear cryptanalysis for ciphers that have a linear tweak schedule. It turns out that the tweak can often be used to get zero-correlation linear hulls covering more rounds compared to just searching zero-correlation linear hulls on the data-path of a cipher. Moreover, this also implies the existence of integral distinguishers on the same number of rounds. We have applied our technique on round reduced versions of Qarma, Mantis, and Skinny. As a result, we can present – to the best of our knowledge – the best attack (with respect to number of rounds) on a round-reduced variant of Qarma.

2019

TOSC

Related-Tweak Statistical Saturation Cryptanalysis and Its Application on QARMA
📺 Abstract

Statistical saturation attack takes advantage of a set of plaintext with some bits fixed while the others vary randomly, and then track the evolution of a non-uniform plaintext distribution through the cipher. Previous statistical saturation attacks are all implemented under single-key setting, and there is no public attack models under related-key/tweak setting. In this paper, we propose a new cryptanalytic method which can be seen as related-key/tweak statistical saturation attack by revealing the link between the related-key/tweak statistical saturation distinguishers and KDIB (Key Difference Invariant Bias) / TDIB (Tweak Difference Invariant Bias) ones. KDIB cryptanalysis was proposed by Bogdanov et al. at ASIACRYPT’13 and utilizes the property that there can exist linear trails such that their biases are deterministically invariant under key difference. And this method can be easily extended to TDIB distinguishers if the tweak is also alternated. The link between them provides a new and more efficient way to find related-key/tweak statistical saturation distinguishers in ciphers. Thereafter, an automatic searching algorithm for KDIB/TDIB distinguishers is also given in this paper, which can be implemented to find word-level KDIB distinguishers for S-box based key-alternating ciphers. We apply this algorithm to QARMA-64 and give related-tweak statistical saturation attack for 10-round QARMA-64 with outer whitening key. Besides, an 11-round attack on QARMA-128 is also given based on the TDIB technique. Compared with previous public attacks on QARMA including outer whitening key, all attacks presented in this paper are the best ones in terms of the number of rounds.

2019

TOSC

General Diffusion Analysis: How to Find Optimal Permutations for Generalized Type-II Feistel Schemes
📺 Abstract

Type-II Generalized Feistel Schemes are one of the most popular versions of Generalized Feistel Schemes. Their round function consists in applying a classical Feistel transformation to p sub-blocks of two consecutive words and then shifting the k = 2p words cyclically. The low implementation costs it offers are balanced by a low diffusion, limiting its efficiency. Diffusion of such structures may however be improved by replacing the cyclic shift with a different permutation without any additional implementation cost. In this paper, we study ways to determine permutations with the fastest diffusion called optimal permutations.To do so, two ideas are used. First, we study the natural equivalence classes of permutations that preserve cryptographic properties; second, we use the representation of permutations as coloured trees.For both heuristic and historical reasons, we focus first on even-odd permutations, that is, those permutations for which images of even numbers are odd. We derive from their structure an upper bound on the number of their equivalence classes together with a strategy to perform exhaustive searches on classes. We performed those exhaustive searches for sizes k ≤ 24, while previous exhaustive searches on all permutations were limited to k ≤ 16. For sizes beyond the reach of this method, we use tree representations to find permutations with good intermediate diffusion properties. This heuristic leads to an optimal even-odd permutation for k = 26 and best-known results for sizes k = 64 and k = 128.Finally, we transpose these methods to all permutations. Using a new strategy to exhaust equivalence classes, we perform exhaustive searches on classes for sizes k ≤ 20 whose results confirmed the initial heuristic: there always exist optimal permutations that are even-odd and furthermore for k = 18 all optimal permutations are even-odd permutations.

2019

TOSC

Partitions in the S-Box of Streebog and Kuznyechik
📺 Abstract

Streebog and Kuznyechik are the latest symmetric cryptographic primitives standardized by the Russian GOST. They share the same S-Box, π, whose design process was not described by its authors. In previous works, Biryukov, Perrin and Udovenko recovered two completely different decompositions of this S-Box.We revisit their results and identify a third decomposition of π. It is an instance of a fairly small family of permutations operating on 2m bits which we call TKlog and which is closely related to finite field logarithms. Its simplicity and the small number of components it uses lead us to claim that it has to be the structure intentionally used by the designers of Streebog and Kuznyechik.The 2m-bit permutations of this type have a very strong algebraic structure: they map multiplicative cosets of the subfield GF(2m)* to additive cosets of GF(2m)*. Furthermore, the function relating each multiplicative coset to the corresponding additive coset is always essentially the same. To the best of our knowledge, we are the first to expose this very strong algebraic structure.We also investigate other properties of the TKlog and show in particular that it can always be decomposed in a fashion similar to the first decomposition of Biryukov et al., thus explaining the relation between the two previous decompositions. It also means that it is always possible to implement a TKlog efficiently in hardware and that it always exhibits a visual pattern in its LAT similar to the one present in π. While we could not find attacks based on these new results, we discuss the impact of our work on the security of Streebog and Kuznyechik. To this end, we provide a new simpler representation of the linear layer of Streebog as a matrix multiplication in the exact same field as the one used to define π. We deduce that this matrix interacts in a non-trivial way with the partitions preserved by π.

2019

TOSC

PEIGEN – a Platform for Evaluation, Implementation, and Generation of S-boxes
📺 Abstract

In this paper, a platform named PEIGEN is presented to evaluate security, find efficient software/hardware implementations, and generate cryptographic S-boxes. Continuously developed for decades, S-boxes are constantly evolving in terms of the design criteria for both security requirements and software/hardware performances. PEIGEN is aimed to be a platform covering a comprehensive check-list of design criteria of S-boxes appearing in the literature. To do so, the security requirements are first intensively surveyed, existing tools of S-boxes are then comprehensively compared, and finally our platform PEIGEN is presented. The survey part is aimed to be a systematic reference for the theoretical study of S-boxes. The platform is aimed to be an assistant tool for the experimental study and practical use of S-boxes. PEIGEN not only integrates most of the features in existing tools, but also equips with functionalities to evaluate new security-related properties, improves the efficiency of the search algorithms for optimized implementations in several aspects. With the help of this powerful platform, many interesting observations are made in-between the security notations, as well as on the S-boxes used in the existing symmetrickey cryptographic primitives. PEIGEN will become an open platform and welcomes contributions from all parties to help the community to facilitate the research and use of S-boxes.

2018

CRYPTO

TinyKeys: A New Approach to Efficient Multi-Party Computation
📺 Abstract

We present a new approach to designing concretely efficient MPC protocols with semi-honest security in the dishonest majority setting. Motivated by the fact that within the dishonest majority setting the efficiency of most practical protocols does not depend on the number of honest parties, we investigate how to construct protocols which improve in efficiency as the number of honest parties increases. Our central idea is to take a protocol which is secure for
$$n-1$$
n-1 corruptions and modify it to use short symmetric keys, with the aim of basing security on the concatenation of all honest parties’ keys. This results in a more efficient protocol tolerating fewer corruptions, whilst also introducing an LPN-style syndrome decoding assumption.We first apply this technique to a modified version of the semi-honest GMW protocol, using OT extension with short keys, to improve the efficiency of standard GMW with fewer corruptions. We also obtain more efficient constant-round MPC, using BMR-style garbled circuits with short keys, and present an implementation of the online phase of this protocol. Our techniques start to improve upon existing protocols when there are around
$$n=20$$
n=20 parties with
$$h=6$$
h=6 honest parties, and as these increase we obtain up to a 13 times reduction (for
$$n=400, h=120$$
n=400,h=120) in communication complexity for our GMW variant, compared with the best-known GMW-based protocol modified to use the same threshold.

2018

CRYPTO

Two-Round Multiparty Secure Computation Minimizing Public Key Operations
📺 Abstract

We show new constructions of semi-honest and malicious two-round multiparty secure computation protocols using only (a fixed)
$$\mathsf {poly}(n,\lambda )$$
poly(n,λ) invocations of a two-round oblivious transfer protocol (which use expensive public-key operations) and
$$\mathsf {poly}(\lambda , |C|)$$
poly(λ,|C|) cheaper one-way function calls, where
$$\lambda $$
λ is the security parameter, n is the number of parties, and C is the circuit being computed. All previously known two-round multiparty secure computation protocols required
$$\mathsf {poly}(\lambda ,|C|)$$
poly(λ,|C|) expensive public-key operations.

2018

CRYPTO

Limits of Practical Sublinear Secure Computation
📺 Abstract

Secure computations on big data call for protocols that have sublinear communication complexity in the input length. While fully homomorphic encryption (FHE) provides a general solution to the problem, employing it on a large scale is currently quite far from being practical. This is also the case for secure computation tasks that reduce to weaker forms of FHE such as “somewhat homomorphic encryption” or single-server private information retrieval (PIR).Quite unexpectedly, Aggarwal, Mishra, and Pinkas (Eurocrypt 2004), Brickell and Shmatikov (Asiacrypt 2005), and Shelat and Venkitasubramaniam (Asiacrypt 2015) have shown that in several natural instances of secure computation on big data, there are practical sublinear communication protocols that only require sublinear local computation and minimize the use of expensive public-key operations. This raises the question of whether similar protocols exist for other natural problems.In this paper we put forward a framework for separating “practical” sublinear protocols from “impractical” ones, and establish a methodology for identifying “provably hard” big-data problems that do not admit practical protocols. This is akin to the use of NP-completeness to separate hard algorithmic problems from easy ones. We show that while the previous protocols of Aggarwal et al., Brickell and Shmatikov, and Shelat and Venkitasubramaniam are indeed classified as being “practical” in this framework, slight variations of the problems they solve and other natural computational problems on big data are hard.Our negative results are established by showing that the problem at hand is “PIR-hard” in the sense that any secure protocol for the problem implies PIR on a large database. This imposes a barrier on the local computational cost of secure protocols for the problem. We also identify a new natural relaxation of PIR that we call semi-PIR, which is useful for establishing “intermediate hardness” of several practically motivated secure computation tasks. We show that semi-PIR implies slightly sublinear PIR via an adaptive black-box reduction and that ruling out a stronger black-box reduction would imply a major breakthrough in complexity theory. We also establish information-theoretic separations between semi-PIR and PIR, showing that some problems that we prove to be semi-PIR-hard are not PIR-hard.

2018

CRYPTO

Limits on the Power of Garbling Techniques for Public-Key Encryption
📺 Abstract

Understanding whether public-key encryption can be based on one-way functions is a fundamental open problem in cryptography. The seminal work of Impagliazzo and Rudich [STOC’89] shows that black-box constructions of public-key encryption from one-way functions are impossible. However, this impossibility result leaves open the possibility of using non-black-box techniques for achieving this goal.One of the most powerful classes of non-black-box techniques, which can be based on one-way functions (OWFs) alone, is Yao’s garbled circuit technique [FOCS’86]. As for the non-black-box power of this technique, the recent work of Döttling and Garg [CRYPTO’17] shows that the use of garbling allows us to circumvent known black-box barriers in the context of identity-based encryption.We prove that garbling of circuits that have OWF (or even random oracle) gates in them are insufficient for obtaining public-key encryption. Additionally, we show that this model also captures (non-interactive) zero-knowledge proofs for relations with OWF gates. This indicates that currently known OWF-based non-black-box techniques are perhaps insufficient for realizing public-key encryption.

2018

CRYPTO

Optimizing Authenticated Garbling for Faster Secure Two-Party Computation
📺 Abstract

Wang et al. (CCS 2017) recently proposed a protocol for malicious secure two-party computation that represents the state-of-the-art with regard to concrete efficiency in both the single-execution and amortized settings, with or without preprocessing. We show here several optimizations of their protocol that result in a significant improvement in the overall communication and running time. Specifically:We show how to make the “authenticated garbling” at the heart of their protocol compatible with the half-gate optimization of Zahur et al. (Eurocrypt 2015). We also show how to avoid sending an information-theoretic MAC for each garbled row. These two optimizations give up to a 2.6$$\times $$× improvement in communication, and make the communication of the online phase essentially equivalent to that of state-of-the-art semi-honest secure computation.We show various optimizations to their protocol for generating AND triples that, overall, result in a 1.5$$\times $$× improvement in the communication and a 2$$\times $$× improvement in the computation for that step.

2018

CRYPTO

Amortized Complexity of Information-Theoretically Secure MPC Revisited
📺 Abstract

A fundamental and widely-applied paradigm due to Franklin and Yung (STOC 1992) on Shamir-secret-sharing based general n-player MPC shows how one may trade the adversary thresholdt against amortized communication complexity, by using a so-called packed version of Shamir’s scheme. For e.g. the BGW-protocol (with active security), this trade-off means that if
$$t + 2k -2 < n/3$$
t+2k-2<n/3, then kparallel evaluations of the same arithmetic circuit on different inputs can be performed at the overall cost corresponding to a single BGW-execution.In this paper we propose a novel paradigm for amortized MPC that offers a different trade-off, namely with the size of the field of the circuit which is securely computed, instead of the adversary threshold. Thus, unlike the Franklin-Yung paradigm, this leaves the adversary threshold unchanged. Therefore, for instance, this paradigm may yield constructions enjoying the maximal adversary threshold
$$\lfloor (n-1)/3 \rfloor $$
⌊(n-1)/3⌋ in the BGW-model (secure channels, perfect security, active adversary, synchronous communication).Our idea is to compile an MPC for a circuit over an extension field to a parallel MPC of the same circuit but with inputs defined over its base field and with the same adversary threshold. Key technical handles are our notion of reverse multiplication-friendly embeddings (RMFE) and our proof, by algebraic-geometric means, that these are constant-rate, as well as efficient auxiliary protocols for creating “subspace-randomness” with good amortized complexity. In the BGW-model, we show that the latter can be constructed by combining our tensored-up linear secret sharing with protocols based on hyper-invertible matrices á la Beerliova-Hirt (or variations thereof). Along the way, we suggest alternatives for hyper-invertible matrices with the same functionality but which can be defined over a large enough constant size field, which we believe is of independent interest.As a demonstration of the merits of the novel paradigm, we show that, in the BGW-model and with an optimal adversary threshold
$$\lfloor (n-1)/3 \rfloor $$
⌊(n-1)/3⌋, it is possible to securely compute a binary circuit with amortized complexity O(n) of bits per gate per instance. Known results would give
$$n \log n$$
nlogn bits instead. By combining our result with the Franklin-Yung paradigm, and assuming a sub-optimal adversary (i.e., an arbitrarily small
$$\epsilon >0$$
ϵ>0 fraction below 1/3), this is improved to O(1) bits instead of O(n).

2018

CRYPTO

Private Circuits: A Modular Approach
📺 Abstract

We consider the problem of protecting general computations against constant-rate random leakage. That is, the computation is performed by a randomized boolean circuit that maps a randomly encoded input to a randomly encoded output, such that even if the value of every wire is independently leaked with some constant probability
$$p > 0$$
p>0, the leakage reveals essentially nothing about the input.In this work we provide a conceptually simple, modular approach for solving the above problem, providing a simpler and self-contained alternative to previous constructions of Ajtai (STOC 2011) and Andrychowicz et al. (Eurocrypt 2016). We also obtain several extensions and generalizations of this result. In particular, we show that for every leakage probability
$$p<1$$
p<1, there is a finite basis
$$\mathbb {B}$$
B such that leakage-resilient computation with leakage probability p can be realized using circuits over the basis
$$\mathbb {B}$$
B. We obtain similar positive results for the stronger notion of leakage tolerance, where the input is not encoded, but the leakage from the entire computation can be simulated given random
$$p'$$
p′-leakage of input values alone, for any
$$p<p'<1$$
p<p′<1. Finally, we complement this by a negative result, showing that for every basis
$$\mathbb {B}$$
B there is some leakage probability
$$p<1$$
p<1 such that for any
$$p'<1$$
p′<1, leakage tolerance as above cannot be achieved in general.We show that our modular approach is also useful for protecting computations against worst case leakage. In this model, we require that leakage of any
$$\mathbf{t}$$
t (adversarially chosen) wires reveal nothing about the input. By combining our construction with a previous derandomization technique of Ishai et al. (ICALP 2013), we show that security in this setting can be achieved with
$$O(\mathbf{t}^{1+\varepsilon })$$
O(t1+ε) random bits, for every constant
$$\varepsilon > 0$$
ε>0. This (near-optimal) bound significantly improves upon previous constructions that required more than
$$\mathbf{t}^{3}$$
t3 random bits.

2018

CRYPTO

A New Public-Key Cryptosystem via Mersenne Numbers
📺 Abstract

In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number
$$p = 2^n - 1$$
p=2n-1, where n is a prime, a positive integer h, and two n-bit integers T, R, decide whether their exist n-bit integers F, G each of Hamming weight less than h such that
$$T = F\cdot R + G$$
T=F·R+G modulo p.

2018

CRYPTO

Fast Homomorphic Evaluation of Deep Discretized Neural Networks
📺 Abstract

The rise of machine learning as a service multiplies scenarios where one faces a privacy dilemma: either sensitive user data must be revealed to the entity that evaluates the cognitive model (e.g., in the Cloud), or the model itself must be revealed to the user so that the evaluation can take place locally. Fully Homomorphic Encryption (FHE) offers an elegant way to reconcile these conflicting interests in the Cloud-based scenario and also preserve non-interactivity. However, due to the inefficiency of existing FHE schemes, most applications prefer to use Somewhat Homomorphic Encryption (SHE), where the complexity of the computation to be performed has to be known in advance, and the efficiency of the scheme depends on this global complexity.In this paper, we present a new framework for homomorphic evaluation of neural networks, that we call FHE–DiNN, whose complexity is strictly linear in the depth of the network and whose parameters can be set beforehand. To obtain this scale-invariance property, we rely heavily on the bootstrapping procedure. We refine the recent FHE construction by Chillotti et al. (ASIACRYPT 2016) in order to increase the message space and apply the sign function (that we use to activate the neurons in the network) during the bootstrapping. We derive some empirical results, using TFHE library as a starting point, and classify encrypted images from the MNIST dataset with more than 96% accuracy in less than 1.7 s.Finally, as a side contribution, we analyze and introduce some variations to the bootstrapping technique of Chillotti et al. that offer an improvement in efficiency at the cost of increasing the storage requirements.

2018

CRYPTO

On the Round Complexity of OT Extension
📺 Abstract

We show that any OT extension protocol based on one-way functions (or more generally any symmetric-key primitive) either requires an additional round compared to the base OTs or must make a non-black-box use of one-way functions. This result also holds in the semi-honest setting or in the case of certain setup models such as the common random string model. This implies that OT extension in any secure computation protocol must come at the price of an additional round of communication or the non-black-box use of symmetric key primitives. Moreover, we observe that our result is tight in the sense that positive results can indeed be obtained using non-black-box techniques or at the cost of one additional round of communication.

2018

CRYPTO

Fast Large-Scale Honest-Majority MPC for Malicious Adversaries
📺 Abstract

Protocols for secure multiparty computation enable a set of parties to compute a function of their inputs without revealing anything but the output. The security properties of the protocol must be preserved in the presence of adversarial behavior. The two classic adversary models considered are semi-honest (where the adversary follows the protocol specification but tries to learn more than allowed by examining the protocol transcript) and malicious (where the adversary may follow any arbitrary attack strategy). Protocols for semi-honest adversaries are often far more efficient, but in many cases the security guarantees are not strong enough.In this paper, we present new protocols for securely computing any functionality represented by an arithmetic circuit. We utilize a new method for verifying that the adversary does not cheat, that yields a cost of just twice that of semi-honest protocols in some settings. Our protocols are information-theoretically secure in the presence of a malicious adversaries, assuming an honest majority. We present protocol variants for small and large fields, and show how to efficiently instantiate them based on replicated secret sharing and Shamir sharing. As with previous works in this area aiming to achieve high efficiency, our protocol is secure with abort and does not achieve fairness, meaning that the adversary may receive output while the honest parties do not.We implemented our protocol and ran experiments for different numbers of parties, different network configurations and different circuit depths. Our protocol significantly outperforms the previous best for this setting (Lindell and Nof, CCS 2017); for a large number of parties, our implementation runs almost an order of magnitude faster than theirs.

2018

CRYPTO

Non-Malleable Codes for Partial Functions with Manipulation Detection
📺 Abstract

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs (ICS ’10) and its main application is the protection of cryptographic devices against tampering attacks on memory. In this work, we initiate a comprehensive study on non-malleable codes for the class of partial functions, that read/write on an arbitrary subset of codeword bits with specific cardinality. Our constructions are efficient in terms of information rate, while allowing the attacker to access asymptotically almost the entire codeword. In addition, they satisfy a notion which is stronger than non-malleability, that we call non-malleability with manipulation detection, guaranteeing that any modified codeword decodes to either the original message or to $$\bot $$⊥. Finally, our primitive implies All-Or-Nothing Transforms (AONTs) and as a result our constructions yield efficient AONTs under standard assumptions (only one-way functions), which, to the best of our knowledge, was an open question until now. In addition to this, we present a number of additional applications of our primitive in tamper resilience.

2018

CRYPTO

Continuously Non-Malleable Codes in the Split-State Model from Minimal Assumptions
📺 Abstract

At ICS 2010, Dziembowski, Pietrzak and Wichs introduced the notion of non-malleable codes, a weaker form of error-correcting codes guaranteeing that the decoding of a tampered codeword either corresponds to the original message or to an unrelated value. The last few years established non-malleable codes as one of the recently invented cryptographic primitives with the highest impact and potential, with very challenging open problems and applications.In this work, we focus on so-called continuously non-malleable codes in the split-state model, as proposed by Faust et al. (TCC 2014), where a codeword is made of two shares and an adaptive adversary makes a polynomial number of attempts in order to tamper the target codeword, where each attempt is allowed to modify the two shares independently (yet arbitrarily). Achieving continuous non-malleability in the split-state model has been so far very hard. Indeed, the only known constructions require strong setup assumptions (i.e., the existence of a common reference string) and strong complexity-theoretic assumptions (i.e., the existence of non-interactive zero-knowledge proofs and collision-resistant hash functions).As our main result, we construct a continuously non-malleable code in the split-state model without setup assumptions, requiring only one-to-one one-way functions (i.e., essentially optimal computational assumptions). Our result introduces several new ideas that make progress towards understanding continuous non-malleability, and shows interesting connections with protocol-design and proof-approach techniques used in other contexts (e.g., look-ahead simulation in zero-knowledge proofs, non-malleable commitments, and leakage resilience).

2018

CRYPTO

Non-Interactive Zero-Knowledge Proofs for Composite Statements
📺 Abstract

The two most common ways to design non-interactive zero-knowledge (NIZK) proofs are based on Sigma protocols and QAP-based SNARKs. The former is highly efficient for proving algebraic statements while the latter is superior for arithmetic representations. Motivated by applications such as privacy-preserving credentials and privacy-preserving audits in cryptocurrencies, we study the design of NIZKs for composite statements that compose algebraic and arithmetic statements in arbitrary ways. Specifically, we provide a framework for proving statements that consist of ANDs, ORs and function compositions of a mix of algebraic and arithmetic components. This allows us to explore the full spectrum of trade-offs between proof size, prover cost, and CRS size/generation cost. This leads to proofs for statements of the form: knowledge of x such that $$SHA(g^x)=y$$SHA(gx)=y for some public y where the prover’s work is 500 times fewer exponentiations compared to a QAP-based SNARK at the cost of increasing the proof size to 2404 group and field elements. In application to anonymous credentials, our techniques result in 8 times fewer exponentiations for the prover at the cost of increasing the proof size to 298 elements.

2018

CRYPTO

From Laconic Zero-Knowledge to Public-Key Cryptography
📺 Abstract

Since its inception, public-key encryption (
$$\mathsf {PKE}$$
PKE) has been one of the main cornerstones of cryptography. A central goal in cryptographic research is to understand the foundations of public-key encryption and in particular, base its existence on a natural and generic complexity-theoretic assumption. An intriguing candidate for such an assumption is the existence of a cryptographically hard language .In this work we prove that public-key encryption can be based on the foregoing assumption, as long as the (honest) prover in the zero-knowledge protocol is efficient and laconic. That is, messages that the prover sends should be efficiently computable (given the witness) and short (i.e., of sufficiently sub-logarithmic length). Actually, our result is stronger and only requires the protocol to be zero-knowledge for an honest-verifier and sound against computationally bounded cheating provers.Languages in with such laconic zero-knowledge protocols are known from a variety of computational assumptions (e.g., Quadratic Residuocity, Decisional Diffie-Hellman, Learning with Errors, etc.). Thus, our main result can also be viewed as giving a unifying framework for constructing
$$\mathsf {PKE}$$
PKE which, in particular, captures many of the assumptions that were already known to yield
$$\mathsf {PKE}$$
PKE.We also show several extensions of our result. First, that a certain weakening of our assumption on laconic zero-knowledge is actually equivalent to
$$\mathsf {PKE}$$
PKE, thereby giving a complexity-theoretic characterization of
$$\mathsf {PKE}$$
PKE. Second, a mild strengthening of our assumption also yields a (2-message) oblivious transfer protocol.

2018

CRYPTO

Updatable and Universal Common Reference Strings with Applications to zk-SNARKs
📺 Abstract

By design, existing (pre-processing) zk-SNARKs embed a secret trapdoor in a relation-dependent common reference strings (CRS). The trapdoor is exploited by a (hypothetical) simulator to prove the scheme is zero knowledge, and the secret-dependent structure facilitates a linear-size CRS and linear-time prover computation. If known by a real party, however, the trapdoor can be used to subvert the security of the system. The structured CRS that makes zk-SNARKs practical also makes deploying zk-SNARKS problematic, as it is difficult to argue why the trapdoor would not be available to the entity responsible for generating the CRS. Moreover, for pre-processing zk-SNARKs a new trusted CRS needs to be computed every time the relation is changed.In this paper, we address both issues by proposing a model where a number of users can update a universal CRS. The updatable CRS model guarantees security if at least one of the users updating the CRS is honest. We provide both a negative result, by showing that zk-SNARKs with private secret-dependent polynomials in the CRS cannot be updatable, and a positive result by constructing a zk-SNARK based on a CRS consisting only of secret-dependent monomials. The CRS is of quadratic size, is updatable, and is universal in the sense that it can be specialized into one or more relation-dependent CRS of linear size with linear-time prover computation.

2018

CRYPTO

A Simple Obfuscation Scheme for Pattern-Matching with Wildcards
📺 Abstract

We give a simple and efficient method for obfuscating pattern matching with wildcards. In other words, we construct a way to check an input against a secret pattern, which is described in terms of prescribed values interspersed with unconstrained “wildcard” slots. As long as the support of the pattern is sufficiently sparse and the pattern itself is chosen from an appropriate distribution, we prove that a polynomial-time adversary cannot find a matching input, except with negligible probability. We rely upon the generic group heuristic (in a regular group, with no multilinearity). Previous work [9, 10, 32] provided less efficient constructions based on multilinear maps or LWE.

2018

CRYPTO

On the Complexity of Compressing Obfuscation
📺 Abstract

Indistinguishability obfuscation has become one of the most exciting cryptographic primitives due to its far reaching applications in cryptography and other fields. However, to date, obtaining a plausibly secure construction has been an illusive task, thus motivating the study of seemingly weaker primitives that imply it, with the possibility that they will be easier to construct.In this work, we provide a systematic study of compressing obfuscation, one of the most natural and simple to describe primitives that is known to imply indistinguishability obfuscation when combined with other standard assumptions. A compressing obfuscator is roughly an indistinguishability obfuscator that outputs just a slightly compressed encoding of the truth table. This generalizes notions introduced by Lin et al. (PKC 2016) and Bitansky et al. (TCC 2016) by allowing for a broader regime of parameters.We view compressing obfuscation as an independent cryptographic primitive and show various positive and negative results concerning its power and plausibility of existence, demonstrating significant differences from full-fledged indistinguishability obfuscation.First, we show that as a cryptographic building block, compressing obfuscation is weak. In particular, when combined with one-way functions, it cannot be used (in a black-box way) to achieve public-key encryption, even under (sub-)exponential security assumptions. This is in sharp contrast to indistinguishability obfuscation, which together with one-way functions implies almost all cryptographic primitives.Second, we show that to construct compressing obfuscation with perfect correctness, one only needs to assume its existence with a very weak correctness guarantee and polynomial hardness. Namely, we show a correctness amplification transformation with optimal parameters that relies only on polynomial hardness assumptions. This implies a universal construction assuming only polynomially secure compressing obfuscation with approximate correctness. In the context of indistinguishability obfuscation, we know how to achieve such a result only under sub-exponential security assumptions together with derandomization assumptions.Lastly, we characterize the existence of compressing obfuscation with statistical security. We show that in some range of parameters and for some classes of circuits such an obfuscator exists, whereas it is unlikely to exist with better parameters or for larger classes of circuits. These positive and negative results reveal a deep connection between compressing obfuscation and various concepts in complexity theory and learning theory.

2018

CRYPTO

Quantum FHE (Almost) As Secure As Classical
📺 Abstract

Fully homomorphic encryption schemes (FHE) allow to apply arbitrary efficient computation to encrypted data without decrypting it first. In Quantum FHE (QFHE) we may want to apply an arbitrary quantumly efficient computation to (classical or quantum) encrypted data.We present a QFHE scheme with classical key generation (and classical encryption and decryption if the encrypted message is itself classical) with comparable properties to classical FHE. Security relies on the hardness of the learning with errors (LWE) problem with polynomial modulus, which translates to the worst case hardness of approximating short vector problems in lattices to within a polynomial factor. Up to polynomial factors, this matches the best known assumption for classical FHE. Similarly to the classical setting, relying on LWE alone only implies leveled QFHE (where the public key length depends linearly on the maximal allowed evaluation depth). An additional circular security assumption is required to support completely unbounded depth. Interestingly, our circular security assumption is the same assumption that is made to achieve unbounded depth multi-key classical FHE.Technically, we rely on the outline of Mahadev (arXiv 2017) which achieves this functionality by relying on super-polynomial LWE modulus and on a new circular security assumption. We observe a connection between the functionality of evaluating quantum gates and the circuit privacy property of classical homomorphic encryption. While this connection is not sufficient to imply QFHE by itself, it leads us to a path that ultimately allows using classical FHE schemes with polynomial modulus towards constructing QFHE with the same modulus.

2018

CRYPTO

IND-CCA-Secure Key Encapsulation Mechanism in the Quantum Random Oracle Model, Revisited
📺 Abstract

With the gradual progress of NIST’s post-quantum cryptography standardization, the Round-1 KEM proposals have been posted for public to discuss and evaluate. Among the IND-CCA-secure KEM constructions, mostly, an IND-CPA-secure (or OW-CPA-secure) public-key encryption (PKE) scheme is first introduced, then some generic transformations are applied to it. All these generic transformations are constructed in the random oracle model (ROM). To fully assess the post-quantum security, security analysis in the quantum random oracle model (QROM) is preferred. However, current works either lacked a QROM security proof or just followed Targhi and Unruh’s proof technique (TCC-B 2016) and modified the original transformations by adding an additional hash to the ciphertext to achieve the QROM security.In this paper, by using a novel proof technique, we present QROM security reductions for two widely used generic transformations without suffering any ciphertext overhead. Meanwhile, the security bounds are much tighter than the ones derived by utilizing Targhi and Unruh’s proof technique. Thus, our QROM security proofs not only provide a solid post-quantum security guarantee for NIST Round-1 KEM schemes, but also simplify the constructions and reduce the ciphertext sizes. We also provide QROM security reductions for Hofheinz-Hövelmanns-Kiltz modular transformations (TCC 2017), which can help to obtain a variety of combined transformations with different requirements and properties.

2018

CRYPTO

Pseudorandom Quantum States
📺 Abstract

We propose the concept of pseudorandom quantum states, which appear random to any quantum polynomial-time adversary. It offers a computational approximation to perfectly random quantum states analogous in spirit to cryptographic pseudorandom generators, as opposed to statistical notions of quantum pseudorandomness that have been studied previously, such as quantum t-designs analogous to t-wise independent distributions.Under the assumption that quantum-secure one-way functions exist, we present efficient constructions of pseudorandom states, showing that our definition is achievable. We then prove several basic properties of pseudorandom states, which show the utility of our definition. First, we show a cryptographic no-cloning theorem: no efficient quantum algorithm can create additional copies of a pseudorandom state, when given polynomially-many copies as input. Second, as expected for random quantum states, we show that pseudorandom quantum states are highly entangled on average. Finally, as a main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.

2018

CRYPTO

Cryptanalyses of Branching Program Obfuscations over GGH13 Multilinear Map from the NTRU Problem
📺 Abstract

In this paper, we propose cryptanalyses of all existing indistinguishability obfuscation (iO) candidates based on branching programs (BP) over GGH13 multilinear map for all recommended parameter settings. To achieve this, we introduce two novel techniques, program converting using NTRU-solver and matrix zeroizing, which can be applied to a wide range of obfuscation constructions and BPs compared to previous attacks. We then prove that, for the suggested parameters, the existing general-purpose BP obfuscations over GGH13 do not have the desired security. Especially, the first candidate indistinguishability obfuscation with input-unpartitionable branching programs (FOCS 2013) and the recent BP obfuscation (TCC 2016) are not secure against our attack when they use the GGH13 with recommended parameters. Previously, there has been no known polynomial time attack for these cases.Our attack shows that the lattice dimension of GGH13 must be set much larger than previous thought in order to maintain security. More precisely, the underlying lattice dimension of GGH13 should be set to $$n=\tilde{\varTheta }( \kappa ^2 \lambda )$$n=Θ~(κ2λ) to rule out attacks from the subfield algorithm for NTRU where $$\kappa $$κ is the multilinearity level and $$\lambda $$λ the security parameter.

2018

CRYPTO

An Optimal Distributed Discrete Log Protocol with Applications to Homomorphic Secret Sharing
📺 Abstract

The distributed discrete logarithm (DDL) problem was introduced by Boyle et al. at CRYPTO 2016. A protocol solving this problem was the main tool used in the share conversion procedure of their homomorphic secret sharing (HSS) scheme which allows non-interactive evaluation of branching programs among two parties over shares of secret inputs.Let g be a generator of a multiplicative group $$\mathbb {G}$$G. Given a random group element $$g^{x}$$gx and an unknown integer $$b \in [-M,M]$$b∈[-M,M] for a small M, two parties A and B (that cannot communicate) successfully solve DDL if $$A(g^{x}) - B(g^{x+b}) = b$$A(gx)-B(gx+b)=b. Otherwise, the parties err. In the DDL protocol of Boyle et al., A and B run in time T and have error probability that is roughly linear in M/T. Since it has a significant impact on the HSS scheme’s performance, a major open problem raised by Boyle et al. was to reduce the error probability as a function of T.In this paper we devise a new DDL protocol that substantially reduces the error probability to $$O(M \cdot T^{-2})$$O(M·T-2). Our new protocol improves the asymptotic evaluation time complexity of the HSS scheme by Boyle et al. on branching programs of size S from $$O(S^2)$$O(S2) to $$O(S^{3/2})$$O(S3/2). We further show that our protocol is optimal up to a constant factor for all relevant cryptographic group families, unless one can solve the discrete logarithm problem in a short interval of length R in time $$o(\sqrt{R})$$o(R).Our DDL protocol is based on a new type of random walk that is composed of several iterations in which the expected step length gradually increases. We believe that this random walk is of independent interest and will find additional applications.

2018

CRYPTO

Must the Communication Graph of MPC Protocols be an Expander?
📺 Abstract

Secure multiparty computation (MPC) on incomplete communication networks has been studied within two primary models: (1) Where a partial network is fixed a priori, and thus corruptions can occur dependent on its structure, and (2) Where edges in the communication graph are determined dynamically as part of the protocol. Whereas a rich literature has succeeded in mapping out the feasibility and limitations of graph structures supporting secure computation in the fixed-graph model (including strong classical lower bounds), these bounds do not apply in the latter dynamic-graph setting, which has recently seen exciting new results, but remains relatively unexplored.In this work, we initiate a similar foundational study of MPC within the dynamic-graph model. As a first step, we investigate the property of graph expansion. All existing protocols (implicitly or explicitly) yield communication graphs which are expanders, but it is not clear whether this is inherent. Our results consist of two types:Upper bounds: We demonstrate secure protocols whose induced communication graphs are not expanders, within a wide range of settings (computational, information theoretic, with low locality, and adaptive security), each assuming some form of input-independent setup.Lower bounds: In the setting without setup and adaptive corruptions, we demonstrate that for certain functionalities, no protocol can maintain a non-expanding communication graph against all adversarial strategies. Our lower bound relies only on protocol correctness (not privacy), and requires a surprisingly delicate argument.

2018

CRYPTO

Simplifying Game-Based Definitions
📺 Abstract

Often the simplest way of specifying game-based cryptographic definitions is apparently barred because the adversary would have some trivial win. Disallowing or invalidating these wins can lead to complex or unconvincing definitions. We suggest a generic way around this difficulty. We call it indistinguishability up to correctness, or IND$$\vert $$C. Given games $${{\text {G}}}$$ and $${{\text {H}}}$$ and a correctness condition $${{\text {C}}}$$ we define an advantage measure $${\mathbf {Adv}_{{{\text {G}}},{{\text {H}}},{{\text {C}}}}^{{\text {indc}}}}$$ wherein $${{{\text {G}}}}$$/$${{{\text {H}}}}$$ distinguishing attacks are effaced to the extent that they are inevitable due to $${{\text {C}}}$$. We formalize this in the language of oracle silencing, an alternative to exclusion-style and penalty-style definitions. We apply our ideas to a domain where game-based definitions have been cumbersome: stateful authenticated-encryption (sAE). We rework existing sAE notions and encompass new ones, like replay-free AE permitting a specified degree of out-of-order message delivery.

2018

CRYPTO

Combiners for Backdoored Random Oracles
📺 Abstract

We formulate and study the security of cryptographic hash functions in the backdoored random-oracle (BRO) model, whereby a big brother designs a “good” hash function, but can also see arbitrary functions of its table via backdoor capabilities. This model captures intentional (and unintentional) weaknesses due to the existence of collision-finding or inversion algorithms, but goes well beyond them by allowing, for example, to search for structured preimages. The latter can easily break constructions that are secure under random inversions.BROs make the task of bootstrapping cryptographic hardness somewhat challenging. Indeed, with only a single arbitrarily backdoored function no hardness can be bootstrapped as any construction can be inverted. However, when two (or more) independent hash functions are available, hardness emerges even with unrestricted and adaptive access to all backdoor oracles. At the core of our results lie new reductions from cryptographic problems to the communication complexities of various two-party tasks. Along the way we establish a communication complexity lower bound for set-intersection for cryptographically relevant ranges of parameters and distributions and where set-disjointness can be easy.

2018

CRYPTO

On Distributional Collision Resistant Hashing
📺 Abstract

Collision resistant hashing is a fundamental concept that is the basis for many of the important cryptographic primitives and protocols. Collision resistant hashing is a family of compressing functions such that no efficient adversary can find any collision given a random function in the family.In this work we study a relaxation of collision resistance called distributional collision resistance, introduced by Dubrov and Ishai (STOC ’06). This relaxation of collision resistance only guarantees that no efficient adversary, given a random function in the family, can sample a pair (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x.Our first result shows that distributional collision resistance can be based on the existence of multi-collision resistance hash (with no additional assumptions). Multi-collision resistance is another relaxation of collision resistance which guarantees that an efficient adversary cannot find any tuple of $$k>2$$ inputs that collide relative to a random function in the family. The construction is non-explicit, non-black-box, and yields an infinitely-often secure family. This partially resolves a question of Berman et al. (EUROCRYPT ’18). We further observe that in a black-box model such an implication (from multi-collision resistance to distributional collision resistance) does not exist.Our second result is a construction of a distributional collision resistant hash from the average-case hardness of SZK. Previously, this assumption was not known to imply any form of collision resistance (other than the ones implied by one-way functions).

2018

CRYPTO

Fast Distributed RSA Key Generation for Semi-honest and Malicious Adversaries
📺 Abstract

We present two new, highly efficient, protocols for securely generating a distributed RSA key pair in the two-party setting. One protocol is semi-honestly secure and the other maliciously secure. Both are constant round and do not rely on any specific number-theoretic assumptions and improve significantly over the state-of-the-art by allowing a slight leakage (which we show to not affect security).For our maliciously secure protocol our most significant improvement comes from executing most of the protocol in a “strong” semi-honest manner and then doing a single, light, zero-knowledge argument of correct execution. We introduce other significant improvements as well. One such improvement arrives in showing that certain, limited leakage does not compromise security, which allows us to use lightweight subprotocols. Another improvement, which may be of independent interest, comes in our approach for multiplying two large integers using OT, in the malicious setting, without being susceptible to a selective-failure attack.Finally, we implement our malicious protocol and show that its performance is an order of magnitude better than the best previous protocol, which provided only semi-honest security.

2018

CRYPTO

Trapdoor Functions from the Computational Diffie-Hellman Assumption
📺 Abstract

Trapdoor functions (TDFs) are a fundamental primitive in cryptography. Yet, the current set of assumptions known to imply TDFs is surprisingly limited, when compared to public-key encryption. We present a new general approach for constructing TDFs. Specifically, we give a generic construction of TDFs from any Chameleon Encryption (Döttling and Garg [CRYPTO’17]) satisfying a novel property which we call recyclability. By showing how to adapt current Computational Diffie-Hellman (CDH) based constructions of chameleon encryption to yield recyclability, we obtain the first construction of TDFs with security proved under the CDH assumption. While TDFs from the Decisional Diffie-Hellman (DDH) assumption were previously known, the possibility of basing them on CDH had remained open for more than 30 years.

2018

CRYPTO

Round-Optimal Secure Multiparty Computation with Honest Majority
📺 Abstract

We study the exact round complexity of secure multiparty computation (MPC) in the honest majority setting. We construct several round-optimaln-party protocols, tolerating any $$t<\frac{n}{2}$$ corruptions.
1.Security with abort: We give the first construction of two round MPC for general functions that achieves security with abort against malicious adversaries in the plain model. The security of our protocol only relies on one-way functions.2.Guaranteed output delivery: We also construct protocols that achieve security with guaranteed output delivery: (i) Against fail-stop adversaries, we construct two round MPC either in the (bare) public-key infrastructure model with no additional assumptions, or in the plain model assuming two-round semi-honest oblivious transfer. In three rounds, however, we can achieve security assuming only one-way functions. (ii) Against malicious adversaries, we construct three round MPC in the plain model, assuming public-key encryption and Zaps.Previously, such protocols were only known based on specific learning assumptions and required the use of common reference strings.
All of our results are obtained via general compilers that may be of independent interest.

2018

CRYPTO

On the Exact Round Complexity of Secure Three-Party Computation
📺 Abstract

We settle the exact round complexity of three-party computation (3PC) in honest-majority setting, for a range of security notions such as selective abort, unanimous abort, fairness and guaranteed output delivery. Selective abort security, the weakest in the lot, allows the corrupt parties to selectively deprive some of the honest parties of the output. In the mildly stronger version of unanimous abort, either all or none of the honest parties receive the output. Fairness implies that the corrupted parties receive their output only if all honest parties receive output and lastly, the strongest notion of guaranteed output delivery implies that the corrupted parties cannot prevent honest parties from receiving their output. It is a folklore that the implication holds from the guaranteed output delivery to fairness to unanimous abort to selective abort. We focus on two network settings– pairwise-private channels without and with a broadcast channel.In the minimal setting of pairwise-private channels, 3PC with selective abort is known to be feasible in just two rounds, while guaranteed output delivery is infeasible to achieve irrespective of the number of rounds. Settling the quest for exact round complexity of 3PC in this setting, we show that three rounds are necessary and sufficient for unanimous abort and fairness. Extending our study to the setting with an additional broadcast channel, we show that while unanimous abort is achievable in just two rounds, three rounds are necessary and sufficient for fairness and guaranteed output delivery. Our lower bound results extend for any number of parties in honest majority setting and imply tightness of several known constructions.The fundamental concept of garbled circuits underlies all our upper bounds. Concretely, our constructions involve transmitting and evaluating only constant number of garbled circuits. Assumption-wise, our constructions rely on injective (one-to-one) one-way functions.

2018

CRYPTO

Promise Zero Knowledge and Its Applications to Round Optimal MPC
📺 Abstract

We devise a new partitioned simulation technique for MPC where the simulator uses different strategies for simulating the view of aborting adversaries and non-aborting adversaries. The protagonist of this technique is a new notion of promise zero knowledge (ZK) where the ZK property only holds against non-aborting verifiers. We show how to realize promise ZK in three rounds in the simultaneous-message model assuming polynomially hard DDH (or QR or N$$^{th}$$-Residuosity).We demonstrate the following applications of our new technique:We construct the first round-optimal (i.e., four round) MPC protocol for general functions based on polynomially hard DDH (or QR or N$$^{th}$$-Residuosity).We further show how to overcome the four-round barrier for MPC by constructing a three-round protocol for “list coin-tossing” – a slight relaxation of coin-tossing that suffices for most conceivable applications – based on polynomially hard DDH (or QR or N$$^{th}$$-Residuosity). This result generalizes to randomized input-less functionalities.
Previously, four round MPC protocols required sub-exponential-time hardness assumptions and no multi-party three-round protocols were known for any relaxed security notions with polynomial-time simulation against malicious adversaries.In order to base security on polynomial-time standard assumptions, we also rely upon a leveled rewinding security technique that can be viewed as a polynomial-time alternative to leveled complexity leveraging for achieving “non-malleability” across different primitives.

2018

CRYPTO

Round-Optimal Secure Multi-Party Computation
📺 Abstract

Secure multi-party computation (MPC) is a central cryptographic task that allows a set of mutually distrustful parties to jointly compute some function of their private inputs where security should hold in the presence of a malicious adversary that can corrupt any number of parties. Despite extensive research, the precise round complexity of this “standard-bearer” cryptographic primitive is unknown. Recently, Garg, Mukherjee, Pandey and Polychroniadou, in EUROCRYPT 2016 demonstrated that the round complexity of any MPC protocol relying on black-box proofs of security in the plain model must be at least four. Following this work, independently Ananth, Choudhuri and Jain, CRYPTO 2017 and Brakerski, Halevi, and Polychroniadou, TCC 2017 made progress towards solving this question and constructed four-round protocols based on non-polynomial time assumptions. More recently, Ciampi, Ostrovsky, Siniscalchi and Visconti in TCC 2017 closed the gap for two-party protocols by constructing a four-round protocol from polynomial-time assumptions. In another work, Ciampi, Ostrovsky, Siniscalchi and Visconti TCC 2017 showed how to design a four-round multi-party protocol for the specific case of multi-party coin-tossing.In this work, we resolve this question by designing a four-round actively secure multi-party (two or more parties) protocol for general functionalities under standard polynomial-time hardness assumptions with a black-box proof of security.

2018

CRYPTO

Yes, There is an Oblivious RAM Lower Bound!
📺 Abstract

★ Best Paper Award

An Oblivious RAM (ORAM) introduced by Goldreich and Ostrovsky [JACM’96] is a (possibly randomized) RAM, for which the memory access pattern reveals no information about the operations performed. The main performance metric of an ORAM is the bandwidth overhead, i.e., the multiplicative factor extra memory blocks that must be accessed to hide the operation sequence. In their seminal paper introducing the ORAM, Goldreich and Ostrovsky proved an amortized
$$\varOmega (\lg n)$$
bandwidth overhead lower bound for ORAMs with memory size n. Their lower bound is very strong in the sense that it applies to the “offline” setting in which the ORAM knows the entire sequence of operations ahead of time.However, as pointed out by Boyle and Naor [ITCS’16] in the paper “Is there an oblivious RAM lower bound?”, there are two caveats with the lower bound of Goldreich and Ostrovsky: (1) it only applies to “balls in bins” algorithms, i.e., algorithms where the ORAM may only shuffle blocks around and not apply any sophisticated encoding of the data, and (2), it only applies to statistically secure constructions. Boyle and Naor showed that removing the “balls in bins” assumption would result in super linear lower bounds for sorting circuits, a long standing open problem in circuit complexity. As a way to circumventing this barrier, they also proposed a notion of an “online” ORAM, which is an ORAM that remains secure even if the operations arrive in an online manner. They argued that most known ORAM constructions work in the online setting as well.Our contribution is an
$$\varOmega (\lg n)$$
lower bound on the bandwidth overhead of any online ORAM, even if we require only computational security and allow arbitrary representations of data, thus greatly strengthening the lower bound of Goldreich and Ostrovsky in the online setting. Our lower bound applies to ORAMs with memory size n and any word size
$$r \ge 1$$
. The bound therefore asymptotically matches the known upper bounds when
$$r = \varOmega (\lg ^2 n)$$
.

2018

CRYPTO

Constrained PRFs for $\mathrm{NC}^1$ in Traditional Groups
📺 Abstract

We propose new constrained pseudorandom functions (CPRFs) in traditional groups. Traditional groups mean cyclic and multiplicative groups of prime order that were widely used in the 1980s and 1990s (sometimes called “pairing free” groups). Our main constructions are as follows.
We propose a selectively single-key secure CPRF for circuits with depth$$O(\log n)$$(that is,NC$$^1$$circuits) in traditional groups where n is the input size. It is secure under the L-decisional Diffie-Hellman inversion (L-DDHI) assumption in the group of quadratic residues $$\mathbb {QR}_q$$ and the decisional Diffie-Hellman (DDH) assumption in a traditional group of order qin the standard model.We propose a selectively single-key private bit-fixing CPRF in traditional groups. It is secure under the DDH assumption in any prime-order cyclic group in the standard model.We propose adaptively single-key secure CPRF for NC$$^1$$ and private bit-fixing CPRF in the random oracle model.
To achieve the security in the standard model, we develop a new technique using correlated-input secure hash functions.

2018

CRYPTO

The Algebraic Group Model and its Applications
📺 Abstract

One of the most important and successful tools for assessing hardness assumptions in cryptography is the Generic Group Model (GGM). Over the past two decades, numerous assumptions and protocols have been analyzed within this model. While a proof in the GGM can certainly provide some measure of confidence in an assumption, its scope is rather limited since it does not capture group-specific algorithms that make use of the representation of the group.To overcome this limitation, we propose the Algebraic Group Model (AGM), a model that lies in between the Standard Model and the GGM. It is the first restricted model of computation covering group-specific algorithms yet allowing to derive simple and meaningful security statements. To prove its usefulness, we show that several important assumptions, among them the Computational Diffie-Hellman, the Strong Diffie-Hellman, and the interactive LRSW assumptions, are equivalent to the Discrete Logarithm (DLog) assumption in the AGM. On the more practical side, we prove tight security reductions for two important schemes in the AGM to DLog or a variant thereof: the BLS signature scheme and Groth’s zero-knowledge SNARK (EUROCRYPT 2016), which is the most efficient SNARK for which only a proof in the GGM was known. Our proofs are quite simple and therefore less prone to subtle errors than those in the GGM.Moreover, in combination with known lower bounds on the Discrete Logarithm assumption in the GGM, our results can be used to derive lower bounds for all the above-mentioned results in the GGM.

2018

CRYPTO

GGH15 Beyond Permutation Branching Programs: Proofs, Attacks, and Candidates
📺 Abstract

We carry out a systematic study of the GGH15 graded encoding scheme used with general branching programs. This is motivated by the fact that general branching programs are more efficient than permutation branching programs and also substantially more expressive in the read-once setting. Our main results are as follows:Proofs. We present new constructions of private constrained PRFs and lockable obfuscation, for constraints (resp. functions to be obfuscated) that are computable by general branching programs. Our constructions are secure under LWE with subexponential approximation factors. Previous constructions of this kind crucially rely on the permutation structure of the underlying branching programs. Using general branching programs allows us to obtain more efficient constructions for certain classes of constraints (resp. functions), while posing new challenges in the proof, which we overcome using new proof techniques.Attacks. We extend the previous attacks on indistinguishability obfuscation (iO) candidates that use GGH15 encodings. The new attack simply uses the rank of a matrix as the distinguisher, so we call it a “rank attack”. The rank attack breaks, among others, the iO candidate for general read-once branching programs by Halevi, Halevi, Shoup and Stephens-Davidowitz (CCS 2017).Candidate Witness Encryption and iO. Drawing upon insights from our proofs and attacks, we present simple candidates for witness encryption and iO that resist the existing attacks, using GGH15 encodings. Our candidate for witness encryption crucially exploits the fact that formulas in conjunctive normal form (CNFs) can be represented by general, read-once branching programs.

2018

CRYPTO

Lower Bounds on Lattice Enumeration with Extreme Pruning
📺 Abstract

At Eurocrypt ’10, Gama, Nguyen and Regev introduced lattice enumeration with extreme pruning: this algorithm is implemented in state-of-the-art lattice reduction software and used in challenge records. They showed that extreme pruning provided an exponential speed-up over full enumeration. However, no limit on its efficiency was known, which was problematic for long-term security estimates of lattice-based cryptosystems. We prove the first lower bounds on lattice enumeration with extreme pruning: if the success probability is lower bounded, we can lower bound the global running time taken by extreme pruning. Our results are based on geometric properties of cylinder intersections and some form of isoperimetry. We discuss their impact on lattice security estimates.

2018

CRYPTO

Dissection-BKW
📺 Abstract

The slightly subexponential algorithm of Blum, Kalai and Wasserman (BKW) provides a basis for assessing LPN/LWE security. However, its huge memory consumption strongly limits its practical applicability, thereby preventing precise security estimates for cryptographic LPN/LWE instantiations.We provide the first time-memory trade-offs for the BKW algorithm. For instance, we show how to solve LPN in dimension k in time $$2^{\frac{4}{3} \frac{k}{\log k} }$$ and memory $$2^{\frac{2}{3} \frac{k}{\log k} }$$. Using the Dissection technique due to Dinur et al. (Crypto ’12) and a novel, slight generalization thereof, we obtain fine-grained trade-offs for any available (subexponential) memory while the running time remains subexponential.Reducing the memory consumption of BKW below its running time also allows us to propose a first quantum version QBKW for the BKW algorithm.

2018

CRYPTO

Sub-linear Lattice-Based Zero-Knowledge Arguments for Arithmetic Circuits
📺 Abstract

We propose the first zero-knowledge argument with sub-linear communication complexity for arithmetic circuit satisfiability over a prime
$${p}$$
whose security is based on the hardness of the short integer solution (SIS) problem. For a circuit with
$${N}$$
gates, the communication complexity of our protocol is
$$O\left( \sqrt{{N}{\lambda }\log ^3{{N}}}\right) $$
, where
$${\lambda }$$
is the security parameter. A key component of our construction is a surprisingly simple zero-knowledge proof for pre-images of linear relations whose amortized communication complexity depends only logarithmically on the number of relations being proved. This latter protocol is a substantial improvement, both theoretically and in practice, over the previous results in this line of research of Damgård et al. (CRYPTO 2012), Baum et al. (CRYPTO 2016), Cramer et al. (EUROCRYPT 2017) and del Pino and Lyubashevsky (CRYPTO 2017), and we believe it to be of independent interest.

2018

CRYPTO

Lattice-Based Zero-Knowledge Arguments for Integer Relations
📺 Abstract

We provide lattice-based protocols allowing to prove relations among committed integers. While the most general zero-knowledge proof techniques can handle arithmetic circuits in the lattice setting, adapting them to prove statements over the integers is non-trivial, at least if we want to handle exponentially large integers while working with a polynomial-size modulus q. For a polynomial L, we provide zero-knowledge arguments allowing a prover to convince a verifier that committed L-bit bitstrings x, y and z are the binary representations of integers X, Y and Z satisfying $$Z=X+Y$$ over $$\mathbb {Z}$$. The complexity of our arguments is only linear in L. Using them, we construct arguments allowing to prove inequalities $$X<Z$$ among committed integers, as well as arguments showing that a committed X belongs to a public interval $$[\alpha ,\beta ]$$, where $$\alpha $$ and $$\beta $$ can be arbitrarily large. Our range arguments have logarithmic cost (i.e., linear in L) in the maximal range magnitude. Using these tools, we obtain zero-knowledge arguments showing that a committed element X does not belong to a public set S using $$\widetilde{\mathcal {O}}(n \cdot \log |S|)$$ bits of communication, where n is the security parameter. We finally give a protocol allowing to argue that committed L-bit integers X, Y and Z satisfy multiplicative relations $$Z=XY$$ over the integers, with communication cost subquadratic in L. To this end, we use our protocol for integer addition to prove the correct recursive execution of Karatsuba’s multiplication algorithm. The security of our protocols relies on standard lattice assumptions with polynomial modulus and polynomial approximation factor.

2018

CRYPTO

Multi-Theorem Preprocessing NIZKs from Lattices
📺 Abstract

★ Best Young Researcher Paper

Non-interactive zero-knowledge (NIZK) proofs are fundamental to modern cryptography. Numerous NIZK constructions are known in both the random oracle and the common reference string (CRS) models. In the CRS model, there exist constructions from several classes of cryptographic assumptions such as trapdoor permutations, pairings, and indistinguishability obfuscation. Notably absent from this list, however, are constructions from standard lattice assumptions. While there has been partial progress in realizing NIZKs from lattices for specific languages, constructing NIZK proofs (and arguments) for all of $$\mathsf {NP}$$ from standard lattice assumptions remains open. In this work, we make progress on this problem by giving the first construction of a multi-theorem NIZK argument for $$\mathsf {NP}$$ from standard lattice assumptions in the preprocessing model. In the preprocessing model, a (trusted) setup algorithm generates proving and verification keys. The proving key is needed to construct proofs and the verification key is needed to check proofs. In the multi-theorem setting, the proving and verification keys should be reusable for an unbounded number of theorems without compromising soundness or zero-knowledge. Existing constructions of NIZKs in the preprocessing model (or even the designated-verifier model) that rely on weaker assumptions like one-way functions or oblivious transfer are only secure in a single-theorem setting. Thus, constructing multi-theorem NIZKs in the preprocessing model does not seem to be inherently easier than constructing them in the CRS model. We begin by constructing a multi-theorem preprocessing NIZK directly from context-hiding homomorphic signatures. Then, we show how to efficiently implement the preprocessing step using a new cryptographic primitive called blind homomorphic signatures. This primitive may be of independent interest. Finally, we show how to leverage our new lattice-based preprocessing NIZKs to obtain new malicious-secure MPC protocols purely from standard lattice assumptions.

2018

CRYPTO

SPD$\mathbb {Z}_{2^k}$: Efficient MPC mod $2^k$ for Dishonest Majority
📺 Abstract

Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime. In the more natural setting of integer computations modulo $$2^{k}$$, which are useful for simplifying implementations and applications, no solutions with active security are known unless the majority of the participants are honest.We present a new scheme for information-theoretic MACs that are homomorphic modulo $$2^k$$, and are as efficient as the well-known standard solutions that are homomorphic over fields. We apply this to construct an MPC protocol for dishonest majority in the preprocessing model that has efficiency comparable to the well-known SPDZ protocol (Damgård et al., CRYPTO 2012), with operations modulo $$2^k$$ instead of over a field. We also construct a matching preprocessing protocol based on oblivious transfer, which is in the style of the MASCOT protocol (Keller et al., CCS 2016) and almost as efficient.

2018

CRYPTO

Yet Another Compiler for Active Security or: Efficient MPC Over Arbitrary Rings
📺 Abstract

We present a very simple yet very powerful idea for turning any passively secure MPC protocol into an actively secure one, at the price of reducing the threshold of tolerated corruptions.Our compiler leads to a very efficient MPC protocols for the important case of secure evaluation of arithmetic circuits over arbitrary rings (e.g., the natural case of $${\mathbb {Z}}_{2^{\ell }}\!$$) for a small number of parties. We show this by giving a concrete protocol in the preprocessing model for the popular setting with three parties and one corruption. This is the first protocol for secure computation over rings that achieves active security with constant overhead.

2018

CRYPTO

On Tightly Secure Non-Interactive Key Exchange
📺 Abstract

We consider the reduction loss of security reductions for non-interactive key exchange (NIKE) schemes. Currently, no tightly secure NIKE schemes exist, and in fact Bader et al. (EUROCRYPT 2016) provide a lower bound (of $$\varOmega (n^2)$$, where $$n$$ is the number of parties an adversary interacts with) on the reduction loss for a large class of NIKE schemes.We offer two results: the first NIKE scheme with a reduction loss of $$n/2$$ that circumvents the lower bound of Bader et al., but is of course still far from tightly secure. Second, we provide a generalization of Bader et al.’s lower bound to a larger class of NIKE schemes (that also covers our NIKE scheme), with an adapted lower bound of $$n/2$$ on the reduction loss. Hence, in that sense, the reduction for our NIKE scheme is optimal.

2018

CRYPTO

Practical and Tightly-Secure Digital Signatures and Authenticated Key Exchange
📺 Abstract

Tight security is increasingly gaining importance in real-world cryptography, as it allows to choose cryptographic parameters in a way that is supported by a security proof, without the need to sacrifice efficiency by compensating the security loss of a reduction with larger parameters. However, for many important cryptographic primitives, including digital signatures and authenticated key exchange (AKE), we are still lacking constructions that are suitable for real-world deployment.We construct the first truly practical signature scheme with tight security in a real-world multi-user setting with adaptive corruptions. The scheme is based on a new way of applying the Fiat-Shamir approach to construct tightly-secure signatures from certain identification schemes.Then we use this scheme as a building block to construct the first practical AKE protocol with tight security. It allows the establishment of a key within 1 RTT in a practical client-server setting, provides forward security, is simple and easy to implement, and thus very suitable for practical deployment. It is essentially the “signed Diffie-Hellman” protocol, but with an additional message, which is crucial to achieve tight security. This additional message is used to overcome a technical difficulty in constructing tightly-secure AKE protocols.For a theoretically-sound choice of parameters and a moderate number of users and sessions, our protocol has comparable computational efficiency to the simple signed Diffie-Hellman protocol with EC-DSA, while for large-scale settings our protocol has even better computational performance, at moderately increased communication complexity.

2018

CRYPTO

Fast Correlation Attack Revisited
📺 Abstract

A fast correlation attack (FCA) is a well-known cryptanalysis technique for LFSR-based stream ciphers. The correlation between the initial state of an LFSR and corresponding key stream is exploited, and the goal is to recover the initial state of the LFSR. In this paper, we revisit the FCA from a new point of view based on a finite field, and it brings a new property for the FCA when there are multiple linear approximations. Moreover, we propose a novel algorithm based on the new property, which enables us to reduce both time and data complexities. We finally apply this technique to the Grain family, which is a well-analyzed class of stream ciphers. There are three stream ciphers, Grain-128a, Grain-128, and Grain-v1 in the Grain family, and Grain-v1 is in the eSTREAM portfolio and Grain-128a is standardized by ISO/IEC. As a result, we break them all, and especially for Grain-128a, the cryptanalysis on its full version is reported for the first time.

2018

CRYPTO

A Key-Recovery Attack on 855-round Trivium
📺 Abstract

In this paper, we propose a key-recovery attack on Trivium reduced to 855 rounds. As the output is a complex Boolean polynomial over secret key and IV bits and it is hard to find the solution of the secret keys, we propose a novel nullification technique of the Boolean polynomial to reduce the output Boolean polynomial of 855-round Trivium. Then we determine the degree upper bound of the reduced nonlinear boolean polynomial and detect the right keys. These techniques can be applicable to most stream ciphers based on nonlinear feedback shift registers (NFSR). Our attack on 855-round Trivium costs time complexity $$2^{77}$$. As far as we know, this is the best key-recovery attack on round-reduced Trivium. To verify our attack, we also give some experimental data on 721-round reduced Trivium.

2018

CRYPTO

Bernstein Bound on WCS is Tight
📺 Abstract

In Eurocrypt 2018, Luykx and Preneel described hash-key-recovery and forgery attacks against polynomial hash based Wegman-Carter-Shoup (WCS) authenticators. Their attacks require
$$2^{n/2}$$
message-tag pairs and recover hash-key with probability about
$$1.34\, \times \, 2^{-n}$$
where n is the bit-size of the hash-key. Bernstein in Eurocrypt 2005 had provided an upper bound (known as Bernstein bound) of the maximum forgery advantages. The bound says that all adversaries making
$$O(2^{n/2})$$
queries of WCS can have maximum forgery advantage
$$O(2^{-n})$$
. So, Luykx and Preneel essentially analyze WCS in a range of query complexities where WCS is known to be perfectly secure. Here we revisit the bound and found that WCS remains secure against all adversaries making
$$q \ll \sqrt{n} \times 2^{n/2}$$
queries. So it would be meaningful to analyze adversaries with beyond birthday bound complexities.In this paper, we show that the Bernstein bound is tight by describing two attacks (one in the “chosen-plaintext model” and other in the “known-plaintext model”) which recover the hash-key (hence forges) with probability at leastbased on
$$\sqrt{n} \times 2^{n/2}$$
message-tag pairs. We also extend the forgery adversary to the Galois Counter Mode (or GCM). More precisely, we recover the hash-key of GCM with probability at least
$$\frac{1}{2}$$
based on only
$$\sqrt{\frac{n}{\ell }} \times 2^{n/2}$$
encryption queries, where
$$\ell $$
is the number of blocks present in encryption queries.

2018

CRYPTO

Correcting Subverted Random Oracles
📺 Abstract

The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes, and can often act as an effective bridge between theory and practice. In this paper, we focus on the basic problem of correcting faulty—or adversarially corrupted—random oracles, so that they can be confidently applied for such cryptographic purposes.We prove that a simple construction can transform a “subverted” random oracle—which disagrees with the original one at a negligible fraction of inputs—into a construction that is indifferentiable from a random function. Our results permit future designers of cryptographic primitives in typical kleptographic settings (i.e., with adversaries who may subvert the implementation of cryptographic algorithms but undetectable via blackbox testing) to use random oracles as a trusted black box, in spite of not trusting the implementation. Our analysis relies on a general rejection re-sampling lemma which is a tool of possible independent interest.

2018

CRYPTO

Towards Bidirectional Ratcheted Key Exchange
📺 Abstract

Ratcheted key exchange (RKE) is a cryptographic technique used in instant messaging systems like Signal and the WhatsApp messenger for attaining strong security in the face of state exposure attacks. RKE received academic attention in the recent works of Cohn-Gordon et al. (EuroS&P 2017) and Bellare et al. (CRYPTO 2017). While the former is analytical in the sense that it aims primarily at assessing the security that one particular protocol does achieve (which might be weaker than the notion that it should achieve), the authors of the latter develop and instantiate a notion of security from scratch, independently of existing implementations. Unfortunately, however, their model is quite restricted, e.g. for considering only unidirectional communication and the exposure of only one of the two parties.In this article we resolve the limitations of prior work by developing alternative security definitions, for unidirectional RKE as well as for RKE where both parties contribute. We follow a purist approach, aiming at finding strong yet convincing notions that cover a realistic communication model with fully concurrent operation of both participants. We further propose secure instantiations (as the protocols analyzed or proposed by Cohn-Gordon et al. and Bellare et al. turn out to be weak in our models). While our scheme for the unidirectional case builds on a generic KEM as the main building block (differently to prior work that requires explicitly Diffie–Hellman), our schemes for bidirectional RKE require a stronger, HIBE-like component.

2018

CRYPTO

Improved Division Property Based Cube Attacks Exploiting Algebraic Properties of Superpoly
📺 Abstract

The cube attack is an important technique for the cryptanalysis of symmetric key primitives, especially for stream ciphers. Aiming at recovering some secret key bits, the adversary reconstructs a superpoly with the secret key bits involved, by summing over a set of the plaintexts/IV which is called a cube. Traditional cube attack only exploits linear/quadratic superpolies. Moreover, for a long time after its proposal, the size of the cubes has been largely confined to an experimental range, e.g., typically 40. These limits were first overcome by the division property based cube attacks proposed by Todo et al. at CRYPTO 2017. Based on MILP modelled division property, for a cube (index set) I, they identify the small (index) subset J of the secret key bits involved in the resultant superpoly. During the precomputation phase which dominates the complexity of the cube attacks, $$2^{|I|+|J|}$$2|I|+|J| encryptions are required to recover the superpoly. Therefore, their attacks can only be available when the restriction $$|I|+|J|<n$$|I|+|J|<n is met.In this paper, we introduced several techniques to improve the division property based cube attacks by exploiting various algebraic properties of the superpoly.
1.We propose the “flag” technique to enhance the preciseness of MILP models so that the proper non-cube IV assignments can be identified to obtain a non-constant superpoly.2.A degree evaluation algorithm is presented to upper bound the degree of the superpoly. With the knowledge of its degree, the superpoly can be recovered without constructing its whole truth table. This enables us to explore larger cubes I’s even if $$|I|+|J|\ge n$$|I|+|J|≥n.3.We provide a term enumeration algorithm for finding the monomials of the superpoly, so that the complexity of many attacks can be further reduced.
As an illustration, we apply our techniques to attack the initialization of several ciphers. To be specific, our key recovery attacks have mounted to 839-round Trivium, 891-round Kreyvium, 184-round Grain-128a and 750-round Acornrespectively.

2018

CRYPTO

Generic Attacks Against Beyond-Birthday-Bound MACs
📺 Abstract

In this work, we study the security of several recent MAC constructions with provable security beyond the birthday bound. We consider block-cipher based constructions with a double-block internal state, such as SUM-ECBC, PMAC+, 3kf9, GCM-SIV2, and some variants (LightMAC+, 1kPMAC+). All these MACs have a security proof up to $$2^{2n/3}$$ queries, but there are no known attacks with less than $$2^{n}$$ queries.We describe a new cryptanalysis technique for double-block MACs based on finding quadruples of messages with four pairwise collisions in halves of the state. We show how to detect such quadruples in SUM-ECBC, PMAC+, 3kf9, GCM-SIV2 and their variants with $$\mathcal {O}(2^{3n/4})$$ queries, and how to build a forgery attack with the same query complexity. The time complexity of these attacks is above $$2^n$$, but it shows that the schemes do not reach full security in the information theoretic model. Surprisingly, our attack on LightMAC+ also invalidates a recent security proof by Naito.Moreover, we give a variant of the attack against SUM-ECBC and GCM-SIV2 with time and data complexity $$\tilde{\mathcal {O}}(2^{6n/7})$$. As far as we know, this is the first attack with complexity below $$2^n$$ against a deterministic beyond-birthday-bound secure MAC.As a side result, we also give a birthday attack against 1kf9, a single-key variant of 3kf9 that was withdrawn due to issues with the proof.

2018

CRYPTO

Searchable Encryption with Optimal Locality: Achieving Sublogarithmic Read Efficiency
📺 Abstract

We propose the first linear-space searchable encryption scheme with constant locality and sublogarithmic read efficiency, strictly improving the previously best known read efficiency bound (Asharov et al., STOC 2016) from $$\varTheta (\log N \log \log N)$$Θ(logNloglogN) to $$O(\log ^{\gamma } N)$$O(logγN) where $$\gamma =\frac{2}{3}+\delta $$γ=23+δ for any fixed $$\delta >0$$δ>0 and where N is the number of keyword-document pairs. Our scheme employs four different allocation algorithms for storing the keyword lists, depending on the size of the list considered each time. For our construction we develop (i) new probability bounds for the offline two-choice allocation problem; (ii) and a new I/O-efficient oblivious RAM with $$\tilde{O}(n^{1/3})$$O~(n1/3) bandwidth overhead and zero failure probability, both of which can be of independent interest.

2018

CRYPTO

Tight Tradeoffs in Searchable Symmetric Encryption
📺 Abstract

A searchable symmetric encryption (SSE) scheme enables a client to store data on an untrusted server while supporting keyword searches in a secure manner. Recent experiments have indicated that the practical relevance of such schemes heavily relies on the tradeoff between their space overhead, locality (the number of non-contiguous memory locations that the server accesses with each query), and read efficiency (the ratio between the number of bits the server reads with each query and the actual size of the answer). These experiments motivated Cash and Tessaro (EUROCRYPT ’14) and Asharov et al. (STOC ’16) to construct SSE schemes offering various such tradeoffs, and to prove lower bounds for natural SSE frameworks. Unfortunately, the best-possible tradeoff has not been identified, and there are substantial gaps between the existing schemes and lower bounds, indicating that a better understanding of SSE is needed.We establish tight bounds on the tradeoff between the space overhead, locality and read efficiency of SSE schemes within two general frameworks that capture the memory access pattern underlying all existing schemes. First, we introduce the “pad-and-split” framework, refining that of Cash and Tessaro while still capturing the same existing schemes. Within our framework we significantly strengthen their lower bound, proving that any scheme with locality L must use space $$\varOmega ( N \log N / \log L )$$Ω(NlogN/logL) for databases of size N. This is a tight lower bound, matching the tradeoff provided by the scheme of Demertzis and Papamanthou (SIGMOD ’17) which is captured by our pad-and-split framework.Then, within the “statistical-independence” framework of Asharov et al. we show that their lower bound is essentially tight: We construct a scheme whose tradeoff matches their lower bound within an additive $$O(\log \log \log N)$$O(logloglogN) factor in its read efficiency, once again improving upon the existing schemes. Our scheme offers optimal space and locality, and nearly-optimal read efficiency that depends on the frequency of the queried keywords: For a keyword that is associated with $$n = N^{1 - \epsilon (n)}$$n=N1-ϵ(n) document identifiers, the read efficiency is $$\omega (1) \cdot {\epsilon }(n)^{-1}+ O(\log \log \log N)$$ω(1)·ϵ(n)-1+O(logloglogN) when retrieving its identifiers (where the $$\omega (1)$$ω(1) term may be arbitrarily small, and $$\omega (1) \cdot {\epsilon }(n)^{-1}$$ω(1)·ϵ(n)-1 is the lower bound proved by Asharov et al.). In particular, for any keyword that is associated with at most $$N^{1 - 1/o(\log \log \log N)}$$N1-1/o(logloglogN) document identifiers (i.e., for any keyword that is not exceptionally common), we provide read efficiency $$O(\log \log \log N)$$O(logloglogN) when retrieving its identifiers.

2018

CRYPTO

Hardness of Non-interactive Differential Privacy from One-Way Functions
📺 Abstract

A central challenge in differential privacy is to design computationally efficient non-interactive algorithms that can answer large numbers of statistical queries on a sensitive dataset. That is, we would like to design a differentially private algorithm that takes a dataset $$D \in X^n$$D∈Xn consisting of some small number of elements n from some large data universe X, and efficiently outputs a summary that allows a user to efficiently obtain an answer to any query in some large family Q.Ignoring computational constraints, this problem can be solved even when X and Q are exponentially large and n is just a small polynomial; however, all algorithms with remotely similar guarantees run in exponential time. There have been several results showing that, under the strong assumption of indistinguishability obfuscation, no efficient differentially private algorithm exists when X and Q can be exponentially large. However, there are no strong separations between information-theoretic and computationally efficient differentially private algorithms under any standard complexity assumption.In this work we show that, if one-way functions exist, there is no general purpose differentially private algorithm that works when X and Q are exponentially large, and n is an arbitrary polynomial. In fact, we show that this result holds even if X is just subexponentially large (assuming only polynomially-hard one-way functions). This result solves an open problem posed by Vadhan in his recent survey [52].

2018

CRYPTO

Non-malleable Secret Sharing for General Access Structures
📺 Abstract

Goyal and Kumar (STOC’18) recently introduced the notion of non-malleable secret sharing. Very roughly, the guarantee they seek is the following: the adversary may potentially tamper with all of the shares, and still, either the reconstruction procedure outputs the original secret, or, the original secret is “destroyed” and the reconstruction outputs a string which is completely “unrelated” to the original secret. Prior works on non-malleable codes in the 2 split-state model imply constructions which can be seen as 2-out-of-2 non-malleable secret sharing (NMSS) schemes. Goyal and Kumar proposed constructions of t-out-of-n NMSS schemes. These constructions have already been shown to have a number of applications in cryptography.We continue this line of research and construct NMSS for more general access structures. We give a generic compiler that converts any statistical (resp. computational) secret sharing scheme realizing any access structure into another statistical (resp. computational) secret sharing scheme that not only realizes the same access structure but also ensures statistical non-malleability against a computationally unbounded adversary who tampers each of the shares arbitrarily and independently. Instantiating with known schemes we get unconditional NMMS schemes that realize any access structures generated by polynomial size monotone span programs. Similarly, we also obtain conditional NMMS schemes realizing access structure in
$$\mathbf {monotone \;P}$$
monotoneP (resp.
$$\mathbf {monotone \;NP}$$
monotoneNP) assuming one-way functions (resp. witness encryption).Towards considering more general tampering models, we also propose a construction of n-out-of-n NMSS. Our construction is secure even if the adversary could divide the shares into any two (possibly overlapping) subsets and then arbitrarily tamper the shares in each subset. Our construction is based on a property of inner product and an observation that the inner-product based construction of Aggarwal, Dodis and Lovett (STOC’14) is in fact secure against a tampering class that is stronger than 2 split-states. We also show applications of our construction to the problem of non-malleable message transmission.

2018

CRYPTO

On the Local Leakage Resilience of Linear Secret Sharing Schemes
📺 Abstract

We consider the following basic question: to what extent are standard secret sharing schemes and protocols for secure multiparty computation that build on them resilient to leakage? We focus on a simple local leakage model, where the adversary can apply an arbitrary function of a bounded output length to the secret state of each party, but cannot otherwise learn joint information about the states.We show that additive secret sharing schemes and high-threshold instances of Shamir’s secret sharing scheme are secure under local leakage attacks when the underlying field is of a large prime order and the number of parties is sufficiently large. This should be contrasted with the fact that any linear secret sharing scheme over a small characteristic field is clearly insecure under local leakage attacks, regardless of the number of parties. Our results are obtained via tools from Fourier analysis and additive combinatorics.We present two types of applications of the above results and techniques. As a positive application, we show that the “GMW protocol” for honest-but-curious parties, when implemented using shared products of random field elements (so-called “Beaver Triples”), is resilient in the local leakage model for sufficiently many parties and over certain fields. This holds even when the adversary has full access to a constant fraction of the views. As a negative application, we rule out multi-party variants of the share conversion scheme used in the 2-party homomorphic secret sharing scheme of Boyle et al. (Crypto 2016).

2018

CRYPTO

Threshold Cryptosystems from Threshold Fully Homomorphic Encryption
📺 Abstract

We develop a general approach to adding a threshold functionality to a large class of (non-threshold) cryptographic schemes. A threshold functionality enables a secret key to be split into a number of shares, so that only a threshold of parties can use the key, without reconstructing the key. We begin by constructing a threshold fully-homomorphic encryption scheme (ThFHE) from the learning with errors (LWE) problem. We next introduce a new concept, called a universal thresholdizer, from which many threshold systems are possible. We show how to construct a universal thresholdizer from our ThFHE. A universal thresholdizer can be used to add threshold functionality to many systems, such as CCA-secure public-key encryption (PKE), signature schemes, pseudorandom functions, and others primitives. In particular, by applying this paradigm to a (non-threshold) lattice signature system, we obtain the first single-round threshold signature scheme from LWE.

2018

CRYPTO

Optimal Channel Security Against Fine-Grained State Compromise: The Safety of Messaging
📺 Abstract

We aim to understand the best possible security of a (bidirectional) cryptographic channel against an adversary that may arbitrarily and repeatedly learn the secret state of either communicating party. We give a formal security definition and a proven-secure construction. This construction provides better security against state compromise than the Signal Double Ratchet Algorithm or any other known channel construction. To facilitate this we define and construct new forms of public-key encryption and digital signatures that update their keys over time.

2018

CRYPTO

Multi-Input Functional Encryption for Inner Products: Function-Hiding Realizations and Constructions Without Pairings
📺 Abstract

We present new constructions of multi-input functional encryption (MIFE) schemes for the inner-product functionality that improve the state of the art solution of Abdalla et al. (Eurocrypt 2017) in two main directions.First, we put forward a novel methodology to convert single-input functional encryption for inner products into multi-input schemes for the same functionality. Our transformation is surprisingly simple, general and efficient. In particular, it does not require pairings and it can be instantiated with all known single-input schemes. This leads to two main advances. First, we enlarge the set of assumptions this primitive can be based on, notably, obtaining new MIFEs for inner products from plain DDH, LWE, and Decisional Composite Residuosity. Second, we obtain the first MIFE schemes from standard assumptions where decryption works efficiently even for messages of super-polynomial size.Our second main contribution is the first function-hiding MIFE scheme for inner products based on standard assumptions. To this end, we show how to extend the original, pairing-based, MIFE by Abdalla et al. in order to make it function hiding, thus obtaining a function-hiding MIFE from the MDDH assumption.

2018

CRYPTO

Encrypt or Decrypt? To Make a Single-Key Beyond Birthday Secure Nonce-Based MAC
📺 Abstract

At CRYPTO 2016, Cogliati and Seurin have proposed a highly secure nonce-based MAC called Encrypted Wegman-Carter with Davies-Meyer ($$\textsf {EWCDM}$$EWCDM) construction, as $$\textsf {E}_{K_2}\bigl (\textsf {E}_{K_1}(N)\oplus N\oplus \textsf {H}_{K_h}(M)\bigr )$$EK2(EK1(N)⊕N⊕HKh(M)) for a nonce N and a message M. This construction achieves roughly $$2^{2n/3}$$22n/3 bit MAC security with the assumption that $$\textsf {E}$$E is a PRP secure n-bit block cipher and $$\textsf {H}$$H is an almost xor universal n-bit hash function. In this paper we propose Decrypted Wegman-Carter with Davies-Meyer ($$\textsf {DWCDM}$$DWCDM) construction, which is structurally very similar to its predecessor $$\textsf {EWCDM}$$EWCDM except that the outer encryption call is replaced by decryption. The biggest advantage of $$\textsf {DWCDM}$$DWCDM is that we can make a truly single key MAC: the two block cipher calls can use the same block cipher key $$K=K_1=K_2$$K=K1=K2. Moreover, we can derive the hash key as $$K_h=\textsf {E}_K(1)$$Kh=EK(1), as long as $$|K_h|=n$$|Kh|=n. Whether we use encryption or decryption in the outer layer makes a huge difference; using the decryption instead enables us to apply an extended version of the mirror theory by Patarin to the security analysis of the construction. $$\textsf {DWCDM}$$DWCDM is secure beyond the birthday bound, roughly up to $$2^{2n/3}$$22n/3 MAC queries and $$2^n$$2n verification queries against nonce-respecting adversaries. $$\textsf {DWCDM}$$DWCDM remains secure up to $$2^{n/2}$$2n/2 MAC queries and $$2^n$$2n verification queries against nonce-misusing adversaries.

2018

CRYPTO

Rasta: A Cipher with Low ANDdepth and Few ANDs per Bit
📺 Abstract

Recent developments in multi party computation (MPC) and fully homomorphic encryption (FHE) promoted the design and analysis of symmetric cryptographic schemes that minimize multiplications in one way or another. In this paper, we propose with Rastaa design strategy for symmetric encryption that has ANDdepth d and at the same time only needs d ANDs per encrypted bit. Even for very low values of d between 2 and 6 we can give strong evidence that attacks may not exist. This contributes to a better understanding of the limits of what concrete symmetric-key constructions can theoretically achieve with respect to AND-related metrics, and is to the best of our knowledge the first attempt that minimizes both metrics simultaneously. Furthermore, we can give evidence that for choices of d between 4 and 6 the resulting implementation properties may well be competitive by testing our construction in the use-case of removing the large ciphertext-expansion when using the BGV scheme.

2018

CRYPTO

Non-Uniform Bounds in the Random-Permutation, Ideal-Cipher, and Generic-Group Models
📺 Abstract

The random-permutation model (RPM) and the ideal-cipher model (ICM) are idealized models that offer a simple and intuitive way to assess the conjectured standard-model security of many important symmetric-key and hash-function constructions. Similarly, the generic-group model (GGM) captures generic algorithms against assumptions in cyclic groups by modeling encodings of group elements as random injections and allows to derive simple bounds on the advantage of such algorithms.Unfortunately, both well-known attacks, e.g., based on rainbow tables (Hellman, IEEE Transactions on Information Theory ’80), and more recent ones, e.g., against the discrete-logarithm problem (Corrigan-Gibbs and Kogan, EUROCRYPT ’18), suggest that the concrete security bounds one obtains from such idealized proofs are often completely inaccurate if one considers non-uniform or preprocessing attacks in the standard model. To remedy this situation, this workdefines the auxiliary-input (AI) RPM/ICM/GGM, which capture both non-uniform and preprocessing attacks by allowing an attacker to leak an arbitrary (bounded-output) function of the oracle’s function table;derives the first non-uniform bounds for a number of important practical applications in the AI-RPM/ICM, including constructions based on the Merkle-Damgård and sponge paradigms, which underly the SHA hashing standards, and for AI-RPM/ICM applications with computational security; andusing simpler proofs, recovers the AI-GGM security bounds obtained by Corrigan-Gibbs and Kogan against preprocessing attackers, for a number of assumptions related to cyclic groups, such as discrete logarithms and Diffie-Hellman problems, and provides new bounds for two assumptions.
An important step in obtaining these results is to port the tools used in recent work by Coretti et al. (EUROCRYPT ’18) from the ROM to the RPM/ICM/GGM, resulting in very powerful and easy-to-use tools for proving security bounds against non-uniform and preprocessing attacks.

2018

CRYPTO

Provable Security of (Tweakable) Block Ciphers Based on Substitution-Permutation Networks
📺 Abstract

Substitution-Permutation Networks (SPNs) refer to a family of constructions which build a wn-bit block cipher from n-bit public permutations (often called S-boxes), which alternate keyless and “local” substitution steps utilizing such S-boxes, with keyed and “global” permutation steps which are non-cryptographic. Many widely deployed block ciphers are constructed based on the SPNs, but there are essentially no provable-security results about SPNs.In this work, we initiate a comprehensive study of the provable security of SPNs as (possibly tweakable) wn-bit block ciphers, when the underlying n-bit permutation is modeled as a public random permutation. When the permutation step is linear (which is the case for most existing designs), we show that 3 SPN rounds are necessary and sufficient for security. On the other hand, even 1-round SPNs can be secure when non-linearity is allowed. Moreover, 2-round non-linear SPNs can achieve “beyond-birthday” (up to
$$2^{2n/3}$$
22n/3 adversarial queries) security, and, as the number of non-linear rounds increases, our bounds are meaningful for the number of queries approaching
$$2^n$$
2n. Finally, our non-linear SPNs can be made tweakable by incorporating the tweak into the permutation layer, and provide good multi-user security.As an application, our construction can turn two public n-bit permutations (or fixed-key block ciphers) into a tweakable block cipher working on wn-bit inputs, 6n-bit key and an n-bit tweak (for any
$$w\ge 2$$
w≥2); the tweakable block cipher provides security up to
$$2^{2n/3}$$
22n/3 adversarial queries in the random permutation model, while only requiring w calls to each permutation, and 3w field multiplications for each wn-bit input.

2018

CRYPTO

Verifiable Delay Functions
📺 Abstract

We study the problem of building a verifiable delay function (VDF). A $$\text {VDF}$$VDFrequires a specified number of sequential steps to evaluate, yet produces a unique output that can be efficiently and publicly verified. $$\text {VDF}$$VDFs have many applications in decentralized systems, including public randomness beacons, leader election in consensus protocols, and proofs of replication. We formalize the requirements for $$\text {VDF}$$VDFs and present new candidate constructions that are the first to achieve an exponential gap between evaluation and verification time.

2018

CRYPTO

Proofs of Work From Worst-Case Assumptions
📺 Abstract

We give Proofs of Work (PoWs) whose hardness is based on well-studied worst-case assumptions from fine-grained complexity theory. This extends the work of (Ball et al., STOC ’17), that presents PoWs that are based on the Orthogonal Vectors, 3SUM, and All-Pairs Shortest Path problems. These, however, were presented as a ‘proof of concept’ of provably secure PoWs and did not fully meet the requirements of a conventional PoW: namely, it was not shown that multiple proofs could not be generated faster than generating each individually. We use the considerable algebraic structure of these PoWs to prove that this non-amortizability of multiple proofs does in fact hold and further show that the PoWs’ structure can be exploited in ways previous heuristic PoWs could not.This creates full PoWs that are provably hard from worst-case assumptions (previously, PoWs were either only based on heuristic assumptions or on much stronger cryptographic assumptions (Bitansky et al., ITCS ’16)) while still retaining significant structure to enable extra properties of our PoWs. Namely, we show that the PoWs of (Ball et al., STOC ’17) can be modified to have much faster verification time, can be proved in zero knowledge, and more.Finally, as our PoWs are based on evaluating low-degree polynomials originating from average-case fine-grained complexity, we prove an average-case direct sum theorem for the problem of evaluating these polynomials, which may be of independent interest. For our context, this implies the required non-amortizability of our PoWs.

2018

CRYPTO

Out-of-Band Authentication in Group Messaging: Computational, Statistical, Optimal
📺 Abstract

Extensive efforts are currently put into securing messaging platforms, where a key challenge is that of protecting against man-in-the-middle attacks when setting up secure end-to-end channels. The vast majority of these efforts, however, have so far focused on securing user-to-user messaging, and recent attacks indicate that the security of group messaging is still quite fragile.We initiate the study of out-of-band authentication in the group setting, extending the user-to-user setting where messaging platforms (e.g., Telegram and WhatsApp) protect against man-in-the-middle attacks by assuming that users have access to an external channel for authenticating one short value (e.g., two users who recognize each other’s voice can compare a short value). Inspired by the frameworks of Vaudenay (CRYPTO ’05) and Naor et al. (CRYPTO ’06) in the user-to-user setting, we assume that users communicate over a completely-insecure channel, and that a group administrator can out-of-band authenticate one short message to all users. An adversary may read, remove, or delay this message (for all or for some of the users), but cannot undetectably modify it.Within our framework we establish tight bounds on the tradeoff between the adversary’s success probability and the length of the out-of-band authenticated message (which is a crucial bottleneck given that the out-of-band channel is of low bandwidth). We consider both computationally-secure and statistically-secure protocols, and for each flavor of security we construct an authentication protocol and prove a lower bound showing that our protocol achieves essentially the best possible tradeoff.In particular, considering groups that consist of an administrator and k additional users, for statistically-secure protocols we show that at least
$$(k+1)\cdot (\log (1/\epsilon ) - \varTheta (1))$$
(k+1)·(log(1/ϵ)-Θ(1)) bits must be out-of-band authenticated, whereas for computationally-secure ones
$$\log (1/\epsilon ) + \log k$$
log(1/ϵ)+logk bits suffice, where
$$\epsilon $$
ϵ is the adversary’s success probability. Moreover, instantiating our computationally-secure protocol in the random-oracle model yields an efficient and practically-relevant protocol (which, alternatively, can also be based on any one-way function in the standard model).

2018

CRYPTO

Faster Homomorphic Linear Transformations in HElib
📺 Abstract

HElib is a software library that implements homomorphic encryption (HE), with a focus on effective use of “packed” ciphertexts. An important operation is applying a known linear map to a vector of encrypted data. In this paper, we describe several algorithmic improvements that significantly speed up this operation: in our experiments, our new algorithms are 30–75 times faster than those previously implemented in HElib for typical parameters.One application that can benefit from faster linear transformations is bootstrapping (in particular, “thin bootstrapping” as described in [Chen and Han, Eurocrypt 2018]). In some settings, our new algorithms for linear transformations result in a $$6{\times }$$6× speedup for the entire thin bootstrapping operation.Our techniques also reduce the size of the large public evaluation key, often using 33%–50% less space than the previous HElib implementation. We also implemented a new tradeoff that enables a drastic reduction in size, resulting in a $$25{\times }$$25× factor or more for some parameters, paying only a penalty of a 2–$$4{\times }$$4× times slowdown in running time (and giving up some parallelization opportunities).

2018

CRYPTO

CAPA: The Spirit of Beaver Against Physical Attacks
📺 Abstract

In this paper we introduce two things: On one hand we introduce the Tile-Probe-and-Fault model, a model generalising the wire-probe model of Ishai et al. extending it to cover both more realistic side-channel leakage scenarios on a chip and also to cover fault and combined attacks. Secondly we introduce CAPA: a combined Countermeasure Against Physical Attacks. Our countermeasure is motivated by our model, and aims to provide security against higher-order SCA, multiple-shot FA and combined attacks. The tile-probe-and-fault model leads one to naturally look (by analogy) at actively secure multi-party computation protocols. Indeed, CAPA draws much inspiration from the MPC protocol SPDZ. So as to demonstrate that the model, and the CAPA countermeasure, are not just theoretical constructions, but could also serve to build practical countermeasures, we present initial experiments of proof-of-concept designs using the CAPA methodology. Namely, a hardware implementation of the KATAN and AES block ciphers, as well as a software bitsliced AES S-box implementation. We demonstrate experimentally that the design can resist second-order DPA attacks, even when the attacker is presented with many hundreds of thousands of traces. In addition our proof-of-concept can also detect faults within our model with high probability in accordance to the methodology.

2018

CRYPTO

Fast Message Franking: From Invisible Salamanders to Encryptment
📺 Abstract

Message franking enables cryptographically verifiable reporting of abusive messages in end-to-end encrypted messaging. Grubbs, Lu, and Ristenpart recently formalized the needed underlying primitive, what they call compactly committing authenticated encryption (AE), and analyze security of a number of approaches. But all known secure schemes are still slow compared to the fastest standard AE schemes. For this reason Facebook Messenger uses AES-GCM for franking of attachments such as images or videos.We show how to break Facebook’s attachment franking scheme: a malicious user can send an objectionable image to a recipient but that recipient cannot report it as abuse. The core problem stems from use of fast but non-committing AE, and so we build the fastest compactly committing AE schemes to date. To do so we introduce a new primitive, called encryptment, which captures the essential properties needed. We prove that, unfortunately, schemes with performance profile similar to AES-GCM won’t work. Instead, we show how to efficiently transform Merkle-Damgärd-style hash functions into secure encryptments, and how to efficiently build compactly committing AE from encryptment. Ultimately our main construction allows franking using just a single computation of SHA-256 or SHA-3. Encryptment proves useful for a variety of other applications, such as remotely keyed AE and concealments, and our results imply the first single-pass schemes in these settings as well.

2018

CRYPTO

Indifferentiable Authenticated Encryption
📺 Abstract

We study Authenticated Encryption with Associated Data (AEAD) from the viewpoint of composition in arbitrary (single-stage) environments. We use the indifferentiability framework to formalize the intuition that a “good” AEAD scheme should have random ciphertexts subject to decryptability. Within this framework, we can then apply the indifferentiability composition theorem to show that such schemes offer extra safeguards wherever the relevant security properties are not known, or cannot be predicted in advance, as in general-purpose crypto libraries and standards.We show, on the negative side, that generic composition (in many of its configurations) and well-known classical and recent schemes fail to achieve indifferentiability. On the positive side, we give a provably indifferentiable Feistel-based construction, which reduces the round complexity from at least 6, needed for blockciphers, to only 3 for encryption. This result is not too far off the theoretical optimum as we give a lower bound that rules out the indifferentiability of any construction with less than 2 rounds.

2018

CRYPTO

The Curse of Small Domains: New Attacks on Format-Preserving Encryption
📺 Abstract

Format-preserving encryption (FPE) produces ciphertexts which have the same format as the plaintexts. Building secure FPE is very challenging, and recent attacks (Bellare, Hoang, Tessaro, CCS ’16; Durak and Vaudenay, CRYPTO ’17) have highlighted security deficiencies in the recent NIST SP800-38G standard. This has left the question open of whether practical schemes with high security exist.In this paper, we continue the investigation of attacks against FPE schemes. Our first contribution are new known-plaintext message recovery attacks against Feistel-based FPEs (such as FF1/FF3 from the NIST SP800-38G standard) which improve upon previous work in terms of amortized complexity in multi-target scenarios, where multiple ciphertexts are to be decrypted. Our attacks are also qualitatively better in that they make no assumptions on the correlation between the targets to be decrypted and the known plaintexts. We also surface a new vulnerability specific to FF3 and how it handles odd length domains, which leads to a substantial speedup in our attacks.We also show the first attacks against non-Feistel based FPEs. Specifically, we show a strong message-recovery attack for FNR, a construction proposed by Cisco which replaces two rounds in the Feistel construction with a pairwise-independent permutation, following the paradigm by Naor and Reingold (JoC, ’99). We also provide a strong ciphertext-only attack against a variant of the DTP construction by Brightwell and Smith, which is deployed by Protegrity within commercial applications. All of our attacks show that existing constructions fall short of achieving desirable security levels. For Feistel and the FNR schemes, our attacks become feasible on small domains, e.g., 8 bits, for suggested round numbers. Our attack against the DTP construction is practical even for large domains. We provide proof-of-concept implementations of our attacks that verify our theoretical findings.

2018

CRYPTO

Cryptanalysis via Algebraic Spans
📺 Abstract

We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic group theory based key exchange protocol that could not be cryptanalyzed by earlier methods.

2018

EUROCRYPT

2018

EUROCRYPT

2018

EUROCRYPT

2018

EUROCRYPT

2018

EUROCRYPT

2018

TCHES

FPGA-based Accelerator for Post-Quantum Signature Scheme SPHINCS-256
📺 Abstract

In recent years, a substantial amount of research has been conducted and progress made in the area of quantum computers. Small functional prototypes have already been reported. If they scale as expected, they will eventually be able to break current public-key cryptosystems. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against attacks originating from both quantum and classical computers. Frequently referred post-quantum signature schemes are based on the security of hash functions. A promising candidate in this group is SPHINCS-256. This paper presents the first FPGA-based hardware accelerator for SPHINCS-256. It can be implemented on an entry-level FPGA, occupying roughly 19,000 LUTs, 38,000 FFs and 36 BRAMs. On a Kintex-7 Xilinx FPGA, signing takes 1.53 milliseconds, and verification needs only 65 microseconds. Area and throughput of the accelerator are in a range that outperform today’s widely used RSA signature scheme. The performance can even keep up with ECDSA accelerators. Hence, SPHINCS-256 is a hot candidate to replace RSA and ECDSA in a post-quantum world.

2018

TCHES

High Order Masking of Look-up Tables with Common Shares
📺 Abstract

Masking is an effective countermeasure against side-channel attacks. In this paper, we improve the efficiency of the high-order masking of look-up tables countermeasure introduced at Eurocrypt 2014, based on a combination of three techniques, and still with a proof of security in the Ishai-Sahai-Wagner (ISW) probing model. The first technique consists in proving security under the stronger t-SNI definition, which enables to use n = t+1 shares instead of n = 2t+1 against t-th order attacks. The second technique consists in progressively incrementing the number of shares within the countermeasure, from a single share to n, thereby reducing the complexity of the countermeasure. The third technique consists in adapting the common shares approach introduced by Coron et al. at CHES 2016, so that half of a randomized look-up table can be pre-computed for multiple SBoxes. We show that our techniques perform well in practice. In theory, the combination of the three techniques should lead to a factor 10.7 improvement in efficiency, for a large number of shares. For a practical implementation with a reasonable number of shares, we get a 4.8 speed-up factor for AES.

2018

TCHES

A Cautionary Note When Looking for a Truly Reconfigurable Resistive RAM PUF
📺 Abstract

The reconfigurable physically unclonable function (PUF) is an advanced security hardware primitive, suitable for applications requiring key renewal or similar refresh functions. The Oxygen vacancies-based resistive RAM (RRAM), has been claimed to be a physically reconfigurable PUF due to its intrinsic switching variability. This paper first analyzes and compares various previously published RRAM-based PUFs with a physics-based RRAM model. We next discuss their possible reconfigurability assuming an ideal configuration-to-configuration behavior. The RRAM-to-RRAM variability, which mainly originates from a variable number of unremovable vacancies inside the RRAM filament, however, has been observed to have significant impact on the reconfigurability. We show by quantitative analysis on the clear uniqueness degradation from the ideal situation in all the discussed implementations. Thus we conclude that true reconfigurability with RRAM PUFs might be unachievable due to this physical phenomena.

2018

TCHES

EM Analysis in the IoT Context: Lessons Learned from an Attack on Thread
📺 Abstract

The distinguishing feature of the Internet of Things is that many devices get interconnected. The threat of side-channel attacks in this setting is less understood than the threat of traditional network and software exploitation attacks that are perceived to be more powerful.This work is a case study of Thread, an emerging network and transport level stack designed to facilitate secure communication between heterogeneous IoT devices. We perform the first side-channel vulnerability analysis of the Thread networking stack. We leverage various network mechanisms to trigger manipulations of the security material or to get access to the network credentials. We choose the most feasible attack vector to build a complete attack that combines network specific mechanisms and Differential Electromagnetic Analysis. When successfully applied on a Thread network, the attack gives full network access to the adversary. We evaluate the feasibility of our attack in a TI CC2538 setup running OpenThread, a certified open-source implementation of the stack.The full attack does not succeed in our setting. The root cause for this failure is not any particular security feature of the protocol or the implementation, but a side-effect of a feature not related to security. We summarize the problems that we find in the protocol with respect to side-channel analysis, and suggest a range of countermeasures to prevent our attack and the other attack vectors we identified during the vulnerability analysis.In general, we demonstrate that elaborate security mechanisms of Thread make a side-channel attack not trivial to mount. Similar to a modern software exploit, it requires chaining multiple vulnerabilities. Nevertheless, such attacks are feasible. Being perhaps too expensive for settings like smart homes, they pose a relatively higher threat to the commercial setting. We believe our experience provides a useful lesson to designers of IoT protocols and devices.

2018

TCHES

Stealthy Opaque Predicates in Hardware - Obfuscating Constant Expressions at Negligible Overhead
📺 Abstract

Opaque predicates are a well-established fundamental building block for software obfuscation. Simplified, an opaque predicate implements an expression that provides constant Boolean output, but appears to have dynamic behavior for static analysis. Even though there has been extensive research regarding opaque predicates in software, techniques for opaque predicates in hardware are barely explored. In this work, we propose a novel technique to instantiate opaque predicates in hardware, such that they (1) are resource-efficient, and (2) are challenging to reverse engineer even with dynamic analysis capabilities. We demonstrate the applicability of opaque predicates in hardware for both, protection of intellectual property and obfuscation of cryptographic hardware Trojans. Our results show that we are able to implement stealthy opaque predicates in hardware with minimal overhead in area and no impact on latency.

2018

TCHES

Dismantling the AUT64 Automotive Cipher
📺 Abstract

AUT64 is a 64-bit automotive block cipher with a 120-bit secret key used in a number of security sensitive applications such as vehicle immobilization and remote keyless entry systems. In this paper, we present for the first time full details of AUT64 including a complete specification and analysis of the block cipher, the associated authentication protocol, and its implementation in a widely-used vehicle immobiliser system that we have reverse engineered. Secondly, we reveal a number of cryptographic weaknesses in the block cipher design. Finally, we study the concrete use of AUT64 in a real immobiliser system, and pinpoint severe weaknesses in the key diversification scheme employed by the vehicle manufacturer. We present two key-recovery attacks based on the cryptographic weaknesses that, combined with the implementation flaws, break both the 8 and 24 round configurations of AUT64. Our attack on eight rounds requires only 512 plaintext-ciphertext pairs and, in the worst case, just 237.3 offline encryptions. In most cases, the attack can be executed within milliseconds on a standard laptop. Our attack on 24 rounds requires 2 plaintext-ciphertext pairs and 248.3 encryptions to recover the 120-bit secret key in the worst case. We have strong indications that a large part of the key is kept constant across vehicles, which would enable an attack using a single communication with the transponder and negligible offline computation.

2018

TCHES

Generic Low-Latency Masking in Hardware
📺 Abstract

In this work, we introduce a generalized concept for low-latency masking that is applicable to any implementation and protection order, and (in its most extreme form) does not require on-the-fly randomness. The main idea of our approach is to avoid collisions of shared variables in nonlinear circuit parts and to skip the share compression. We show the feasibility of our approach on a full implementation of a one-round unrolled Ascon variant and on an AES S-box case study. Additionally, we discuss possible trade-offs to make our approach interesting for practical implementations. As a result, we obtain a first-order masked AES S-box that is calculated in a single clock cycle with rather high implementation costs (60.7 kGE), and a two-cycle variant with much less implementation costs (6.7 kGE). The side-channel resistance of our Ascon S-box designs up to order three are then verified using the formal analysis tool of [BGI+18]. Furthermore, we introduce a taint checking based verification approach that works specifically for our low-latency approach and allows us to verify large circuits like our low-latency AES S-box design in reasonable time.

2018

TCHES

Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve
📺 Abstract

We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost’s genus-2 curve targeting a 128-bit security level. We describe a single-core architecture for lowlatency applications and a multi-core architecture for high-throughput applications. Synthesized on a Xilinx Zynq-7020 FPGA, our architectures perform a key exchange with lower latency and higher throughput than any other reported implementation using prime-field elliptic curves at the same security level. Our single-core architecture performs a scalar multiplication with a latency of 82 microseconds while our multicore architecture achieves a throughput of 91,226 scalar multiplications per second. When compared to similar implementations of Microsoft’s Fourℚ on the same FPGA, this translates to an improvement of 48% in latency and 40% in throughput for the single-core and multi-core architecture, respectively. Both our designs exhibit constant-time execution to thwart timing attacks, use the Montgomery ladder for improved resistance against SPA, and support a countermeasure against fault attacks.

2018

TCHES

Hardware Masking, Revisited
📺 Abstract

MaskingHardware masking schemes have shown many advances in the past few years. Through a series of publications their implementation cost has dropped significantly and flaws have been fixed where present. Despite these advancements it seems that a limit has been reached when implementing masking schemes on FPGA platforms. Indeed, even with a correct transition from the masking scheme to the masking realization (i.e., when the implementation is not buggy) it has been shown that the implementation can still exhibit unexpected leakage, e.g., through variations in placement and routing. In this work, we show that the reason for such unexpected leakages is the violation of an underlying assumption made by all masking schemes, i.e., that the leakage of the circuit is a linear sum of leakages associated to each share. In addition to the theory of VLSI which supports our claim, we perform a wide range of experiments based on an FPGA) to find out under what circumstances this causes a masked hardware implementation to show undesirable leakage. We further illustrate case studies, where publicly-known secure designs exhibit first-order leakage when being operated at certain conditions.

2018

TCHES

Mixing Additive and Multiplicative Masking for Probing Secure Polynomial Evaluation Methods
📺 Abstract

Masking is a sound countermeasure to protect implementations of block- cipher algorithms against Side Channel Analysis (SCA). Currently, the most efficient masking schemes use Lagrange’s Interpolation Theorem in order to represent any S- box by a polynomial function over a binary finite field. Masking the processing of an S-box is then achieved by masking every operation involved in the evaluation of its polynomial representation. While the common approach requires to use the well- known Ishai-Sahai-Wagner (ISW) scheme in order to secure this processing, there exist alternatives. In the particular case of power functions, Genelle, Prouff and Quisquater proposed an efficient masking scheme (GPQ). However, no generalization has been suggested for polynomial functions so far. In this paper, we solve the open problem of extending GPQ for polynomials, and we also solve the open problem of proving that both the original scheme and its variants for polynomials satisfy the t-SNI security definition. Our approach to extend GPQ is based on the cyclotomic method and results in an alternate cyclotomic method which is three times faster in practice than the original proposal in almost all scenarios we address. The best- known method for polynomial evaluation is currently CRV which requires to use the cyclotomic method for one of its step. We also show how to plug our alternate cyclo- tomic approach into CRV and again provide an alternate approach that outperforms the original in almost all scenarios. We consider the masking of n-bit S-boxes for n ∈ [4;8] and we get in practice 35% improvement of efficiency for S-boxes with dimension n ∈ {5,7,8} and 25% for 6-bit S-boxes.

2018

TCHES

Smashing the Implementation Records of AES S-box
📺 Abstract

Canright S-box has been known as the most compact S-box design since its