International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Recent videos of IACR talks

Year
Venue
Title
2019
CRYPTO
Cryptanalysis of OCB2: Attacks on Authenticity and Confidentiality 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 $\mathsf {MORUS}$ 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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! 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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
CRYPTO
2019
CRYPTO
Contextual Integrity 📺
Invited Talk
2019
EUROCRYPT
2019
EUROCRYPT
2019
EUROCRYPT
Lower Bounds for Differentially Private RAMs 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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
EUROCRYPT
Differential Privacy and the People's Data 📺
IACR Distingished Lecture
2019
FSE
On Invariant Attacks 📺
Invited talk
2019
TOSC
CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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
2018
CRYPTO
TinyKeys: A New Approach to Efficient Multi-Party Computation 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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? 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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! 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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
CRYPTO
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EUROCRYPT
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2018
TCHES
FPGA-based Accelerator for Post-Quantum Signature Scheme SPHINCS-256 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
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 📺
Canright S-box has been known as the most compact S-box design since its introduction back in CHES’05. Boyar-Peralta proposed logic-minimization heuristics that could reduce the gate count of Canright S-box from 120 gates to 113 gates, however synthesis results did not reflect much improvement. In CHES’15, Ueno et al. proposed an S-box that has a slightly higher area, but significantly faster than the previous designs, hence it was the most efficient (measured by area×delay) S-box implementation to date. In this paper, we propose two new designs for the AES S-box. One design has a smaller implementation area than both Canright and the 113-gate S-boxes. Hence, our first design is the smallest AES S-box to date, breaking the 13 years implementation record of Canright. The second design is faster and smaller than the Ueno S-box. Hence, our second design is both the fastest and the most efficient S-box design to date. While doing so, we also propose new logicminimization heuristics that outperform the previous algorithms of Boyar-Peralta. Finally, we conduct an exhaustive evaluation of each and every block in the S-box circuit, using both structural and behavioral HDL modeling, to reach the optimum synergy between theoretical algorithms and technology-supported optimization tools. We show that involving the technology-supported CAD tools in the analysis results in several counter-intuitive results.
2018
TCHES
High-Performance FV Somewhat Homomorphic Encryption on GPUs: An Implementation using CUDA 📺
Homomorphic encryption (HE) offers great capabilities that can solve a wide range of privacy-preserving computing problems. This tool allows anyone to process encrypted data producing encrypted results that only the decryption key’s owner can decrypt. Although HE has been realized in several public implementations, its performance is quite demanding. The reason for this is attributed to the huge amount of computation required by secure HE schemes. In this work, we present a CUDAbased implementation of the Fan and Vercauteren (FV) Somewhat HomomorphicEncryption (SHE) scheme. We demonstrate several algebraic tools such as the Chinese Remainder Theorem (CRT), Residual Number System (RNS) and Discrete Galois Transform (DGT) to accelerate and facilitate FV computation on GPUs. We also show how the entire FV computation can be done on GPU without multi-precision arithmetic. We compare our GPU implementation with two mature state-of-the-art implementations: 1) Microsoft SEAL v2.3.0-4 and 2) NFLlib-FV. Our implementation outperforms them and achieves on average 5.37x, 7.37x, 22.22x, 5.11x and 13.18x (resp. 2.03x, 2.94x, 27.86x, 8.53x and 18.69x) for key generation, encryption, decryption, homomorphic addition and homomorphic multiplication against SEAL-FVRNS (resp. NFLlib-FV).
2018
TCHES
Rhythmic Keccak: SCA Security and Low Latency in HW 📺
Glitches entail a great issue when securing a cryptographic implementation in hardware. Several masking schemes have been proposed in the literature that provide security even in the presence of glitches. The key property that allows this protection was introduced in threshold implementations as non-completeness. We address crucial points to ensure the right compliance of this property especially for low-latency implementations. Specifically, we first discuss the existence of a flaw in DSD 2017 implementation of Keccak by Gross et al. in violation of the non-completeness property and propose a solution. We perform a side-channel evaluation on the first-order and second-order implementations of the proposed design where no leakage is detected with up to 55 million traces. Then, we present a method to ensure a non-complete scheme of an unrolled implementation applicable to any order of security or algebraic degree of the shared function. By using this method we design a two-rounds unrolled first-order Keccak-
2018
TCHES
CacheQuote: Efficiently Recovering Long-term Secrets of SGX EPID via Cache Attacks 📺
Intel Software Guard Extensions (SGX) allows users to perform secure computation on platforms that run untrusted software. To validate that the computation is correctly initialized and that it executes on trusted hardware, SGX supports attestation providers that can vouch for the user’s computation. Communication with these attestation providers is based on the Extended Privacy ID (EPID) protocol, which not only validates the computation but is also designed to maintain the user’s privacy. In particular, EPID is designed to ensure that the attestation provider is unable to identify the host on which the computation executes. In this work we investigate the security of the Intel implementation of the EPID protocol. We identify an implementation weakness that leaks information via a cache side channel. We show that a malicious attestation provider can use the leaked information to break the unlinkability guarantees of EPID. We analyze the leaked information using a lattice-based approach for solving the hidden number problem, which we adapt to the zero-knowledge proof in the EPID scheme, extending prior attacks on signature schemes.
2018
TCHES
Practical CCA2-Secure and Masked Ring-LWE Implementation 📺
During the last years public-key encryption schemes based on the hardness of ring-LWE have gained significant popularity. For real-world security applications assuming strong adversary models, a number of practical issues still need to be addressed. In this work we thus present an instance of ring-LWE encryption that is protected against active attacks (i.e., adaptive chosen-ciphertext attacks) and equipped with countermeasures against side-channel analysis. Our solution is based on a postquantum variant of the Fujisaki-Okamoto (FO) transform combined with provably secure first-order masking. To protect the key and message during decryption, we developed a masked binomial sampler that secures the re-encryption process required by FO. Our work shows that CCA2-secured RLWE-based encryption can be achieved with reasonable performance on constrained devices but also stresses that the required transformation and handling of decryption errors implies a performance overhead that has been overlooked by the community so far. With parameters providing 233 bits of quantum security, our implementation requires 4,176,684 cycles for encryption and 25,640,380 cycles for decryption with masking and hiding countermeasures on a Cortex-M4F. The first-order security of our masked implementation is also practically verified using the non-specific t-test evaluation methodology.
2018
TCHES
ExpFault: An Automated Framework for Exploitable Fault Characterization in Block Ciphers 📺
Malicious exploitation of faults for extracting secrets is one of the most practical and potent threats to modern cryptographic primitives. Interestingly, not every possible fault for a cryptosystem is maliciously exploitable, and evaluation of the exploitability of a fault is nontrivial. In order to devise precise defense mechanisms against such rogue faults, a comprehensive knowledge is required about the exploitable part of the fault space of a cryptosystem. Unfortunately, the fault space is diversified and of formidable size even while a single cryptoprimitive is considered and traditional manual fault analysis techniques may often fall short to practically cover such a fault space within reasonable time. An automation for analyzing individual fault instances for their exploitability is thus inevitable. Such an automation is supposed to work as the core engine for analyzing the fault spaces of cryptographic primitives. In this paper, we propose an automation for evaluating the exploitability status of fault instances from block ciphers, mainly in the context of Differential Fault Analysis (DFA) attacks. The proposed framework is generic and scalable, which are perhaps the two most important features for covering diversified fault spaces of formidable size originating from different ciphers. As a proof-of-concept, we reconstruct some known attack examples on AES and PRESENT using the framework and finally analyze a recently proposed cipher GIFT [BPP+17] for the first time. It is found that the secret key of GIFT can be uniquely determined with 1 nibble fault instance injected at the beginning of the 25th round with a reasonable computational complexity of 214.
2018
TCHES
Attacking GlobalPlatform SCP02-compliant Smart Cards Using a Padding Oracle Attack 📺
We describe in this paper how to perform a padding oracle attack against the GlobalPlatform SCP02 protocol. SCP02 is implemented in smart cards and used by transport companies, in the banking world and by mobile network operators (UICC/SIM cards). The attack allows an adversary to efficiently retrieve plaintext bytes from an encrypted data field. We provide results of our experiments done with 10 smart cards from six different card manufacturers, and show that, in our experimental setting, the attack is fully practical. Given that billions SIM cards are produced every year, the number of affected cards, although difficult to estimate, is potentially high. To the best of our knowledge, this is the first successful attack against SCP02.
2018
TCHES
Beetle Family of Lightweight and Secure Authenticated Encryption Ciphers 📺
This paper presents a lightweight, sponge-based authenticated encryption (AE) family called Beetle. When instantiated with the PHOTON permutation from CRYPTO 2011, Beetle achieves the smallest footprint—consuming only a few more than 600 LUTs on FPGA while maintaining 64-bit security. This figure is significantly smaller than all known lightweight AE candidates which consume more than 1,000 LUTs, including the latest COFB-AES from CHES 2017. In order to realize such small hardware implementation, we equip Beetle with an “extremely tight” bound of security. The trick is to use combined feedback to create a difference between the cipher text block and the rate part of the next feedback (in traditional sponge these two values are the same). Then we are able to show that Beetle is provably secure up to min{c − log r, b/2, r} bits, where b is the permutation size and r and c are parameters called rate and capacity, respectively. The tight security bound allows us to select the smallest security parameters, which in turn result in the smallest footprint.
2018
TCHES
Improved High-Order Conversion From Boolean to Arithmetic Masking 📺
Masking is a very common countermeasure against side channel attacks. When combining Boolean and arithmetic masking, one must be able to convert between the two types of masking, and the conversion algorithm itself must be secure against side-channel attacks. An efficient high-order Boolean to arithmetic conversion scheme was recently described at CHES 2017, with complexity independent of the register size. In this paper we describe a simplified variant with fewer mask refreshing, and still with a proof of security in the ISW probing model. In practical implementations, our variant is roughly 25% faster.
2018
TCHES
Fault Attacks Made Easy: Differential Fault Analysis Automation on Assembly Code 📺
Over the past decades, fault injection attacks have been extensively studied due to their capability to efficiently break cryptographic implementations. Fault injection attack models are normally determined by analyzing the cipher structure and finding exploitable spots in non-linear and permutation layers. However, this level of abstraction is often too high to distinguish vulnerable parts of software implementations, due to specific operations and optimizations. On the other hand, manually analyzing the assembly code requires non-negligible amount of time and expertise. In this paper, we propose an automated approach for analyzing cipher implementations in assembly. We represent the whole assembly program as a data flow graph so that the vulnerable spots can be found efficiently. Fault propagation is analyzed in a subgraph constructed from each vulnerable spot, allowing equations for Differential Fault Analysis (DFA) to be automatically generated. We have created a tool that implements our approach: DATAC – DFA Automation Tool for Assembly Code. We have successfully used this tool for attacking PRESENT- 80, being able to find implementation-specific vulnerabilities that can be exploited in order to recover the last round key with 16 faults. Our results show that DATAC is useful in finding attack spots that are not visible from the cipher structure, but can be easily exploited when dealing with real-world implementations.
2018
TCHES
Linear Repairing Codes and Side-Channel Attacks 📺
To strengthen the resistance of countermeasures based on secret sharing,several works have suggested to use the scheme introduced by Shamir in 1978, which proposes to use the evaluation of a random d-degree polynomial into n ≥ d + 1 public points to share the sensitive data. Applying the same principles used against the classical Boolean sharing, all these works have assumed that the most efficient attack strategy was to exploit the minimum number of shares required to rebuild the sensitive value; which is d + 1 if the reconstruction is made with Lagrange’s interpolation. In this paper, we highlight first an important difference between Boolean and Shamir’s sharings which implies that, for some signal-to-noise ratio, it is more advantageous for the adversary to observe strictly more than d + 1 shares. We argue that this difference is related to the existence of so-called linear exact repairing codes, which themselves come with reconstruction formulae that need (much) less information (counted in bits) than Lagrange’s interpolation. In particular, this result implies that the choice of the public points in Shamir’s sharing has an impact on the countermeasure strength, which confirms previous observations made by Wang et al. at CARDIS 2016 for the so-called inner product sharing which is a generalization of Shamir’s scheme. As another contribution, we exhibit a positive impact of the existence of linear exact repairing schemes; we indeed propose to use them to improve the state-of-the-art multiplication algorithms dedicated to Shamir’s sharing. We argue that the improvement can be effective when the multiplication operation in the sub-fields is at least two times smaller than that of the base field.
2018
TCHES
Leakage Detection with the x2-Test 📺
We describe how Pearson’s χ2-test can be used as a natural complement to Welch’s t-test for black box leakage detection. In particular, we show that by using these two tests in combination, we can mitigate some of the limitations due to the moment-based nature of existing detection techniques based on Welch’s t-test (e.g., for the evaluation of higher-order masked implementations with insufficient noise). We also show that Pearson’s χ2-test is naturally suited to analyze threshold implementations with information lying in multiple statistical moments, and can be easily extended to a distinguisher for key recovery attacks. As a result, we believe the proposed test and methodology are interesting complementary ingredients of the side-channel evaluation toolbox, for black box leakage detection and non-profiled attacks, and as a preliminary before more demanding advanced analyses.
2018
TCHES
SAEB: A Lightweight Blockcipher-Based AEAD Mode of Operation 📺
Lightweight cryptography in computationally constrained devices is actively studied. In contrast to advances of lightweight blockcipher in the last decade, lightweight mode of operation is seemingly not so mature, yet it has large impact in performance. Therefore, there is a great demand for lightweight mode of operation, especially that for authenticated encryption with associated data (AEAD). Among many known properties of conventional modes of operation, the following four properties are essential for constrained devices: Minimum State Size: the state size equals to a block size of a blockcipher. Inverse Free: no need for a blockcipher decryption. XOR Only: only XOR is needed in addition to a blockcipher encryption. Online: a data block is processed only once. The properties 1 and 4 contribute to small memory usage, and the properties 2 and 3 contribute to small program/circuit footprint. On top of the above properties, the fifth property regarding associated data (AD) is also important for performance: Efficient Handling of Static AD: static AD can be precomputed. We design a lightweight blockcipher-based AEAD mode of operation called SAEB: the first mode of operation that satisfies all the five properties to the best of our knowledge. Performance of SAEB is evaluated in various software and hardware platforms. The evaluation results show that SAEB outperforms conventional blockcipher-based AEAD modes of operation in various performance metrics for lightweight cryptography.
2018
TOSC
Towards Low Energy Stream Ciphers 📺
Energy optimization is an important design aspect of lightweight cryptography. Since low energy ciphers drain less battery, they are invaluable components of devices that operate on a tight energy budget such as handheld devices or RFID tags. At Asiacrypt 2015, Banik et al. presented the block cipher family Midori which was designed to optimize the energy consumed per encryption and which reduces the energy consumption by more than 30% compared to previous block ciphers. However, if one has to encrypt/decrypt longer streams of data, i.e. for bulk data encryption/decryption, it is expected that a stream cipher should perform even better than block ciphers in terms of energy required to encrypt. In this paper, we address the question of designing low energy stream ciphers. To this end, we analyze for common stream cipher design components their impact on the energy consumption. Based on this, we give arguments why indeed stream ciphers allow for encrypting long data streams with less energy than block ciphers and validate our findings by implementations. Afterwards, we use the analysis results to identify energy minimizing design principles for stream ciphers.
2018
TOSC
ShiftRows Alternatives for AES-like Ciphers and Optimal Cell Permutations for Midori and Skinny 📺
We study possible alternatives for ShiftRows to be used as cell permutations in AES-like ciphers. As observed during the design process of the block cipher Midori, when using a matrix with a non-optimal branch number for the MixColumns operation, the choice of the cell permutation, i.e., an alternative for ShiftRows, can actually improve the security of the primitive. In contrast, when using an MDS matrix it is known that one cannot increase the minimum number of active S-boxes by deviating from the ShiftRows-type permutation. However, finding the optimal choice for the cell permutation for a given, non-optimal, MixColumns operation is a highly non-trivial problem. In this work, we propose techniques to speed up the search for the optimal cell permutations significantly. As case studies, we apply those techniques to Midori and Skinny and provide possible alternatives for their cell permutations. We finally state an easy-to-verify sufficient condition on a cell permutation, to be used as an alternative in Midori, that attains a high number of active S-boxes and thus provides good resistance against differential and linear attacks.
2018
TOSC
MDS Matrices with Lightweight Circuits 📺
MDS matrices are an important element for the design of block ciphers such as the AES. In recent years, there has been a lot of work on the construction of MDS matrices with a low implementation cost, in the context of lightweight cryptography. Most of the previous efforts focused on local optimization, constructing MDS matrices with coefficients that can be efficiently computed. In particular, this led to a matrix with a direct xor count of only 106, while a direct implementation of the MixColumn matrix of the AES requires 152 bitwise xors. More recently, techniques based on global optimization have been introduced, where the implementation can reuse some intermediate variables. In particular, Kranz et al. used optimization tools to find a good implementation from the description of an MDS matrix. They have lowered the cost of implementing the MixColumn matrix to 97 bitwise xors, and proposed a new matrix with only 72 bitwise xors, the lowest cost known so far. In this work we propose a different approach to global optimization. Instead of looking for an optimized circuit of a given matrix, we run a search through a space of circuits, to find optimal circuits yielding MDS matrices. This results in MDS matrices with an even lower cost, with only 67 bitwise xors.
2018
TOSC
Separable Statistics and Multidimensional Linear Cryptanalysis 📺
Multidimensional linear cryptanalysis of block ciphers is improved in this work by introducing a number of new ideas. Firstly, formulae is given to compute approximate multidimensional distributions of the encryption algorithm internal bits. Conventional statistics like LLR (Logarithmic Likelihood Ratio) do not fit to work in Matsui’s Algorithm 2 for large dimension data, as the observation may depend on too many cipher key bits. So, secondly, a new statistic which reflects the structure of the cipher round is constructed instead. Thirdly, computing the statistic values that will fall into a critical region is presented as an optimisation problem for which an efficient algorithm is suggested. The algorithm works much faster than brute forcing all relevant key bits to compute the statistic. An attack for 16-round DES was implemented. We got an improvement over Matsui’s attack on DES in data and time complexity keeping success probability the same. With 241.81 plaintext blocks and success rate 0.83 (computed theoretically) we found 241.46 (which is close to the theoretically predicted number 241.81) key-candidates to 56-bit DES key. Search tree to compute the statistic values which fall into the critical region incorporated 245.45 nodes in the experiment and that is at least theoretically inferior in comparison with the final brute force. To get success probability 0.85, which is a fairer comparison to Matsui’s results, we would need 241.85 data and to brute force 241.85 key-candidates. That compares favourably with 243 achieved by Matsui.
2018
TOSC
Clustering Related-Tweak Characteristics: Application to MANTIS-6 📺
The TWEAKEY/STK construction is an increasingly popular approach for designing tweakable block ciphers that notably uses a linear tweakey schedule. Several recent attacks have analyzed the implications of this approach for differential cryptanalysis and other attacks that can take advantage of related tweakeys. We generalize the clustering approach of a recent differential attack on the tweakable block cipher MANTIS5 and describe a tool for efficiently finding and evaluating such clusters. More specifically, we consider the set of all differential characteristics compatible with a given truncated characteristic, tweak difference, and optional constraints for the differential. We refer to this set as a semi-truncated characteristic and estimate its probability by analyzing the distribution of compatible differences at each step. We apply this approach to find a semi-truncated differential characteristic for MANTIS6 with probability about 2−67.73 and derive a key-recovery attack with a complexity of about 255.09 chosen-plaintext queries and 255.52 computations. The data-time product is 2110.61 &lt;&lt; 2126.
2018
TOSC
Mixture Differential Cryptanalysis: a New Approach to Distinguishers and Attacks on round-reduced AES 📺
At Eurocrypt 2017 the first secret-key distinguisher for 5-round AES - based on the “multiple-of-8” property - has been presented. Although it allows to distinguish a random permutation from an AES-like one, it seems rather hard to implement a key-recovery attack different than brute-force like using such a distinguisher. In this paper we introduce “Mixture Differential Cryptanalysis” on round-reduced AESlike ciphers, a way to translate the (complex) “multiple-of-8” 5-round distinguisher into a simpler and more convenient one (though, on a smaller number of rounds). Given a pair of chosen plaintexts, the idea is to construct new pairs of plaintexts by mixing the generating variables of the original pair of plaintexts. Here we theoretically prove that for 4-round AES the corresponding ciphertexts of the original pair of plaintexts lie in a particular subspace if and only if the corresponding pairs of ciphertexts of the new pairs of plaintexts have the same property. Such secret-key distinguisher - which is independent of the secret-key, of the details of the S-Box and of the MixColumns matrix (except for the branch number equal to 5) - can be used as starting point to set up new key-recovery attacks on round-reduced AES. Besides a theoretical explanation, we also provide a practical verification both of the distinguisher and of the attack.
2018
TOSC
Cryptanalysis of AES-PRF and Its Dual 📺
A dedicated pseudorandom function (PRF) called AES-PRF was proposed by Mennink and Neves at FSE 2018 (ToSC 2017, Issue 3). AES-PRF is obtained from AES by using the output of the 5-th round as the feed-forward to the output state. This paper presents extensive security analysis of AES-PRF and its variants. Specifically, we consider unbalanced variants where the output of the s-th round is used as the feed-forward. We also analyze the security of “dual” constructions of the unbalanced variants, where the input state is used as the feed-forward to the output of the s-th round. We apply an impossible differential attack, zero-correlation linear attack, traditional differential attack, zero correlation linear distinguishing attack and a meet-in-the-middle attack on these PRFs and reduced round versions. We show that AES-PRF is broken whenever s ≤ 2 or s ≥ 6, or reduced to 7 rounds, and Dual-AES-PRF is broken whenever s ≤ 4 or s ≥ 8. Our results on AES-PRF improve the initial security evaluation by the designers in various ways, and our results on Dual-AES-PRF give the first insight to its security.
2018
TOSC
SUNDAE: Small Universal Deterministic Authenticated Encryption for the Internet of Things 📺
Lightweight cryptography was developed in response to the increasing need to secure devices for the Internet of Things. After significant research effort, many new block ciphers have been designed targeting lightweight settings, optimizing efficiency metrics which conventional block ciphers did not. However, block ciphers must be used in modes of operation to achieve more advanced security goals such as data confidentiality and authenticity, a research area given relatively little attention in the lightweight setting. We introduce a new authenticated encryption (AE) mode of operation, SUNDAE, specially targeted for constrained environments. SUNDAE is smaller than other known lightweight modes in implementation area, such as CLOC, JAMBU, and COFB, however unlike these modes, SUNDAE is designed as a deterministic authenticated encryption (DAE) scheme, meaning it provides maximal security in settings where proper randomness is hard to generate, or secure storage must be minimized due to expense. Unlike other DAE schemes, such as GCM-SIV, SUNDAE can be implemented efficiently on both constrained devices, as well as the servers communicating with those devices. We prove SUNDAE secure relative to its underlying block cipher, and provide an extensive implementation study, with results in both software and hardware, demonstrating that SUNDAE offers improved compactness and power consumption in hardware compared to other lightweight AE modes, while simultaneously offering comparable performance to GCM-SIV on parallel high-end platforms.
2018
TOSC
Double-block Hash-then-Sum: A Paradigm for Constructing BBB Secure PRF 📺
SUM-ECBC (Yasuda, CT-RSA 2010) is the first beyond birthday bound (BBB) secure block cipher based deterministic MAC. After this work, some more BBB secure deterministic MACs have been proposed, namely PMAC_Plus (Yasuda, CRYPTO 2011), 3kf9 (Zhang et al., ASIACRYPT 2012) and LightMAC_Plus (Naito, ASIACRYPT 2017). In this paper, we have abstracted out the inherent design principle of all these BBB secure MACs and present a generic design paradigm to construct a BBB secure pseudo random function, namely Double-block Hash-then- Sum or in short (DbHtS). A DbHtS construction, as the name implies, computes a double block hash on the message and then sum the encrypted output of the two hash blocks. Our result renders that if the underlying hash function meets certain security requirements (namely cover-free and block-wise universal advantage is low), DbHtS construction provides 2n/3-bit security. We demonstrate the applicability of our result by instantiating all the existing beyond birthday secure deterministic MACs (e.g., SUM-ECBC, PMAC_Plus, 3kf9, LightMAC_Plus) as well as a simple two-keyed variant for each of them and some algebraic hash based constructions.
2018
TOSC
More Accurate Differential Properties of LED64 and Midori64 📺
In differential cryptanalysis, a differential is more valuable than the single trail belonging to it in general. The traditional way to compute the probability of the differential is to sum the probabilities of all trails within it. The automatic tool for the search of differentials based on Mixed Integer Linear Programming (MILP) has been proposed and realises the task of finding multiple trails of a given differential. The problem is whether it is reliable to evaluate the probability of the differential traditionally. In this paper, we focus on two lightweight block ciphers – LED64 and Midori64 and show the more accurate estimation of differential probability considering the key schedule. Firstly, an automated tool based on Boolean Satisfiability Problem (SAT) is put forward to accomplish the automatic search of differentials for ciphers with S-boxes and is applied to LED64 and Midori64. Secondly, we provide an automatic approach to detect the right pairs following a given differential, which can be exploited to calculate the differential property. Applying this technique to the STEP function of LED64, we discover some differentials with enhanced probability. As a result, the previous attacks relying upon high probability differentials can be improved definitely. Thirdly, we present a method to compute an upper-bound of the weak-key ratio for a given differential, which is utilised to analyse 4-round differentials of Midori64. We detect two differentials whose weak-key ratios are much lower than the expected 50%. More than 78% of the keys will make these two differentials being impossible differentials. The idea of the estimation for an upper-bound of the weak-key ratio can be employed for other ciphers and allows us to launch differential attacks more reliably. Finally, we introduce how to compute the enhanced differential probability and evaluate the size of keys achieving the improved probability. Such a property may incur an efficient weak-key attack. For a 4-round differential of Midori64, we obtain an improved differential property for a portion of keys.
2018
TOSC
Cryptanalysis of Reduced round SKINNY Block Cipher 📺
SKINNY is a family of lightweight tweakable block ciphers designed to have the smallest hardware footprint. In this paper, we present zero-correlation linear approximations and the related-tweakey impossible differential characteristics for different versions of SKINNY .We utilize Mixed Integer Linear Programming (MILP) to search all zero-correlation linear distinguishers for all variants of SKINNY, where the longest distinguisher found reaches 10 rounds. Using a 9-round characteristic, we present 14 and 18-round zero correlation attacks on SKINNY-64-64 and SKINNY- 64-128, respectively. Also, for SKINNY-n-n and SKINNY-n-2n, we construct 13 and 15-round related-tweakey impossible differential characteristics, respectively. Utilizing these characteristics, we propose 23-round related-tweakey impossible differential cryptanalysis by applying the key recovery attack for SKINNY-n-2n and 19-round attack for SKINNY-n-n. To the best of our knowledge, the presented zero-correlation characteristics in this paper are the first attempt to investigate the security of SKINNY against this attack and the results on the related-tweakey impossible differential attack are the best reported ones.
2018
TOSC
Cryptanalysis of Low-Data Instances of Full LowMCv2 📺
LowMC is a family of block ciphers designed for a low multiplicative complexity. The specification allows a large variety of instantiations, differing in block size, key size, number of S-boxes applied per round and allowed data complexity. The number of rounds deemed secure is determined by evaluating a number of attack vectors and taking the number of rounds still secure against the best of these. In this paper, we demonstrate that the attacks considered by the designers of LowMC in the version 2 of the round-formular were not sufficient to fend off all possible attacks. In the case of instantiations of LowMC with one of the most useful settings, namely with few applied S-boxes per round and only low allowable data complexities, efficient attacks based on difference enumeration techniques can be constructed. We show that it is most effective to consider tuples of differences instead of simple differences, both to increase the range of the distinguishers and to enable key recovery attacks. All applications for LowMC we are aware of, including signature schemes like Picnic and more recent (ring/group) signature schemes have used version 3 of the roundformular for LowMC, which takes our attack already into account.
2018
TOSC
Cube-Attack-Like Cryptanalysis of Round-Reduced Keccak Using MILP 📺
Cube-attack-like cryptanalysis on round-reduced Keccak was proposed by Dinur et al. at EUROCRYPT 2015. It recovers the key through two phases: the preprocessing phase for precomputing a look-up table and online phase for querying the output and getting the cube sum with which the right key can be retrieved by looking up the precomputed table. It was shown that such attacks are efficient specifically for Keccak-based constructions with small nonce or message block size. In this paper, we provide a mixed integer linear programming (MILP) model for cubeattack- like cryptanalysis on keyed Keccak, which does not impose any unnecessary constraint on cube variables and finds almost optimal cubes by balancing the two phases of cube-attack-like cryptanalysis. Our model is applied to Ketje Jr, Ketje Sr, a Xoodoo-based authenticated encryption and Keccak-MAC-512, all of which have a relatively small nonce or message block size. As a result, time complexities of 5-round attacks on Ketje Jr and 7-round attacks on Ketje Sr can be improved significantly. Meanwhile, 6-round attacks, one more round than the previous best attack, are possible if the key size of Ketje V1 (V2) is reduced to 72 (80) bits. For Xoodoo-based AE in Ketje style, the attack reaches 6 rounds. Additionally, a 7-round attack of Keccak-MAC-512 is achieved. To verify the correctness of our attacks, a 5-round attack on Ketje V1 is implemented and tested practically. It is noted that this work does not threaten the security of any Keccak-based construction.
2018
TOSC
Conditional Linear Cryptanalysis – Cryptanalysis of DES with Less Than 242 Complexity 📺
In this paper we introduce a new extension of linear cryptanalysis that may reduce the complexity of attacks by conditioning linear approximations on other linear approximations. We show that the bias of some linear approximations may increase under such conditions, so that after discarding the known plaintexts that do not satisfy the conditions, the bias of the remaining known plaintexts increases. We show that this extension can lead to improvements of attacks, which may require fewer known plaintexts and time of analysis. We present several types of such conditions, including one that is especially useful for the analysis of Feistel ciphers. We exemplify the usage of such conditions for attacks by a careful application of our extension to Matsui’s attack on the full 16-round DES, which succeeds to reduce the complexity of the best attack on DES to less than 242. We programmed a test implementation of our attack and verified our claimed results with a large number of runs. We also introduce a new type of approximations, to which we call scattered approximations, and discuss its applications.
2018
TOSC
Generating Graphs Packed with Paths Estimation of Linear Approximations and Differentials 📺
When designing a new symmetric-key primitive, the designer must show resistance to known attacks. Perhaps most prominent amongst these are linear and differential cryptanalysis. However, it is notoriously difficult to accurately demonstrate e.g. a block cipher’s resistance to these attacks, and thus most designers resort to deriving bounds on the linear correlations and differential probabilities of their design. On the other side of the spectrum, the cryptanalyst is interested in accurately assessing the strength of a linear or differential attack.While several tools have been developed to search for optimal linear and differential trails, e.g. MILP and SAT based methods, only few approaches specifically try to find as many trails of a single approximation or differential as possible. This can result in an overestimate of a cipher’s resistance to linear and differential attacks, as was for example the case for PRESENT.In this work, we present a new algorithm for linear and differential trail search. The algorithm represents the problem of estimating approximations and differentials as the problem of finding many long paths through a multistage graph. We demonstrate that this approach allows us to find a very large number of good trails for each approximation or differential. Moreover, we show how the algorithm can be used to efficiently estimate the key dependent correlation distribution of a linear approximation, facilitating advanced linear attacks. We apply the algorithm to 17 different ciphers, and present new and improved results on several of these.
2018
TOSC
On the Boomerang Uniformity of Cryptographic Sboxes 📺
The boomerang attack is a cryptanalysis technique against block ciphers which combines two differentials for the upper part and the lower part of the cipher. The dependency between these two differentials then highly affects the complexity of the attack and all its variants. Recently, Cid et al. introduced at Eurocrypt’18 a new tool, called the Boomerang Connectivity Table (BCT) that permits to simplify this complexity analysis, by storing and unifying the different switching probabilities of the cipher’s Sbox in one table. In this seminal paper a brief analysis of the properties of these tables is provided and some open questions are raised. It is being asked in particular whether Sboxes with optimal BCTs exist for even dimensions, where optimal means that the maximal value in the BCT equals the lowest known differential uniformity. When the dimension is even and differs from 6, such optimal Sboxes correspond to permutations such that the maximal value in their DDT and in their BCT equals 4 (unless APN permutations for such dimensions exist). We provide in this work a more in-depth analysis of boomerang connectivity tables, by studying more closely differentially 4-uniform Sboxes. We first completely characterize the BCT of all differentially 4-uniform permutations of 4 bits and then study these objects for some cryptographically relevant families of Sboxes, as the inverse function and quadratic permutations. These two families provide us with the first examples of differentially 4-uniform Sboxes optimal against boomerang attacks for an even number of variables, answering the above open question.
2018
TOSC
Lightweight and Side-channel Secure 4 × 4 S-Boxes from Cellular Automata Rules 📺
This work focuses on side-channel resilient design strategies for symmetrickey cryptographic primitives targeting lightweight applications. In light of NIST’s lightweight cryptography project, design choices for block ciphers must consider not only security against traditional cryptanalysis, but also side-channel security, while adhering to low area and power requirements. In this paper, we explore design strategies for substitution-permutation network (SPN)-based block ciphers that make them amenable to low-cost threshold implementations (TI) - a provably secure strategy against side-channel attacks. The core building blocks for our strategy are cryptographically optimal 4×4 S-Boxes, implemented via repeated iterations of simple cellular automata (CA) rules. We present highly optimized TI circuits for such S-Boxes, that consume nearly 40% less area and power as compared to popular lightweight S-Boxes such as PRESENT and GIFT. We validate our claims via implementation results on ASIC using 180nm technology. We also present a comparison of TI circuits for two popular lightweight linear diffusion layer choices - bit permutations and MixColumns using almost-maximum-distance-separable (almost-MDS) matrices. We finally illustrate design paradigms that combine the aforementioned TI circuits for S-Boxes and diffusion layers to obtain fully side-channel secure SPN block cipher implementations with low area and power requirements.
2018
TOSC
The design of Xoodoo and Xoofff 📺
This paper presents Xoodoo, a 48-byte cryptographic permutation with excellent propagation properties. Its design approach is inspired by Keccak-p, while it is dimensioned like Gimli for efficiency on low-end processors. The structure consists of three planes of 128 bits each, which interact per 3-bit columns through mixing and nonlinear operations, and which otherwise move as three independent rigid objects. We analyze its differential and linear propagation properties and, in particular, prove lower bounds on the weight of trails using the tree search-based technique of Mella et al. (ToSC 2017). Xoodoo’s primary target application is in the Farfalle construction that we instantiate for the doubly-extendable cryptographic keyed (or deck) function Xoofff. Combining a relatively narrow permutation with the parallelism of Farfalle results in very efficient schemes on a wide range of platforms, from low-end devices to high-end processors with vector instructions.
2018
TOSC
Adiantum: length-preserving encryption for entry-level processors 📺
We present HBSH, a simple construction for tweakable length-preserving encryption which supports the fastest options for hashing and stream encryption for processors without AES or other crypto instructions, with a provable quadratic advantage bound. Our composition Adiantum uses NH, Poly1305, XChaCha12, and a single AES invocation. On an ARM Cortex-A7 processor, Adiantum decrypts 4096-byte messages at 10.6 cycles per byte, over five times faster than AES-256-XTS, with a constant-time implementation. We also define HPolyC which is simpler and has excellent key agility at 13.6 cycles per byte.
2018
TOSC
Generalized Nonlinear Invariant Attack and a New Design Criterion for Round Constants 📺
The nonlinear invariant attack was introduced at ASIACRYPT 2016 by Todo et al.. The attack has received extensive attention of cryptographic community due to its practical application on the full-round block ciphers SCREAM, iSCREAM, and Midori64. However, the attack heavily relies on the choice of round constants and it becomes inefficient in the case these constants nonlinearly affect the so-called nonlinear invariants. In this article, to eliminate the impact from the round constants, a generalized nonlinear invariant attack which uses a pair of constants in the input of nonlinear invariants is proposed. The efficiency of this extended framework is practically confirmed by mounting a distinguishing attack on a variant of full-round iSCREAM cipher under a class of 280 weak keys. The considered variant of iSCREAM is however resistant against nonlinear invariant attack of Todo et al.. Furthermore, we investigate the resistance of block ciphers against generalized nonlinear invariant attacks with respect to the choice of round constants in an extended framework. We introduce a useful concept of closed-loop invariants of the substitution box (S-box) and show that the choice of robust round constants is closely related to the existence of linear structure of the closed-loop invariants of the substitution layer. In particular, we demonstrate that the design criteria for the round constants in Beierle et al.’s work at CRYPTO 2017 is not an optimal strategy. The round constants selected using this method may induce certain weaknesses that can be exploited in our generalized nonlinear invariant attack model. This scenario is efficiently demonstrated in the case of a slightly modified variant of the Midori64 block cipher.
2018
TOSC
Nonlinear Approximations in Cryptanalysis Revisited 📺
This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation ±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts.
2018
TOSC
New Yoyo Tricks with AES-based Permutations 📺
In Asiacrypt 2017, Rønjom et al. reported some interesting generic properties of SPNs, leading to what they call the Yoyo trick, and applied it to find the most efficient distinguishers on AES. In this work, we explore the Yoyo idea in distinguishing public permutations for the first time. We introduce the notion of nested zero difference pattern which extends the Yoyo idea and helps to compose it using improbable and impossible differential strategies to penetrate higher number of rounds. We devise a novel inside-out application of Yoyo which enables us to start the Yoyo game from an internal round. As an application, we investigate the AES-based public permutation AESQ used inside the authenticated cipher PAEQ. We achieve the first deterministic distinguisher of AESQ up to 8 rounds and the first 9-round distinguisher of AESQ that start from the first round with a practical complexity of around 226. We manage to augment Yoyo with improbable and impossible differentials leading to distinguishers on 9, 10, 12 rounds with complexities of about 22, 228, 2126 respectively. Further, with impossible differentials and a bi-directional Yoyo strategy, we obtain a 16-round impossible differential distinguisher with a complexity of 2126. Our results outperform all previous records on AESQ by a substantial margin. As another application, we apply the proposed strategies on AES in the known-key setting leading to one of the best 8-round known-key distinguisher with a complexity of 230. Finally, this work amplifies the scope of the Yoyo technique as a generic cryptanalysis tool.
2018
TOSC
Key Prediction Security of Keyed Sponges 📺
The keyed sponge is a well-accepted method for message authentication. It processes data at a certain rate by sequential evaluation of an underlying permutation. If the key size k is smaller than the rate, currently known bounds are tight, but if it exceeds the rate, state of the art only dictates security up to 2k/2. We take closer inspection at the key prediction security of the sponge and close the remaining gap in the existing security analysis: we confirm key security up to close to 2k, regardless of the rate. The result impacts all applications of the keyed sponge and duplex that process at a rate smaller than the key size, including the STROBE protocol framework, as well as the related constructions such as HMAC-SHA-3 and the sandwich sponge.
2018
TOSC
Key Assignment Scheme with Authenticated Encryption 📺
The Key Assignment Scheme (KAS) is a well-studied cryptographic primitive used for hierarchical access control (HAC) in a multilevel organisation where the classes of people with higher privileges can access files of those with lower ones. Our first contribution is the formalization of a new cryptographic primitive, namely, KAS-AE that supports the aforementioned HAC solution with an additional authenticated encryption property. Next, we present three efficient KAS-AE schemes that solve the HAC and the associated authenticated encryption problem more efficiently – both with respect to time and memory – than the existing solutions that achieve it by executing KAS and AE separately. Our first KAS-AE construction is built by using the cryptographic primitive MLE (EUROCRYPT 2013) as a black box; the other two constructions (which are the most efficient ones) have been derived by cleverly tweaking the hash function FP (Indocrypt 2012) and the authenticated encryption scheme APE (FSE 2014). This high efficiency of our constructions is critically achieved by using two techniques: design of a mechanism for reverse decryption used for reduction of time complexity, and a novel key management scheme for optimizing storage requirements when organizational hierarchy forms an arbitrary access graph (instead of a linear graph). We observe that constructing a highly efficient KAS-AE scheme using primitives other than MLE, FP and APE is a non-trivial task. We leave it as an open problem. Finally, we provide a detailed comparison of all the KAS-AE schemes.
2018
TOSC
Sound Hashing Modes of Arbitrary Functions, Permutations, and Block Ciphers 📺
Cryptographic hashing modes come in many flavors, including Merkle-Damgård with various types of strengthening, Merkle trees, and sponge functions. As underlying primitives, these functions use arbitrary functions, permutations, or block ciphers. In this work we provide three simple proofs, one per primitive type, that cover all modes where the input to the primitive consists of message bits, chaining value bits, and bits that only depend on the mode and message length. Our approach generalizes and simplifies over earlier attempts of Dodis et al. (FSE 2009) and Bertoni et al. (Int. J. Inf. Sec. 2014). We prove tight indifferentiability bounds for modes using each of these three primitive types provided that the mode satisfies some easy to verify conditions.
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The Magic of ELFs 📺
Early Career Award
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