## CryptoDB

### Papers from ASIACRYPT 2023

**Year**

**Venue**

**Title**

2023

ASIACRYPT

A Generic Construction of an Anonymous Reputation System and Instantiations from Lattices
Abstract

With an anonymous reputation system one can realize the process of rating sellers anonymously in an online shop.
While raters can stay anonymous, sellers still have the guarantee that they can only be reviewed by raters who bought their product.
We present the first generic construction of a reputation system from basic building blocks, namely digital signatures, encryption schemes, non-interactive zero-knowledge proofs, and linking indistinguishable tags.
We then show the security of the reputation system in a strong security model.
Among others, we instantiate the generic construction with building blocks based on lattice problems, leading to the first module lattice-based reputation system.

2023

ASIACRYPT

A Generic Construction of Tightly Secure Password-based Authenticated Key Exchange
Abstract

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is one-way secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman assumption, which generalizes the work of Liu et al. (PKC 2023), and ``almost'' tightly with lattice-based assumptions, which tightens the security loss of the work of Beguinet et al. (ACNS 2023) and allows more efficient practical implementation with Kyber. Beyond these, it opens an opportunity of constructing tight PAKE based on various assumptions.

2023

ASIACRYPT

A new approach based on quadratic forms to attack the McEliece cryptosystem
Abstract

We introduce a novel algebraic approach for attacking the
McEliece cryptosystem which is currently at the $4$-th round of the
NIST competition. The contributions of the article are twofold.
(1) We present a new distinguisher on alternant and Goppa codes
working in a much broader range of parameters than \cite{FGOPT11}. (2) With this approach we also
provide a polynomial--time key recovery attack on
alternant codes which are distinguishable with the distinguisher
\cite{FGOPT11}.
These results are obtained by introducing a subspace of matrices
representing quadratic forms. Those are associated with quadratic
relations for the component-wise product in the dual of the Goppa
(or alternant) code of the cryptosystem. It turns out that this subspace
of matrices contains matrices of unusually small rank in the case of alternant or
Goppa codes ($2$ or $3$ depending on the field characteristic)
revealing the secret polynomial structure
of the code.
MinRank solvers can then be used to recover the
secret key of the scheme. We devise a dedicated algebraic modeling in
characteristic $2$ where the Gröbner basis techniques to solve it can be analyzed.
This computation behaves differently
when applied to the matrix space associated with a
random code rather than with a Goppa or an alternant code. This
gives a distinguisher of the latter code families, which contrarily
to the one proposed in \cite{FGOPT11} working only in a tiny parameter regime is now
able to work for code rates above $\frac{2}{3}$. It applies to most of the
instantiations of the McEliece cryptosystem in the literature. It coincides with the one of \cite{FGOPT11}
when the latter can be applied (and is therefore of polynomial complexity in this case). However, its complexity
increases significantly when \cite{FGOPT11} does not apply anymore, but stays subexponential as long as the co-dimension of the code is sublinear in the length (with an asymptotic exponent which is below those of all known key recovery or message attacks). For the concrete parameters of the McEliece NIST submission \cite{ABCCGLMMMNPPPSSSTW20}, its
complexity is way too complex to threaten the cryptosystem, but is smaller than known key recovery attacks for most
of the parameters of the submission. This subspace of quadratic forms can also be used in a different manner
to give a polynomial time attack of the McEliece cryptosystem
based on generic alternant codes or Goppa codes provided that these codes are distinguishable by the method of
\cite{FGOPT11}, and in the Goppa case we need the additional assumption that its degree is less than $q-1$, where $q$ is the
alphabet size of the code.

2023

ASIACRYPT

A New Formulation of the Linear Equivalence Problem and Shorter LESS Signatures
Abstract

The Linear Equivalence Problem (LEP) asks to find a linear isometry between a given pair of linear codes; in the Hamming weight this is known as a monomial map.
LEP has been used in cryptography to design the family of LESS signatures, which includes also some advanced schemes, such as ring and identity-based signatures.
All of these schemes are obtained applying the Fiat-Shamir transformation to a Sigma protocol, in which the prover's responses contain a description of how the monomial map acts on all code coordinates; such a description constitutes the vast majority of the signature size.
In this paper, we propose a new formulation of LEP, which we refer to as Information-Set (IS)-LEP.
Exploiting IS-LEP, it is enough for the prover to provide the description of the monomial action only on an information set, instead of all the coordinates.
Thanks to this new formulation, we are able to drastically reduce signature sizes for all LESS signature schemes, without any relevant computational overhead.
We prove that IS-LEP and LEP are completely equivalent (indeed, the same problem), which means that improvement comes with no additional security assumption, either.

2023

ASIACRYPT

A polynomial time attack on instances of M-SIDH and FESTA
Abstract

The recent devastating attacks on SIDH rely on the fact that the protocol reveals the images $\varphi(P)$ and $\varphi(Q)$ of the secret isogeny $\varphi : E_0 \rightarrow E$ on a basis $\{P, Q\}$ of the $N$-torsion subgroup $E_0[N]$ where $N^2 > \deg(\varphi)$. To thwart this attack, two recent proposals, M-SIDH and FESTA, proceed by only revealing the images upto unknown scalars $\lambda_1, \lambda_2 \in \mathbb{Z}_N^\times$, i.e., only $\lambda_1 \varphi(P)$ and $\lambda_2 \varphi(Q)$ are revealed, where $\lambda_1 = \lambda_2$ for M-SIDH and $\lambda_1 = \lambda_2^{-1}$ for FESTA. Similar information is leaked in CSIDH since $\varphi$ maps the eigenspaces of Frobenius on $E_0$ to the corresponding eigenspaces on $E$.
In this paper, we introduce a new polynomial time attack that generalizes the well known "lollipop" attack and analyze how it applies to M-SIDH, FESTA and CSIDH. We show that M-SIDH can be broken in polynomial time whenever $E_0$ or $E$ is $\mathbb{F}_p$-rational, even when the endomorphism rings of $E_0$ and $E$ are unknown. This can be generalized to the case where the starting (or end) curve is not $\mathbb{F}_p$-rational, but is connected to its Frobenius conjugate by an isogeny of small degree.
For FESTA, where the curve $E_0$ is already $\mathbb{F}_p$-rational, we obtain a polynomial time attack under the added requirement that at least one of the basis points $P, Q$ spans an eigenspace of Frobenius, of an endomorphism of low degree, or of a composition of both. We note that the current implementation of FESTA does not choose such a basis. Since it is always possible to construct an endomorphism, typically of large degree, with either $P, Q$ an eigenvector, we conclude that FESTA with overstretched parameters is insecure.
Although the information leaked in CSIDH is very similar to FESTA, we show that our attack does not reveal any new information about the secret isogeny, i.e., we only learn that it is $\mathbb{F}_p$-rational, which is a priori knowledge.
Finally, we analyze if and how it would be possible to backdoor M-SIDH and FESTA by choosing system parameters that look inconspicuous, but in fact reduce to the special cases above via a secret isogeny chosen by the adversary.

2023

ASIACRYPT

A Simple and Efficient Framework of Proof Systems for NP
Abstract

In this work, we propose a simple framework of constructing efficient non-interactive zero-knowledge proof (NIZK) systems for all NP. Compared to the state-of-the-art construction by Groth, Ostrovsky, and Sahai (J. ACM, 2012), our resulting NIZK system reduces the proof size and proving and verification cost without any trade-off, i.e., neither increasing computation cost, CRS size nor resorting to stronger assumptions.
Furthermore, we extend our framework to construct a batch argument (BARG) system for all NP. Our construction remarkably improves the efficiency of BARG by Waters and Wu (Crypto 2022) without any tradeoff.

2023

ASIACRYPT

Adaptive Distributional Security for Garbling Schemes with O(|x|) Online Complexity
Abstract

Garbling schemes allow to garble a circuit C and an input x such that C(x) can be computed while hiding both C and x. In the context of adaptive security, an adversary specifies the input to the circuit after seeing the garbled circuit, so that one can pre-process the garbling of C and later only garble the input x in the online phase. Since the online phase may be time-critical, it is an interesting question how much information needs to be transmitted in this phase and ideally, this should be close to |x|. Unfortunately, Applebaum, Ishai, Kushilevitz, and Waters (AIKW, CRYPTO 2013) show that for some circuits, specifically PRGs, achieving online complexity close to |x| is impossible with simulation-based security, and Hubácek and Wichs (HW, ITCS 2015) show that online complexity of maliciously secure 2-party computation needs to grow with the incompressibility entropy of the function. We thus seek to understand under which circumstances optimal online complexity is feasible despite these strong lower bounds.
Our starting point is the observation that lower bounds (only) concern cryptographic circuits and that, when an embedded secret is not known to the adversary (distinguisher), then the lower bound techniques do not seem to apply. Our main contribution is distributional simulation-based security (DSIM), a framework for capturing weaker, yet meaningful simulation-based (adaptive) security which does not seem to suffer from impossibility results akin to AIKW. We show that DSIM can be used to prove security of a distributed symmetric encryption protocol built around garbling. We also establish a bootstrapping result from DSIM-security for NC0 circuits to DSIM-security for arbitrary polynomial-size circuits while preserving their online complexity.

2023

ASIACRYPT

Algebraic Attacks on Round-Reduced Rain and Full AIM-III
Abstract

Picnic is a NIST PQC Round 3 Alternate signature candidate that builds upon symmetric primitives following the MPC-in-the-head paradigm. Recently, researchers have been exploring more secure/efficient signature schemes from conservative one-way functions based on AES, or new low complexity one-way functions like Rain (CCS 2022) and AIM (CCS 2023). The signature schemes based on Rain and AIM are currently the most efficient among MPC-in-the-head-based schemes, making them promising post-quantum digital signature candidates.
However, the exact hardness of these new one-way functions deserves further study and scrutiny. This work presents algebraic attacks on Rain and AIM for certain instances, where one-round Rain can be compromised in $2^{n/2}$ for security parameter $n\in \{128,192,256\}$, and two-round Rain can be broken in $2^{120.3}$, $2^{180.4}$, and $2^{243.1}$ encryptions, respectively. Additionally, we demonstrate an attack on AIM-III (which aims at 192-bit security) with a complexity of $2^{186.5}$ encryptions. These attacks exploit the algebraic structure of the power function over fields with characteristic 2, which provides potential insights into the algebraic structures of some symmetric primitives and thus might be of independent interest.

2023

ASIACRYPT

Amortized bootstrapping revisited: Simpler, asymptotically-faster, implemented
Abstract

Micciancio and Sorrel (ICALP 2018) proposed a bootstrapping algorithm
that can refresh many messages at once with sublinearly many homomorphic
operations per message.
However, despite the attractive asymptotic cost,
it is unclear if their algorithm could ever be practical,
which reduces the impact of their results.
In this work, we follow their general framework,
but propose an amortized bootstrapping procedure that is
conceptually simpler and asymptotically cheaper.
We reduce the number of homomorphic operations per refreshed message from
$O(3^\rho \cdot n^{1/\rho} \cdot \log n)$ to
$O(\rho \cdot n^{1/\rho})$,
and the noise overhead from
$\tilde{O}(n^{2 + 3 \cdot \rho})$
to $\tilde{O}(n^{1 + \rho})$.
We also make it more general, by handling non-binary messages and applying
programmable bootstrapping.
To obtain a concrete instantiation of our bootstrapping algorithm,
we describe a double-CRT (aka RNS) version of the GSW scheme, including a
new operation, called \emph{shrinking}, used to speed-up homomorphic
operations by reducing the dimension and ciphertext modulus of the
ciphertexts.
We also provide a C++ implementation of our algorithm,
thus showing for the first time the practicability of the amortized
bootstrapping.
Moreover, it is competitive with existing bootstrapping
algorithms, being even around 3.4 times faster than an equivalent
non-amortized version of our bootstrapping.

2023

ASIACRYPT

Amortized Functional Bootstrapping in less than 7ms, with ~O(1) polynomial multiplications
Abstract

Amortized bootstrapping offers a way to refresh multiple ciphertexts of a fully homomorphic encryption scheme in parallel more efficiently than refreshing a single ciphertext at a time. Micciancio and Sorrell (ICALP 2018) first proposed this technique to bootstrap n LWE ciphertexts at a time, reducing the total cost from \tilde{O}(n^2) to \tilde{O}(3^\epsilon n^{1+1/\epsilon}) for arbitrary \epsilon > 0. Several recent follow-up works have further improved the asymptotic cost. Despite these amazing progresses in theoretical efficiency, none of these works have demonstrated the practicality of batched LWE ciphertext bootstrapping. Moreover, most of these works only support limited functional bootstrapping, i.e., they only allow evaluating a specific type of function when bootstrapping.
In this work, we propose a construction that is not only asymptotically efficient (requiring only \tilde{O}(n) polynomial multiplications for bootstrapping of n LWE ciphertexts) but also concretely efficient. We have our scheme implemented as a C++ library and show that it takes <5ms per LWE ciphertext to bootstrap for a binary gate, which is an order of magnitude faster than the state-of-the-art C++ implementation on LWE ciphertext bootstrapping in OpenFHE. Furthermore, our construction supports batched arbitrary functional bootstrapping. For a 9-bit messages space, our scheme takes ~6.7ms per LWE ciphertext to evaluate an arbitrary function with bootstrapping, which is about two to three magnitudes faster than all the existing schemes that achieve a similar functionality and message space.

2023

ASIACRYPT

Amortized NISC over $\mathbb{Z}_{2^k}$ from RMFE
Abstract

Reversed multiplication friendly embedding (RMFE) amortization has been playing an active role in the state-of-the-art constructions of MPC protocols over rings (in particular, the ring $\mathbb{Z}_{2^k}$). As far as we know, this powerful technique has NOT been able to find applications in the crown jewel of two-party computation, the non-interactive secure computation (NISC), where the requirement of the protocol being non-interactive constitutes a formidable technical bottle-neck. We initiate such a study focusing on statistical NISC protocols in the VOLE-hybrid model. Our study begins with making the {\em decomposable affine randomized encoding (DARE)} based semi-honest NISC protocol compatible with RMFE techniques, which together with known techniques for forcing a malicious sender Sam to honestly follow DARE already yield a secure amortized protocol, assuming both parties follow RMFE encoding. Achieving statistical security in the full malicious setting is much more challenging, as applying known techniques for enforcing compliance with RMFE incurs interaction. To solve this problem, we put forward a new notion dubbed non-malleable RMFE (NM-RMFE), which is a randomized RMFE such that, once one party deviates from the encoding specification, the randomness injected by the other party will randomize the output, preventing information from being leaked. NM-RMFE simultaneously forces both parties to follow RMFE encoding, offering a desired {\em non-interactive} solution to amortizing NISC. We believe that NM-RMFE is on its own an important primitive that has applications in secure computation and beyond, interactive and non-interactive alike. With an asymptotically good instantiation of our NM-RMFE, we obtain the first {\em statistical} reusable NISC protocols in the VOLE-hybrid model with {\em constant communication overhead} for arithmetic branching programs over $\mathbb{Z}_{2^k}$.
As side contributions, we consider computational security and present two concretely efficient NISC constructions in the random oracle model from conventional RMFEs.

2023

ASIACRYPT

An Efficient Strong Asymmetric PAKE Compiler Instantiable from Group Actions
Abstract

Password-authenticated key exchange (PAKE) is a class of protocols enabling two parties to convert a shared (possibly low-entropy) password into a high-entropy joint session key. Strong asymmetric PAKE (saPAKE), an extension that models the client-server setting where servers may store a client's password for repeated authentication, was the subject of standardization efforts by the IETF in 2019--20. In this work, we present the most computationally efficient saPAKE protocol so far: a compiler from PAKE to saPAKE which costs only 2 rounds and 7 exponentiations in total (3 for client and 4 for server) when instantiated with suitable underlying PAKE protocols. In addition to being efficient, our saPAKE protocol is conceptually simple and achieves the strongest notion of universally composable (UC) security.
In addition to classical assumptions and classical PAKE, we may instantiate our PAKE-to-saPAKE compiler with cryptographic group actions, such as the isogeny-based CSIDH, and post-quantum PAKE. This yields the first saPAKE protocol from post-quantum assumptions as all previous constructions rely on cryptographic assumptions weak to Shor's algorithm.

2023

ASIACRYPT

Anonymous Counting Tokens
Abstract

We introduce a new primitive called \emph{anonymous counting tokens} (ACTs) which allows clients to obtain blind signatures or MACs (aka tokens) on messages of their choice, while at the same time enabling issuers to enforce rate limits on the number of tokens that a client can obtain for each message. Our constructions enforce that each client will be able to obtain only one token per message and we show a generic transformation to support other rate limiting as well. We achieve this new property while maintaining the unforgeability and unlinkability properties required for anonymous tokens schemes. We present four ACT constructions with various trade-offs for their efficiency and underlying security assumptions. One construction uses factorization-based primitives and a cyclic group. It is secure in the random oracle model under the q-DDHI assumption (in a cyclic group) and the DCR assumption. Our three other constructions use bilinear maps: one is secure in the standard model under q-DDHI and SXDH, one is secure in the random oracle model under SXDH, and the most efficient of the three is secure in the random oracle model and generic bilinear group model.

2023

ASIACRYPT

Antrag: Annular NTRU Trapdoor Generation
Abstract

In this paper, we introduce a novel trapdoor generation technique for Prest's hybrid sampler over NTRU lattices. Prest's sampler is used in particular in the recently proposed Mitaka signature scheme (Eurocrypt 2022), a variant of the Falcon signature scheme, one of the candidates selected by NIST for standardization. Mitaka was introduced to address Falcon's main drawback, namely the fact that the lattice Gaussian sampler used in its signature generation is highly complex, difficult to implement correctly, to parallelize or protect against side-channels, and to instantiate over rings of dimension not a power of two to reach intermediate security levels. Prest's sampler is considerably simpler and solves these various issues, but when applying the same trapdoor generation approach as Falcon, the resulting signatures have far lower security in equal dimension. The Mitaka paper showed how certain randomness-recycling techniques could be used to mitigate this security loss, but the resulting scheme is still substantially less secure than Falcon (by around 20 to 50 bits of CoreSVP security depending on the parameters), and has much slower key generation.
Our new trapdoor generation techniques solves all of those issues satisfactorily: it gives rise to a much simpler and faster key generation algorithm than Mitaka's (achieving similar speeds to Falcon), and is able to comfortably generate trapdoors reaching the same NIST security levels as Falcon as well. It can also be easily adapted to rings of intermediate dimensions, in order to support the same versatility as Mitaka in terms of parameter selection. All in all, this new technique combines all the advantages of both Falcon and Mitaka (and more) with none of the drawbacks.

2023

ASIACRYPT

Automated Meet-in-the-Middle Attack Goes to Feistel
Abstract

Feistel network and its generalizations (GFN) are another important building blocks for constructing hash functions, e.g., Simpiravb, Areion, and the ISO standard Lesamnta-lw. The Meet-in-the-Middle (MitM) is a general paradigm to build preimage and collision attacks on hash functions, which has been automated in several papers. However, those automatic tools mostly focus on hash function with Substitution–Permutation network (SPN) as building blocks, and only one for Feistel network by Schrottenloher and Stevens (at CRYPTO 2022).
In this paper, we introduce a new automatic model for MitM attacks on Feistel networks by generalizing the traditional {\em direct or indirect partial matching strategies} and also Sasaki's multi-round matching strategy. Besides, we find the equivalent transformations of Feistel and GFN can significantly simplify the MILP modellings. Based on our automatic model, we improve the preimage attacks on Feistel-SP-MMO, Simpira-2/-4-DM, Areion-256/-512-DM by 1-2 rounds or significantly reduce the complexities. Furthermore, we fill in the gap left by Schrottenloher and Stevens at CRYPTO 2022 on the large branch ($b>4$) Simpira-$b$'s attack and propose the first 11-round attack on Simpira-6. Besides, we significantly improve the collision attack on the ISO standard hash Lesamnta-lw by increasing the attacked round number from previous 11 to ours 17 rounds.

2023

ASIACRYPT

Bicameral and Auditably Private Signatures
Abstract

This paper introduces Bicameral and Auditably Private Signatures (BAPS) -- a new privacy-preserving signature system with several novel features. In a BAPS system, given a certified attribute $\mathbf{x}$ and a certified policy $P$, a signer can issue
a publicly verifiable signature $\Sigma$ on a message $m$ as long as $(m, \mathbf{x})$ satisfies $P$. A noteworthy characteristic of BAPS is that both attribute $\mathbf{x}$ and policy $P$ are kept hidden from the verifier, yet the latter is convinced that these objects were certified by an attribute-issuing authority and a policy-issuing authority, respectively. By considering \textsf{bicameral certification authorities} and requiring privacy for both attributes and policies, BAPS generalizes the spirit of existing advanced signature primitives with fine-grained controls on signing capabilities (e.g., attribute-based signatures, predicate signatures, policy-based signatures). Furthermore, BAPS provides an appealing feature named \textsf{auditable privacy}, allowing the signer of $\Sigma$ to verifiably disclose various pieces of partial information about $P$ and $\mathbf{x}$ when asked by auditor(s)/court(s) at later times. Auditable privacy is intrinsically different from and can be complementary to the notion of accountable privacy traditionally incorporated in traceable anonymous systems such as group signatures. Equipped with these distinguished features, BAPS can potentially address interesting application scenarios for which existing primitives do not offer a direct solution.
We provide rigorous security definitions for BAPS, following a ``sim-ext'' approach. We then demonstrate a generic construction based on commonly used cryptographic building blocks, which makes use of a \textsf{sign-then-commit-then-prove} design. Finally, we present a concrete instantiation of BAPS, that is proven secure in the random oracle model under lattice assumptions. The scheme can handle arbitrary policies represented by polynomial-size Boolean circuits and can address quadratic disclosing functions. In the construction process, we develop a new technical building block that could be of independent interest: a zero-knowledge argument system allowing to prove the satisfiability of a certified-and-hidden Boolean circuit on certified-and-committed inputs.

2023

ASIACRYPT

Blockwise Rank Decoding Problem and LRPC Codes: Cryptosystems with Smaller Sizes
Abstract

In this paper, we initiate the study of the Rank Decoding (RD) problem and LRPC codes with blockwise structures in rank-based cryptosystems. First, we introduce the blockwise errors ($\ell$-errors) where each error consists of $\ell$ blocks of coordinates with disjoint supports, and define the blockwise RD ($\ell$-RD) problem as a natural generalization of the RD problem whose solutions are $\ell$-errors (note that the standard RD problem is actually a special $\ell$-RD problem with $\ell=1$). We adapt the typical attacks on the RD problem to the $\ell$-RD problem, and find that the blockwise structures do not ease the problem too much: the $\ell$-RD problem is still exponentially hard for appropriate choices of $\ell>1$. Second, we introduce blockwise LRPC ($\ell$-LRPC) codes as generalizations of the standard LPRC codes whose parity-check matrices can be divided into $\ell$ sub-matrices with disjoint supports, i.e., the intersection of two subspaces generated by the entries of any two sub-matrices is a null space, and investigate the decoding algorithms for $\ell$-errors. We find that the gain of using $\ell$-errors in decoding capacity outweighs the complexity loss in solving the $\ell$-RD problem, which makes it possible to design more efficient rank-based cryptosystems with flexible choices of parameters.
As an application, we show that the two rank-based cryptosystems submitted to the NIST PQC competition, namely, RQC and ROLLO, can be greatly improved by using the ideal variants of the $\ell$-RD problem and $\ell$-LRPC codes. Concretely, for 128-bit security, our RQC has total public key and ciphertext sizes of 2.5 KB, which is not only about 50\% more compact than the original RQC, but also smaller than the NIST Round 4 code-based submissions HQC, BIKE, and Classic McEliece.

2023

ASIACRYPT

Breaking the Size Barrier: Universal Circuits meet Lookup Tables
Abstract

A Universal Circuit (UC) is a Boolean circuit of size $\Theta(n \log n)$ that can simulate any Boolean function up to a certain size $n$. Valiant (STOC'76) provided the first two UC constructions of asymptotic sizes $\sim5 n\log n$ and $\sim4.75 n\log n$, and today's most efficient construction of Liu et al. (CRYPTO'21) has size $\sim3n\log n$.
Evaluating a public UC with a secure Multi-Party Computation (MPC) protocol allows efficient Private Function Evaluation (PFE), where a private function is evaluated on private data.
Previously, most UC constructions have only been developed for circuits consisting of 2-input gates. In this work, we generalize UCs to simulate circuits consisting of ($\rho \rightarrow \omega)-Lookup Tables (LUTs) that map $\rho$ input bits to $\omega$ output bits. Our LUT-based UC (LUC) construction has an asymptotic size of $1.5\rho\omega n \log \omega n$ and improves the size of the UC over the best previous UC construction of Liu et al. (CRYPTO'21) by factors 1.12$\times$ - $2.18\times$ for common functions. Our results show that the greatest size improvement is achieved for $\rho=3$ inputs, and it decreases for $\rho>3$.
Furthermore, we introduce Varying Universal Circuits (VUCs), which reduce circuit size at the expense of leaking the number of inputs $\rho$ and outputs $\omega$ of each LUT. Our benchmarks demonstrate that VUCs can improve over the size of the LUC construction by a factor of up to $1.45\times$.

2023

ASIACRYPT

CCA-1 Secure Updatable Encryption with Adaptive Security
Abstract

Updatable encryption (UE) enables a cloud server to update
ciphertexts using client-generated tokens. There are two types of UE:
ciphertext-independent (c-i) and ciphertext-dependent (c-d). In terms of
construction and efficiency, c-i UE utilizes a single token to update all
ciphertexts. The update mechanism relies mainly on the homomorphic
properties of exponentiation, which limits the efficiency of encryption
and updating. Although c-d UE may seem inconvenient as it requires
downloading parts of the ciphertexts during token generation, it allows
for easy implementation of the Dec-then-Enc structure. This methodology significantly simplifies the construction of the update mechanism.
Notably, the c-d UE scheme proposed by Boneh et al. (ASIACRYPT’20)
has been reported to be 200 times faster than prior UE schemes based
on DDH hardness, which is the case for most existing c-i UE schemes.
Furthermore, c-d UE ensures a high level of security as the token does
not reveal any information about the key, which is difficult for c-i UE
to achieve. However, previous security studies on c-d UE only addressed
selective security; the studies for adaptive security remain an open problem.
In this study, we make three significant contributions to ciphertextdependent updatable encryption (c-d UE). Firstly, we provide stronger
security notions compared to previous work, which capture adaptive security and also consider the adversary’s decryption capabilities under
the adaptive corruption setting. Secondly, we propose a new c-d UE
scheme that achieves the proposed security notions. The token generation technique significantly differs from the previous Dec-then-Enc structure, while still preventing key leakages. At last, we introduce a packing
technique that enables the simultaneous encryption and updating of multiple messages within a single ciphertext. This technique helps alleviate
the cost of c-d UE by reducing the need to download partial ciphertexts
during token generation.

2023

ASIACRYPT

Concrete Analysis of Quantum Lattice Enumeration
Abstract

Lattice reduction algorithms such as BKZ (Block-Korkine-Zolotarev) play a central role in estimating the security of lattice-based cryptography. The subroutine in BKZ which needs to find the shortest vector in a projected sublattice can be instantiated with enumeration algorithms. The enumeration procedure can be seen as a depth-first search on some ``enumeration tree'' whose nodes denote a partial assignment of the coefficients, corresponding to lattice points as a linear combination of the lattice basis with the coefficients. This work provides a concrete analysis for the cost of quantum lattice enumeration based on the quantum tree backtracking algorithm of Montanaro (ToC, '18). More precisely, we give a concrete implementation of Montanaro's algorithm for lattice enumeration based on the quantum circuit model. We also show how to optimize the circuit depth by parallelizing the components. Based on the circuit designed, we discuss the concrete quantum resource estimates required for lattice enumeration.

2023

ASIACRYPT

Correlation Cube Attack Revisited:Improved Cube Search and Superpoly Recovery Techniques
Abstract

In this paper, we improve the cube attack by exploiting low-degree factors of the superpoly w.r.t. certain \textit{"special" } index set of cube (\textit{ISoC}). This can be viewed as a special case of the correlation cube attack proposed at Eurocrypt 2018, but under our framework more beneficial equations on the key variables can be obtained in the key-recovery phase. To mount our attack, one has two challenging problems: (1) effectively recover algebraic normal form of the superpoly and extract out its low-degree factors; and (2) efficiently search a large quantity of good \textit{ISoC}s. We bring in new techniques to solve both of them.
First, we propose the \textit{variable substitution technique} for middle rounds of a cipher, in which polynomials on the key variables in the algebraic expressions of internal states are substituted by new variables. This will improve computational complexity of the superpoly recovery and promise more compact superpolys that can be easily decomposed with respect to the new variables. Second, we propose the \textit{vector numeric mapping technique}, which seeks out a tradeoff between efficiency of the numeric mapping technique (Crypto 2019) and accuracy of the monomial prediction technique (Asiacrypt 2020) in degree evaluation of superpolys. Combining with this technique, a fast pruning method is given and modeled by MILP to filter good \textit{ISoC}s of which the algebraic degree satisfies some fixed threshold. Thanks to automated MILP solvers, it becomes practical to comprehensively search for good cubes across the entire search space.
To illustrate the power of our techniques, we apply all of them to Trivium stream cipher. As a result, we have recovered the superpolys of three cubes given by Kesarwani et al. in 2020, only to find they do not have \texttt{zero-sum} property up to 842 rounds as claimed in their paper. To our knowledge, the previous best practical key recovery attack was on 820-round Trivium with complexity $2^{53.17}$. We put forward 820-, 825- and 830-round practical key-recovery attacks, in which there are $\mathbf{2^{80}\times 87.8\%}$, $\mathbf{2^{80}\times 83\%}$ and $\mathbf{2^{80}\times 65.7\%}$ keys that could be practically recovered, respectively, if we consider $\mathbf{2^{60}}$ as the upper bound for practical computational complexity. Besides, even for computers with computational power not exceeding $\mathbf{2^{52}}$ (resp. $\mathbf{2^{55}}$), we can still recover $\mathbf{58\%}$ (resp. $\mathbf{46.6\%}$) of the keys in the key space for 820 rounds (resp. 830 rounds). Our attacks have led 10 rounds more than the previous best practical attack.
\keywords{Correlation cube attack \and Variable substitution \and Vector numeric mapping \and MILP \and Trivium.}

2023

ASIACRYPT

Cryptanalysis of Elisabeth-4
Abstract

Elisabeth-4 is a stream cipher tailored for usage in hybrid homomorphic encryption applications that has been introduced by Cosseron et al. at ASIACRYPT 2022. In this paper, we present several variants of a key-recovery attack on the full Elisabeth-4 that break the 128-bit security claim of that cipher. Our most optimized attack is a chosen-IV attack with a time complexity of 2^88 elementary operations, a memory complexity of 2^54 bits and a data complexity of 2^41 bits.
Our attack applies the linearization technique to a nonlinear system of equations relating some keystream bits to the key bits and exploits specificities of the cipher to solve the resulting linear system efficiently. First, due to the structure of the cipher, the system to solve happens to be very sparse, which enables to rely on sparse linear algebra and most notably on the Block Wiedemann algorithm. Secondly, the algebraic properties of the two nonlinear ingredients of the filtering function cause rank defects which can be leveraged to solve the linearized system more efficiently with a decreased data and time complexity.
We have implemented our attack on a toy version of Elisabeth-4 to verify its correctness. It uses the efficient implementation of the Block Wiedemann algorithm of CADO-NFS for the sparse linear algebra.

2023

ASIACRYPT

Cryptographic Smooth Neighbors
Abstract

We revisit the problem of finding two consecutive $B$-smooth integers by giving an optimised implementation of the Conrey-Holm\-strom-McLaughlin ``smooth neighbors'' algorithm. While this algorithm is not guaranteed to return the complete set of $B$-smooth neighbors, in practice it returns a very close approximation to the complete set but does so in a tiny fraction of the time of its exhaustive counterparts. We exploit this algorithm to find record-sized solutions to the pure twin smooth problem, and subsequently to produce instances of cryptographic parameters whose corresponding isogeny degrees are significantly smoother than prior works. Our methods seem well-suited to finding parameters for the SQISign signature scheme, especially for instantiations looking to minimize the cost of signature generation. We give a number of examples, among which are the first parameter sets geared towards efficient SQISign instantiations at NIST's security levels III and V.

2023

ASIACRYPT

Cuckoo Commitments: Registration-Based Encryption and Key-Value Map Commitments for Large Spaces
Abstract

Registration-Based Encryption (RBE) [Garg et al. TCC’18] is a public-key encryption mechanism in which users generate their own public and secret keys, and register their public keys with a central au- thority called the key curator. Similarly to Identity-Based Encryption (IBE), in RBE users can encrypt by only knowing the public parameters and the public identity of the recipient. Unlike IBE, though, RBE does not suffer the key escrow problem—one of the main obstacles of IBE’s adoption in practice—since the key curator holds no secret.
In this work, we put forward a new methodology to construct RBE schemes that support large users identities (i.e., arbitrary strings). Our main result is the first efficient pairing-based RBE for large identities. Prior to our work, the most efficient RBE is that of [Glaeser et al. ePrint’ 22] which only supports small identities. The only known RBE schemes with large identities are realized either through expensive non-black- box techniques (ciphertexts of 3.6 TB for 1000 users), via a specialized lattice-based construction [Döttling et al. Eurocrypt’23] (ciphertexts of 2.4 GB), or through the more complex notion of Registered Attribute- Based Encryption [Hohenberger et al. Eurocrypt’23]. By unlocking the use of pairings for RBE with large identity space, we enable a further im- provement of three orders of magnitude, as our ciphertexts for a system with 1000 users are 1.7 MB.
The core technique of our approach is a novel use of cuckoo hashing in cryptography that can be of independent interest. We give two main ap- plications. The first one is the aforementioned RBE methodology, where we use cuckoo hashing to compile an RBE with small identities into one for large identities. The second one is a way to convert any vector com- mitment scheme into a key-value map commitment. For instance, this leads to the first algebraic pairing-based key-value map commitments.

2023

ASIACRYPT

Degree-$D$ Reverse Multiplication-Friendly Embeddings: Constructions and Applications
Abstract

In the recent work of (Cheon \& Lee, Eurocrypt'22), the concept of a \emph{degree-$D$ packing method} was formally introduced, which captures the idea of embedding multiple elements of a smaller ring into a larger ring, so that element-wise multiplication in the former is somewhat ``compatible'' with the product in the latter.
Then, several optimal bounds and results are presented, and furthermore, the concept is generalized from one multiplication to degrees larger than two.
These packing methods encompass several constructions seen in the literature in contexts like secure multiparty computation and fully homomorphic encryption.
One such construction is the concept of reverse multiplication-friendly embeddings (RMFEs), which are essentially degree-2 packing methods.
In this work we generalize the notion of RMFEs to \emph{degree-$D$ RMFEs} which, in spite of being ``more algebraic'' than packing methods, turn out to be essentially equivalent.
Then, we present a general construction of degree-$D$ RMFEs by generalizing the ideas on algebraic geometry used to construct traditional degree-$2$ RMFEs which, by the aforementioned equivalence, leads to explicit constructions of packing methods.
Furthermore, our theory is given in a unified manner for general Galois rings, which include both rings of the form $\mathbb{Z}_{p^k}$ and fields like $\mathbb{F}_{p^k}$, which have been treated separately in prior works.
We present multiple concrete sets of parameters for degree-$D$ RMFEs (including $D=2$), which can be useful for future works.
Finally, we discuss interesting applications of our RMFEs, focusing in particular on the case of non-interactively generating high degree correlations for secure multiparty computation protocols.
This requires the use of Shamir secret sharing for a large number of parties, which requires large-degree Galois ring extensions.
Our RMFE enables the generation of such preprocessing data over small rings, without paying for the multiplicative overhead incurred by using Galois ring extensions of large degree.
For our application we also construct along the way, as a side contribution of potential independent interest, a pseudo-random secret-sharing solution for non-interactive generation of packed Shamir-sharings over Galois rings with structured secrets, inspired by the PRSS solutions from (Benhamouda \emph{et al}, TCC 2021).

2023

ASIACRYPT

Differential-Linear Approximation Semi-Unconstrained Searching and Partition Tree: Application to LEA and Speck
Abstract

The differential-linear attack is one of
the most effective attacks against ARX ciphers.
However, two technical problems are preventing it from
being more effective and having more applications:
(1) there is no efficient method to search for
good differential-linear approximations.
Existing methods either have many constraints or are currently inefficient.
(2) partitioning technique has great potential
to reduce the time complexity of the key-recovery attack,
but there is no general tool to construct partitions for ARX ciphers.
In this work, we step forward in solving the two problems.
First, we propose a novel idea for generating new
good differential-linear approximations from known ones,
based on which new searching algorithms are designed.
Second, we propose a general tool named partition tree,
for constructing partitions for ARX ciphers.
Based on these new techniques,
we present better attacks for two ISO/IEC standards,
i.e., LEA and Speck.
For LEA, we present the first 17-round distinguisher which
is 1 round longer than the previous best distinguisher.
Furthermore, we present the first key recovery attacks on
17-round LEA-128, 18-round LEA-192, and 18-round LEA-256,
which attack 3, 4, and 3 rounds more than the previous best attacks.
For Speck, we find better differential-linear distinguishers for Speck48 and Speck64.
The first differential-linear distinguishers for Speck96 and Speck128 are also presented.

2023

ASIACRYPT

Distributed Broadcast Encryption from Bilinear Groups
Abstract

Distributed broadcast encryption (DBE) improves on the
traditional notion of broadcast encryption by eliminating the key-escrow
problem: In a DBE system, users generate their own secret keys non-
interactively without the help of a trusted party. Then anyone can broad-
cast a message for a subset S of the users, in such a way that the resulting
ciphertext size is sublinear in (and, ideally, independent of) |S|. Unfor-
tunately, the only known constructions of DBE requires heavy crypto-
graphic machinery, such as general-purpose indistinguishability obfusca-
tion, or come without a security proof.
In this work, we formally show that obfuscation is not necessary for DBE,
and we present two practical DBE schemes from standard assumptions in
prime-order bilinear groups. Our constructions are conceptually simple,
satisfy the strong notion of adaptive security, and are concretely efficient.
In fact, their performance, in terms of number of group elements and
efficiency of the algorithms, is comparable with that of traditional (non
distributed) broadcast encryption schemes from bilinear groups.

2023

ASIACRYPT

Efficient Secure Storage with Version Control and Key Rotation
Abstract

Periodic key rotation is a widely used technique to enhance key compromise resilience. Updatable encryption (UE) schemes provide an efficient approach to key rotation, ensuring the post compromise security for both confidentiality and integrity. However, these UE techniques cannot be directly applied to frequently updated databases due to the risk of a malicious server inducing the client to accept an outdated version of a file instead of the latest one.
To address this issue, we propose a scheme called Updatable Secure Storage (USS), which provides a secure and updatable solution for dynamic databases. The USS scheme ensures both data confidentiality and integrity, even in the presence of key compromises. By using efficient key rotation and file update procedures, the communication costs of these operations are independent of the size of the database. This makes the USS scheme particularly well-suited for managing large and frequently updated databases with secure version control. Unlike existing UE schemes, the integrity provided by USS holds even when the server learns the current secret key and intentionally violates the key update protocol.

2023

ASIACRYPT

Efficient Updatable Public-Key Encryption from Lattices
Abstract

Updatable public key encryption has recently been introduced as a solution to achieve forward-security in the context of secure group messaging without hurting efficiency, but so far, no efficient lattice-based instantiation of this primitive is known.
In this work, we construct the first LWE-based UPKE scheme with polynomial modulus-to-noise rate, which is CPA-secure in the standard model. At the core of our security analysis is a generalized reduction from the standard LWE problem to (a stronger version of) the Extended LWE problem. We further extend our construction to achieve stronger security notions by proposing two generic transforms. Our first transform allows to obtain CCA security in the random oracle model and adapts the Fujisaki-Okamoto transform to the UPKE setting. Our second transform allows to achieve security against malicious updates by adding a NIZK argument in the update mechanism. In the process, we also introduce the notion of Updatable Key Encapsulation Mechanism (UKEM), as the updatable variant of KEMs. Overall, we obtain a CCA-secure UKEM in the random oracle model whose ciphertext sizes are of the same order of magnitude as that of CRYSTALS-Kyber.

2023

ASIACRYPT

Exact Security Analysis of ASCON
Abstract

The \textsc{ascon} cipher suite, offering both authenticated encryption with associated data (AEAD) and hashing functionality, has recently emerged as the winner of the NIST Lightweight Cryptography (LwC) standardization process. The AEAD schemes within \textsc{ascon}, namely \textsc{ascon}-128 and \textsc{ascon}-128a, have also been previously selected as the preferred lightweight authenticated encryption solutions in the CAESAR competition. In this paper, we present a tight and comprehensive security analysis of the \textsc{ascon} AEAD schemes within the random permutation model. Existing integrity analyses of \textsc{ascon} (and any \textsc{duplex} AEAD scheme in general) commonly include the term $DT/2^c$, where $D$ and $T$ represent data and time complexities respectively, and $c$ denotes the capacity of the underlying sponge. In this paper, we demonstrate that \textsc{ascon} achieves AE security when $T$ is bounded by $\min\{2^{\kappa}, 2^c\}$ (where $\kappa$ is the key size), and $DT$ is limited to $2^b$ (with $b$ being the size of the underlying permutation, which is 320 for \textsc{ascon}). Our findings indicate that in accordance with NIST requirements, \textsc{ascon} allows for a tag size as low as 64 bits while enabling a higher rate of 192 bits, surpassing the recommended rate.

2023

ASIACRYPT

Exploiting Algebraic Structure in Probing Security
Abstract

The so-called $\omega$-encoding, introduced by Goudarzi, Joux and
Rivain (Asiacrypt 2018), generalizes the commonly used arithmetic encoding.
By using the additionnal structure of this encoding, they proposed
a masked multiplication gadget (GJR) with quasilinear (randomness
and operations) complexity. A follow-up contribution by Goudarzi,
Prest, Rivain and Vergnaud in this line of research appeared in TCHES
2021. The authors revisited the aforementioned multiplication gadget
(GPRV), and brought the IOS security notion for refresh gadgets to allow
secure composition between probing secure gadgets.
In this paper, we propose a follow up on GPRV, that is, a region-probing
secure arithmetic circuit masked compiler. Our contribution stems from a
single Lemma, linking algebra and probing security for a wide class of circuits,
further taking advantage of the algebraic structure of !-encoding,
and the extension field structure of the underlying field F that was so far
left unexploited. On the theoretical side, we propose a security notion
for !d-masked circuits which we call Reducible-To-Independent-K-linear
(RTIK). When the number of shares d is less than or equal to the degree
k of F, RTIK circuits achieve region-probing security. Moreover,
RTIK circuits may be composed naively and remain RTIK. We also propose
a weaker version of IOS, which we call KIOS, for refresh gadgets.
This notion allows to compose RTIK circuits with a randomness/security
tradeoff compared to the naive composition.
To substantiate our new definitions, we also provide examples of competitively
efficient gadgets verifying the latter weaker security notions.
Explicitly, we give 1) two refresh gadgets that use d - 1 random field
elements to refresh a length d encoding, both of which are KIOS but not
IOS, and 2) a multiplication gadget with bilinear multiplication complexity
dlog 3 and uses d fresh random elements per run. Our compiler
outperforms ISW asymptotically, but for our security proofs to hold, we
do require that the number of shares d is less than or equal to the degree
of F as an extension, so that there is sufficient structure to exploit.

2023

ASIACRYPT

Exploiting the Symmetry of $\mathbb{Z}^n$: Randomization and the Automorphism Problem
Abstract

$\mathbb{Z}^n$ is one of the simplest types of lattices, but the computational problems on its rotations, such as $\mathbb{Z}$SVP and $\mathbb{Z}$LIP, have been of great interest in cryptography. Recent advances have been made in building cryptographic primitives based on these problems, as well as in developing new algorithms for solving them. However, the theoretical complexity of $\mathbb{Z}$SVP and $\mathbb{Z}$LIP are still not well understood.
In this work, we study the problems on rotations of $\mathbb{Z}^n$ by exploiting the symmetry property. We introduce a randomization framework that can be roughly viewed as `applying random automorphisms’ to the output of an oracle, without accessing the automorphism group. Using this framework, we obtain new reduction results for rotations of $\mathbb{Z}^n$. First, we present a reduction from $\mathbb{Z}$LIP to $\mathbb{Z}$SCVP. Here $\mathbb{Z}$SCVP is the problem of finding the shortest characteristic vectors, which is a special case of CVP where the target vector is a deep hole of the lattice. Moreover, we prove a reduction from $\mathbb{Z}$SVP to $\gamma$-$\mathbb{Z}$SVP for any constant $\gamma = O(1)$ in the same dimension, which implies that $\mathbb{Z}$SVP is as hard as its approximate version for any constant approximation factor. Second, we investigate the problem of finding a nontrivial automorphism for a given lattice, which is called LAP. Specifically, we use the randomization framework to show that $\mathbb{Z}$LAP is as hard as $\mathbb{Z}$LIP. We note that our result can be viewed as a $\mathbb{Z}^n$-analogue of Lenstra and Silverberg's result in [JoC2017], but with a different assumption: they assume the $G$-lattice structure, while we assume the access to an oracle that outputs a nontrivial automorphism.

2023

ASIACRYPT

FESTA: Fast Encryption from Supersingular Torsion Attacks
Abstract

We introduce FESTA, an efficient isogeny-based public-key encryption (PKE) protocol based on a constructive application of the SIDH attacks.
At its core, FESTA is based on a novel trapdoor function, which uses an improved version of the techniques proposed in the SIDH attacks to develop a trapdoor mechanism. Using standard transformations, we construct an efficient PKE that is IND-CCA secure in the QROM. Additionally, using a different transformation, we obtain the first isogeny-based PKE that is IND-CCA secure in the standard model.
Lastly, we propose a method to efficiently find parameters for FESTA, and we develop a proof-of-concept implementation of the protocol. We expect FESTA to offer practical performance that is competitive with existing isogeny-based constructions.

2023

ASIACRYPT

Fiat-Shamir Security of FRI and Related SNARKs
Abstract

We establish new results on the Fiat-Shamir (FS) security of several protocols that are widely used in practice, and we provide general tools for establishing similar results for others. More precisely, we: (1) prove the FS security of the FRI and batched FRI protocols; (2) analyze a general class of protocols, which we call \emph{$\delta$-correlated}, that use low-degree proximity testing as a subroutine (this includes many ``Plonk-like'' protocols (e.g., Plonky2 and Redshift), ethSTARK, RISC Zero, etc.); and (3) prove FS security of the aforementioned ``Plonk-like'' protocols, and sketch how to prove the same for the others.
We obtain our first result by analyzing the round-by-round (RBR) soundness and RBR knowledge soundness of FRI. For the second result, we prove that if a $\delta$-correlated protocol is RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials, then it is RBR (knowledge) sound in general. Equipped with this tool, we prove our third result by formally showing that ``Plonk-like'' protocols are RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials. We then outline analogous arguments for the remainder of the aforementioned protocols.
To the best of our knowledge, ours is the first formal analysis of the Fiat-Shamir security of FRI and widely deployed protocols that invoke it.

2023

ASIACRYPT

Fine-Grained Proxy Re-Encryption: Definitions & Constructions from LWE
Abstract

Proxy re-encryption (PRE) allows a proxy with a re-encryption key to translate a ciphertext intended for Alice (delegator) to another ciphertext intended for Bob (delegatee) without revealing the underlying message. However, with PRE, Bob can obtain the whole message from the re-encrypted ciphertext, and Alice cannot take flexible control of the extent of the message transmitted to Bob.
In this paper, we propose a new variant of PRE, called Fine-Grained PRE (FPRE), to support fine-grained re-encryptions. An FPRE is associated with a function family F, and each re-encryption key rk_{A→B}^f is associated with a function f ∈ F. With FPRE, Alice now can authorize re-encryption power to proxy by issuing rk_{A→B}^f to it, with f chosen by herself. Then the proxy can translate ciphertext encrypting m to Bob's ciphertext encrypting f(m) with such a fine-grained re-encryption key, and Bob only obtains a function of message m. In this way, Alice can take flexible control of the message spread by specifying functions.
For FPRE, we formally define its syntax and formalize security notions including CPA security, ciphertext pseudo-randomness, unidirectionality, non-transitivity, collusion-safety under adaptive corruptions in the multi-user setting. Moreover, we propose a new security notion named {\it ciphertext unlinkability}, which blurs the link between a ciphertext and its re-encrypted ciphertext to hide the proxy connections between users. We establish the relations between those security notions.
As for constructions, we propose two FPRE schemes, one for bounded linear functions and the other for deletion functions, based on the learning-with-errors (LWE) assumption. Our FPRE schemes achieve all the aforementioned desirable securities under adaptive corruptions in the standard model. As far as we know, our schemes provide the {\it first} solution to PRE with security under adaptive corruptions in the standard model.

2023

ASIACRYPT

Forgery Attacks on Several Beyond-Birthday-Bound Secure MACs
Abstract

At CRYPTO'18, Datta et al. proposed nPolyMAC and proved the security up to 2^{2n/3} authentication queries and 2^{n} verification queries. At EUROCRYPT'19, Dutta et al. proposed CWC+ and showed the security up to 2^{2n/3} queries. At FSE'19, Datta et al. proposed
PolyMAC and its key-reduced variant 2k-PolyMAC, and showed the security up to 2^{2n/3} queries. This security bound was then improved by Kim et al. (EUROCRYPT'20) and Datta et al (FSE'23) respectively to 2^{3n/4} and in the multi-user setting. At FSE'20, Chakraborti et al. proposed PDM*MAC and 1k-PDM*MAC and showed the security up to 2^{2n/3} queries. Recently, Chen et al. proposed nEHtM_p^+ and showed the security up to 2^{2n/3} queries. In this paper, we show forgery attacks on nPolyMAC, CWC+, PolyMAC, 2k-PolyMAC, PDM*MAC, 1k-PDM*MAC and nEHtM_p^+. Our attacks exploit some vulnerability in the underlying polynomial hash function, and (i) require only one authentication query and one verification query; (ii) are nonce-respecting; (iii) succeed with probability 1. Thus, our attacks disprove the provable high security claims of these schemes. We then revisit their security analyses and identify what went wrong. Finally, we propose two solutions that can restore the beyond-birthday-bound security.

2023

ASIACRYPT

G+G: A Fiat-Shamir Lattice Signature Based on Convolved Gaussians
Abstract

Abstract. We describe an adaptation of Schnorr’s signature to the lattice setting, which relies on Gaussian convolution rather than flooding or rejection sampling as previous approaches. It does not involve any abort, can be proved secure in the ROM and QROM using existing analyses of the Fiat-Shamir transfom, and enjoys smaller signature sizes (both asymptotically and for concrete security levels).

2023

ASIACRYPT

Generalized Fuzzy Password-Authenticated Key Exchange from Error Correcting Codes
Abstract

Fuzzy Password-Authenticated Key Exchange (fuzzy PAKE)
allows cryptographic keys to be generated from authentication data that
is both fuzzy and of low entropy. The strong protection against offline attacks offered by fuzzy PAKE opens an interesting avenue towards secure
biometric authentication, typo-tolerant password authentication, and automated IoT device pairing. Previous constructions of fuzzy PAKE are
either based on Error Correcting Codes (ECC) or generic multi-party
computation techniques such as Garbled Circuits. While ECC-based constructions are significantly more efficient, they rely on multiple special
properties of error correcting codes such as maximum distance separability and smoothness.
We contribute to the line of research on fuzzy PAKE in two ways. First,
we identify a subtle but devastating gap in the security analysis of the
currently most efficient fuzzy PAKE construction (Dupont et al., Eurocrypt 2018), allowing a man-in-the-middle attacker to test individual
password characters. Second, we provide a new fuzzy PAKE scheme
based on ECC and PAKE that provides a built-in protection against
individual password character guesses and requires fewer, more standard properties of the underlying ECC. Additionally, our construction
offers better error correction capabilities than previous ECC-based fuzzy
PAKEs.

2023

ASIACRYPT

Generic Security of the SAFE API and Its Applications
Abstract

We provide security foundations for SAFE, a recently introduced API framework for sponge-based hash functions tailored to prime-field-based protocols. SAFE aims to provide a robust and foolproof interface, has been implemented in the Neptune hash framework and some zero-knowledge proof projects, but despite its usability and applicability it currently lacks any security proof. Such a proof would not be straightforward as SAFE abuses the inner part of the sponge and fills it with protocol-specific data.
In this work we identify the SAFECore as versatile variant sponge construction underlying SAFE, we prove indifferentiability of SAFECore for all (binary and prime) fields up to around $|\mathbb{F}_p|^{c/2}$ queries, where $\mathbb{F}_p$ is the underlying field and $c$ the capacity, and we apply this security result to various use cases. We show that the SAFE-based protocols of plain hashing, authenticated encryption, verifiable computation, non-interactive proofs, and commitment schemes are secure against a wide class of adversaries, including those dealing with multiple invocations of a sponge in a single application. Our results pave the way of using SAFE with the full taxonomy of hash functions, including SNARK-, lattice-, and x86-friendly hashes.

2023

ASIACRYPT

Hermes: I/O-Efficient Forward-Secure Searchable Symmetric Encryption
Abstract

Dynamic Symmetric Searchable Encryption (SSE) enables a user to outsource the storage of an encrypted database to an untrusted server, while retaining the ability to privately search and update the outsourced database. The performance bottleneck of SSE schemes typically comes from their I/O efficiency. Over the last decade, a line of work has substantially improved that bottleneck. However, all existing I/O-efficient SSE schemes have a common limitation: they are not forward-secure. Since the seminal work of Bost at CCS 2016, forward security has become a de facto standard in SSE. In the same article, Bost conjectures that forward security and I/O efficiency are incompatible. This explains the current status quo, where users are forced to make a difficult choice between security and efficiency.
The central contribution of this paper it to show that, contrary to what the status quo suggests, forward security and I/O efficiency can be realized simultaneously. This result is enabled by two new key techniques. First, we make use of a controlled amount of client buffering, combined with a deterministic update schedule. Second, we introduce the notion of SSE supporting dummy updates. In combination, those two techniques offer a new path to realizing forward security, which is compatible with I/O efficiency. Our new SSE scheme, Hermes, achieves sublogarithmic I/O efficiency O(log log N/p), storage efficiency O(1), with standard leakage, as well as backward and forward security. Practical experiments confirm that Hermes achieves excellent performance.

2023

ASIACRYPT

Hidden Stabilizers, the Isogeny To Endomorphism Ring Problem and the Cryptanalysis of pSIDH
Abstract

The Isogeny to Endomorphism Ring Problem (IsERP) asks to compute the endomorphism ring of the codomain of an isogeny between supersingular curves in characteristic p given only a representation for this isogeny, i.e. some data and an algorithm to evaluate this isogeny on any torsion point. This problem plays a central role in isogeny-based cryptography; it underlies the security of pSIDH protocol (ASIACRYPT 2022) and it is at the heart of the recent attacks that broke the SIDH key exchange. Prior to this work, no efficient algorithm was known to solve IsERP for a generic isogeny degree, the hardest case seemingly when the degree is prime.
In this paper, we introduce a new quantum polynomial-time algorithm to solve IsERP for isogenies whose degrees are odd and have O(log(log p)) many prime factors. As main technical tools, our algorithm uses a quantum algorithm for computing hidden Borel subgroups, a group action on supersingular isogenies from EUROCRYPT 2021, various algorithms for the Deuring correspondence and a new algorithm to lift arbitrary quaternion order elements modulo an odd integer N with O(log(log p)) many prime factors to powersmooth elements.
As a main consequence for cryptography, we obtain a quantum polynomial-time key recovery attack on pSIDH. The technical tools we use may also be of independent interest.

2023

ASIACRYPT

Homomorphic polynomial evaluation using Galois structure and applications to BFV bootstrapping
Abstract

BGV and BFV are among the most widely used fully homomorphic encryption (FHE) schemes. Both schemes have a common plaintext space, with a rich algebraic structure. Our main contribution is to show how this structure can be exploited to more efficiently homomorphically evaluate polynomials. Namely, using Galois automorphisms, we present an algorithm to homomorphically evaluate a polynomial of degree d in only 3 log(d) (in some cases only 2 log(d)) many ciphertext-ciphertext multiplications and automorphism evaluations, where d is bounded by the ring degree. In other words, as long as the degree of the polynomial is bounded, we achieve an exponential speedup compared to the state of the art. In particular, the approach also improves on the theoretical lower bound of 2 sqrt(d) many ciphertext-ciphertext multiplications, which would apply if automorphisms were not available.
We investigate how to apply our improved polynomial evaluation to the bootstrapping procedure for BFV, and show that we are able to significantly improve its performance. We demonstrate this by providing an implementation of our improved BFV bootstrapping using the Microsoft SEAL library. More concretely, we obtain a 1.6× speed up compared to the prior implementation given by Chen and Han (Eurocrypt 2018). The techniques are independent of, and can be combined with, the more recent optimisations presented by Geelen et al. (Eurocrypt 2023).
As an additional contribution, we show how the bootstrapping approach used in schemes such as FHEW and TFHE can be applied in the BFV context. In particular, we demonstrate that programmable bootstrapping can be achieved for BFV. Moreover, we show how this bootstrapping approach can be improved in the BFV context to make better use of the Galois structure. However, we estimate that its complexity is around three orders of magnitude slower than the classical approach to BFV bootstrapping.

2023

ASIACRYPT

Improved Fully Adaptive Decentralized MA-ABE for NC1 from MDDH
Abstract

We improve the first and the only existing prime-order fully adaptively secure decentralized Multi-Authority Attribute-Based Encryption (MA-ABE) scheme for NC1 in Datta-Komargodski-Waters [Eurocrypt '23]. Compared with Datta-Komargodski-Waters, our decentralized MA-ABE scheme extra enjoys shorter parameters and meanwhile supports many-use of attribute. Shorter parameters is always the goal for Attribute-Based Encryption (ABE), and many-use of attribute is a native property of decentralized MA-ABE for NC1. Our scheme relies on the Matrix Decision Diffie-Hellman (MDDH) assumption and is in the random oracle model, as Datta-Komargodski-Waters.

2023

ASIACRYPT

Improved Quantum Circuits for AES: Reducing the Depth and the Number of Qubits
Abstract

Quantum computers hold the potential to solve problems that are intractable for classical computers, thereby driving increased interest in the development of new cryptanalytic ciphers. In NIST's post-quantum standardization process, the security categories are defined by the costs of quantum key search against AES. However, the cost estimates provided by Grassl et al. for the search are high. NIST has acknowledged that these initial classifications should be approached cautiously, since the costs of the most advanced attacks can be significantly reduced. Therefore, accurate resource estimations are crucial for evaluating the security of ciphers against quantum adversaries.
This paper presents a set of generic techniques for implementing AES quantum oracles, which are essential for quantum attacks such as Grover's algorithms. Firstly, we introduce the mixing-XOR technique to reuse the ancilla qubits. At ASIACRYPT 2022, Huang et al. proposed an S-box structure with 120 ancilla qubits. We are able to reduce the number of ancilla qubits to 83 without increasing the T-depth. Secondly, we propose the combined pipeline architecture with the share technique to combine the S-box and its reverse, which achieves it with only 98 ancilla qubits, resulting in a significant reduction of 59% compared to the independent structure. Thirdly, we use a general algorithm to determine the depth of quantum circuits, searching for the in-place circuit of AES MixColumns with depth 16. Applying these improvements, we achieve the lower quantum depth of AES circuits, obtaining more precise resource estimates for Grover's algorithm. For AES-128, -192, and -256, we only require the depth of 730, 876, and 1,018, respectively.
Recently, the community has also focused on the trade-off of the time and space cost of quantum circuits for AES. In this regard, we present quantum implementations of AES circuits with a lower DW-cost on the zig-zag architecture. Compared with the circuit proposed by Huang et al., the DW-cost is reduced by 35%.

2023

ASIACRYPT

Injection-Secure Structured and Searchable Symmetric Encryption
Abstract

Recent work on dynamic structured and searchable symmetric encryption has
focused on achieving the notion of forward-privacy. This is mainly motivated by
the claim that forward privacy protects against adaptive file injection attacks
(Zhang, Katz, Papamanthou, Usenix Security, 2016). In this work, we
revisit the notion of forward-privacy in several respects. First, we observe
that forward-privacy does not necessarily guarantee security against adaptive
file injection attacks if a scheme reveals other leakage patterns like the
query equality. We then propose a notion of security called correlation
security which generalizes forward privacy. We then show how correlation
security can be used to formally define security against different kinds of
injection attacks. We then propose the first injection-secure multi-map
encryption encryption scheme and use it as a building block to design the first
injection-secure searchable symmetric encryption (SSE) scheme. Towards
achieving this, we also propose a new fully-dynamic volume-hiding multi-map
encryption scheme which may be of independent interest.

2023

ASIACRYPT

Just How Fair is an Unreactive World?
Abstract

Fitzi, Garay, Maurer, and Ostrovsky (J. Cryptology 2005) showed that in the presence of a dishonest majority, no primitive of cardinality n − 1 is complete for realizing an arbitrary n-party functionality with guaranteed output delivery. In this work, we show that in the presence of n − 1 corrupt parties, no unreactive primitive of cardinality n − 1 is complete for realizing an arbitrary n-party functionality with fairness. We show more generally that for t > n/2, in the presence of t malicious parties, no unreactive primitive of cardinality t is complete for realizing an arbitrary n-party functionality with fairness. We complement this result by noting that (t + 1)-wise fair exchange is complete for realizing an arbitrary n-party functionality with fairness. In order to prove our results, we utilize the primitive of fair coin tossing and the notion of predictability. While this notion has been considered in some form in past works, we come up with a novel and non-trivial framework to employ it, one that readily generalizes from the setting of two parties to multiple parties, and also to the setting of unreactive functionalities.

2023

ASIACRYPT

Lattice-Based Functional Commitments: Fast Verification and Cryptanalysis
Abstract

A functional commitment allows a user to commit to an input x \in {0, 1}^\ell and later open up the commitment to a value y = f(x) with respect to some function f. In this work, we focus on schemes that support fast verification. Specifically, after a preprocessing step that depends only on $f$, the verification time as well as the size of the commitment and opening should be sublinear in the input length \ell, We also consider the dual setting where the user commits to the function f and later, opens up the commitment at an input x.
In this work, we develop two (non-interactive) functional commitments that support fast verification. The first construction supports openings to constant-degree polynomials and has a shorter CRS for a broad range of settings compared to previous constructions. Our second construction is a dual functional commitment for arbitrary bounded-depth Boolean circuits that supports fast verification with security from falsifiable assumptions. Both schemes are lattice-based and avoid non-black-box use of cryptographic primitives or lattice sampling algorithms. Security of both constructions rely on the \ell-succinct short integer solutions (SIS) assumption, a falsifiable q-type generalization of the SIS assumption (Preprint 2023).
In addition, we study the challenges of extending lattice-based functional commitments to extractable functional commitments, a notion that is equivalent to succinct non-interactive arguments (when considering openings to quadratic relations). We describe a general methodology that heuristically breaks the extractability of our construction and provides evidence for the implausibility of the knowledge k-R-ISIS assumption of Albrecht et al. (CRYPTO 2022) that was used in several constructions of lattice-based succinct arguments. If we additionally assume hardness of the standard inhomogeneous SIS assumption, we obtain a direct attack on a variant of the extractable linear functional commitment of Albrecht et al.

2023

ASIACRYPT

LERNA: Secure Single-Server Aggregation via Key-Homomorphic Masking
Abstract

This paper introduces LERNA, a new framework for single-server secure aggregation. Our protocols are tailored to the setting where multiple consecutive aggregation phases are performed with the same set of clients, a fraction of which can drop out in some of the phases. We rely on an initial secret sharing setup among the clients which is generated once-and-for-all, and reused in all following aggregation phases. Compared to prior works [Bonawitz et al. CCS’17, Bell et al. CCS’20], the reusable setup eliminates one round of communication between the server and clients per aggregation—i.e., we need two rounds for semi-honest security (instead of three), and three rounds (instead of four) in the malicious model. Our approach also significantly reduces the server’s computational costs by only requiring the reconstruction of a single secret-shared value (per aggregation). Prior work required reconstructing a secret-shared value for each client involved in the computation.
We provide instantiations of LERNA based on both the Decisional Composite Residuosity (DCR) and (Ring) Learning with Rounding ((R)LWR) assumptions respectively and evaluate a version based on the latter assumption. In addition to savings in round-complexity (which result in reduced latency), our experiments show that the server computational costs are reduced by two orders of magnitude in comparison to the state-of-the-art. In settings with a large number of clients, we also reduce the computational costs up to twenty-fold for most clients, while a small set of “heavy clients” is subject to a workload that is still smaller than that of prior work.

2023

ASIACRYPT

2023

ASIACRYPT

Memory-Efficient Attacks on Small LWE Keys
Abstract

The LWE problem is one of the prime candidates for building the most efficient post-quantum secure public key cryptosystems. Many of those schemes, like Kyber, Dilithium or those belonging to the NTRU-family, such as NTRU-HPS, -HRSS, BLISS or GLP, make use of small max norm keys to enhance efficiency. The best attack on these schemes is a hybrid attack, which combines combinatorial techniques and lattice reduction. While lattice reduction is not known to be able to exploit the small max norm choices, May recently showed (Crypto 2021) that such choices allow for more efficient combinatorial attacks.
However, these combinatorial attacks suffer enormous memory requirements, which render them inefficient in realistic attack scenarios and, hence, make their general consideration when assessing security questionable. Therefore, more memory-efficient substitutes for these algorithms are needed. In this work, we provide new combinatorial algorithms for recovering small max norm LWE secrets using only a polynomial amount of memory. We provide analyses of our algorithms for secret key distributions of current NTRU, Kyber and Dilithium variants, showing that our new approach outperforms previous memory-efficient algorithms. For instance, considering uniformly random ternary secrets of length $n$ we improve the best known time complexity for polynomial memory algorithms from $2^{1.063n}$ down-to $2^{0.926n}$.
We obtain even larger gains for LWE secrets in $\{-m,\ldots,m\}^n$ with $m=2,3$ as found in Kyber and Dilithium. For example, for uniformly random keys in $\{-2,\ldots,2\}^n$ as is the case for Dilithium we improve the previously best time from $2^{1.742n}$ down-to $2^{1.282n}$.
Our fastest algorithm incorporates various different algorithmic techniques, but at its heart lies a nested collision search procedure inspired by the Nested-Rho technique from Dinur, Dunkelman, Keller and Shamir (Crypto 2016). Additionally, we heavily exploit the representation technique originally introduced in the subset sum context to make our nested approach efficient.

2023

ASIACRYPT

More Insight on Deep Learning-aided Cryptanalysis
Abstract

In CRYPTO 2019, Gohr showed that well-trained neural networks could perform cryptanalytic distinguishing tasks superior to differential distribution table (DDT)-based distinguishers. This suggests that the differential-neural distinguisher (ND) may use additional information besides pure ciphertext differences. However, the explicit knowledge beyond differential distribution is still unclear. In this work, we provide explicit rules that can be used alongside DDTs to enhance the effectiveness of distinguishers compared to pure DDT-based distinguishers. These rules are based on strong correlations between bit values in right pairs of XOR-differential propagation through addition modulo $2^n$. Interestingly, they can be closely linked to the earlier study of the multi-bit constraints and the recent study of the fixed-key differential probability. In contrast, combining these rules does not improve the NDs' performance. This suggests that these rules or their equivalent form have already been exploited by NDs, highlighting the power of neural networks in cryptanalysis.
In addition, we find that to enhance the differential-neural distinguisher's accuracy and the number of rounds, regulating the differential propagation is imperative. Introducing differences into the keys is typically believed to help eliminate differences in encryption states, resulting in stronger differential propagations. However, differential-neural attacks differ from traditional ones as they don't specify output differences or follow a single differential trail. This questions the usefulness of introducing differences in a key in differential-neural attacks and the resistance of Speck against such attacks in the related-key setting. This work shows that the power of differential-neural cryptanalysis in the related-key setting can exceed that in the single-key setting by successfully conducting a 14-round key recovery attack on Speck32/64.

2023

ASIACRYPT

MPC With Delayed Parties Over Star-Like Networks
Abstract

This paper examines multi-party computation protocols in the presence of two major constraints present in deployed systems. Firstly, we consider the situation where the parties are connected not by direct point-to-point connections, but by a star-like topology with a few central post-office style relays. Secondly, we consider MPC protocols with a strong honest majority ($t \gg n/2$) in which we have stragglers (some parties are progressing slower than others). We model stragglers by allowing the adversary to delay messages to and from some parties for a given length of time.
We first show that having only a single honest relay is enough to ensure consensus of the messages sent within a protocol; secondly, we show that special care must be taken to describe multiplication protocols in the case of relays and stragglers; thirdly, we present an efficient honest-majority MPC protocol which can be run ontop of the relays and which provides active-security with abort in the case of a strong honest majority, even when run with stragglers. We back up our protocol presentation with both experimental evaluations and simulations of the effect of the relays and delays on our protocol.

2023

ASIACRYPT

NEV: Faster and Smaller NTRU Encryption using Vector Decoding
Abstract

In this paper, we present $\nev$ -- a faster and smaller NTRU Encryption using Vector decoding,
which is provably IND-CPA secure in the standard model
under the decisional NTRU and RLWE assumptions over the cyclotomic ring $R_q = \ZZ_q[X]/(X^n+1)$.
Our main technique is a novel and non-trivial way to integrate a previously known plaintext
encoding and decoding mechanism into the provably IND-CPA secure NTRU variant by Stehl\'e and Steinfeld (Eurocrypt 2011). Unlike the original NTRU encryption and its variants which encode the plaintext into the least significant bits of the coefficients of a message polynomial, we encode each plaintext bit into the most significant bits of multiple coefficients of the message polynomial,
so that we can use a vector of noised coefficients to decode each plaintext bit in decryption,
and significantly reduce the size of $q$ with a reasonably negligible decryption failure.
Concretely, we can use $q = 769$ to obtain public keys and ciphertexts of 615 bytes
with decryption failure $\leq 2^{-138}$ at NIST level 1 security, and 1229 bytes with decryption failure $\leq 2^{-152}$ at NIST level 5 security. By applying the Fujisaki-Okamoto transformation in a standard way, we obtain an IND-CCA secure KEM from our basic PKE scheme. Compared to NTRU and Kyber in the NIST Round 3 finalists at the same security levels, our KEM is 33-48\% more compact and 5.03-29.94X faster than NTRU in the round-trip time of ephemeral key exchange, and is 21\% more compact and 1.42-1.74X faster than Kyber.
\qquad We also give an optimized encryption scheme $\nev'$ with better noise tolerance (and slightly better efficiency) based on a variant of the RLWE problem, called Subset-Sum Parity RLWE problem, which we show is polynomially equivalent to the standard decisional RLWE problem (with different parameters), and maybe of independent interest.

2023

ASIACRYPT

New SIDH Countermeasures for a More Efficient Key Exchange
Abstract

The Supersingular Isogeny Diffie-Hellman (SIDH) protocol has been the main and most efficient isogeny-based encryption protocol, until a series of breakthroughs led to a polynomial-time key-recovery attack. While some countermeasures have been proposed, the resulting schemes are significantly slower and larger than the original SIDH.
In this work, we propose a new countermeasure technique that leads to significantly more efficient and compact protocols. To do so, we introduce the concept of artificially oriented curves, i.e. curves with an associated pair of subgroups. We show that this information is sufficient to build parallel isogenies and thus obtain an SIDH-like key exchange, while also revealing significantly less information compared to previous constructions.
After introducing artificially oriented curves, we formalize several related computational problems and thoroughly assess their presumed hardness. We then translate the SIDH key exchange to the artificially oriented setting, obtaining the key-exchange protocols binSIDH, or binary SIDH, and terSIDH, or ternary SIDH, which respectively rely on fixed-degree and variable-degree isogenies.
Lastly, we also provide a proof-of-concept implementation of the proposed protocols. Despite being a high-level SageMath implementation, it already outperforms existing implementations of other isogeny-based encryption schemes, which suggests that terSIDH might be the most efficient isogeny-based encryption protocol.

2023

ASIACRYPT

Non-Interactive Commitment from Non-Transitive Group Actions
Abstract

Group actions are becoming a viable option for post-quantum cryptography assumptions. Indeed, in recent years some works have shown how to construct primitives from assumptions based on isogenies of elliptic curves, such as CSIDH, on tensors or on code equivalence problems. This paper presents a bit commitment scheme, built on non-transitive group actions, which is shown to be secure in the standard model, under the decisional Group Action Inversion Problem. In particular, the commitment is computationally hiding and perfectly binding, and is obtained from a novel and general framework that exploits the properties of some orbit-invariant functions, together with group actions. Previous constructions depend on an interaction between the sender and the receiver in the commitment phase, which results in an interactive bit commitment. We instead propose the first non-interactive bit commitment based on group actions. Then we show that, when the sender is honest, the constructed commitment enjoys an additional feature, i.e., it is possible to tell whether two commitments were obtained from the same input, without revealing the input. We define the security properties that such a construction must satisfy, and we call this primitive linkable commitment. Finally, as an example, an instantiation of the scheme using tensors with coefficients in a finite field is provided. In this case, the invariant function is the computation of the rank of a tensor, and the cryptographic assumption is related to the Tensor Isomorphism problem.

2023

ASIACRYPT

Non-Interactive Zero-Knowledge Functional Proofs
Abstract

In this paper, we consider to generalize NIZK by empowering a prover to share a witness in a fine-grained manner with verifiers. Roughly, the prover is able to authorize a verifier to obtain extra information of witness, i.e., besides verifying the truth of the statement, the verifier can additionally obtain certain function of the witness from the accepting proof using a secret key provided by the prover.
To fulfill these requirements, we introduce a new primitive called \emph{non-interactive zero-knowledge functional proofs (fNIZKs)}, and formalize its security notions. We provide a generic construction of fNIZK for any $\NP$ relation $\R$, which enables the prover to share any function of the witness with a verifier. For a widely-used relation about set membership proof (implying range proof), we construct a concrete and efficient fNIZK, through new building blocks (set membership encryption and dual inner-product encryption), which might be of independent interest.

2023

ASIACRYPT

Oblivious Transfer from Zero-Knowledge Proofs, Or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States
Abstract

We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions…) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt.
In particular, by instantiating our construction using Non-Interactive ZK (NIZK), we provide the first round-optimal (2-message) quantum OT protocol secure in the random oracle model, and round-optimal extensions to string and k-out-of-n OT.
At the heart of our construction lies a new method that allows us to prove properties on a received quantum state without revealing additional information on it, even in a non-interactive way and/or with statistical guarantees when using an appropriate classical ZK protocol. We can notably prove that a state has been partially measured (with arbitrary constraints on the set of measured qubits), without revealing any additional information on this set. This notion can be seen as an analog of ZK to quantum states, and we expect it to be of independent interest as it extends complexity theory to quantum languages, as illustrated by the two new complexity classes we introduce, ZKstatesQIP and ZKstatesQMA.

2023

ASIACRYPT

On Black-Box Knowledge-Sound Commit-And-Prove SNARKs
Abstract

Gentry and Wichs proved that adaptively sound SNARGs for hard languages need non-falsifiable assumptions. Lipmaa and Pavlyk claimed Gentry-Wichs is tight by constructing a non-adaptively sound zk-SNARG FANA for NP from falsifiable assumptions. We show that FANA is flawed. We define and construct a fully algebraic $F$-position-binding vector commitment scheme VCF. We construct a concretely efficient commit-and-prove zk-SNARK Punic, a version of FANA with an additional VCF commitment to the witness. Punic satisfies semi-adaptive black-box $G$-knowledge-soundness, a new natural knowledge-soundness notion for commit-and-prove SNARKs. We use a new proof technique to achieve global consistency using a functional somewhere-extractable commitment scheme to extract vector commitment's local proofs.

2023

ASIACRYPT

On Gaussian sampling, smoothing parameter and application to signatures
Abstract

We present a general framework for polynomial-time lattice Gaussian
sampling. It revolves around a systematic study of the discrete
Gaussian measure and its samplers under \emph{extensions} of lattices;
we first show that given lattices $\Lat'\subset \Lat$ we can sample
efficiently in $\Lat$ if we know how to do so in $\Lat'$ and the
quotient $\Lat/\Lat'$, \emph{regardless} of the primitivity of
$\Lat'$. As a direct application, we tackle the problem of domain
extension and restriction for sampling and propose a sampler tailored
for lattice \emph{filtrations}, which can be seen as a broad
generalization of the celebrated Klein's sampler. Then, we demonstrate
how to sample using a change of bases, or even switching the ambient
space, even when the target lattice is not represented as full-rank in
the ambient space. We show how to correct the induced distortion with
the ``convolution-like'' technique of Peikert (Crypto 2010)
(which we encompass as a byproduct). Since our framework aims at
modularity and leverage the combinations of smaller samplers to build
new ones, we also propose ad-hoc samplers for the so-called \emph{root
lattices} $\An_n, \Dn_n, \mathsf{E}_n$ as base cases, extending the
state-of-the-art for root lattice sampling, which was limited to
$\ZZ^n$. We also show how our framework blends with the so-called
$k$ing construction and provides a sampler for the remarkable Leech and
Barnes-Wall lattices.
As a by-product, we obtain novel, quasi-linear samplers
for prime and smooth conductor (as $2^\ell 3^k$) cyclotomic rings,
achieving essentially optimal Gaussian width. In a practice-oriented
application, we showcase the impact of our work on hash-and-sign
signatures over \textsc{ntru} lattices. In the best case, we can gain
around 200 bytes (which corresponds to an improvement greater than
20\%) on the signature size. We also improve the new gadget-based
constructions (Yu, Jia, Wang, Crypto 2023) and gain up to 110 bytes for the
resulting signatures.
Lastly, we sprinkle our exposition with several new estimates for the
smoothing parameter of lattices, stemming from our algorithmic
constructions and by novel methods based on series reversion.

2023

ASIACRYPT

On Quantum Secure Compressing Pseudorandom Functions
Abstract

In this paper we characterize all $2n$-bit-to-$n$-bit Pseudorandom Functions (PRFs) constructed with the minimum number of calls to $n$-bit-to-$n$-bit PRFs and arbitrary number of linear functions. First, we show that all two-round constructions are either classically insecure, or vulnerable to quantum period-finding attacks. Second, we categorize three-round constructions depending on their vulnerability to these types of attacks. This allows us to identify classes of constructions that could be proven secure.
We then proceed to show the security of the following three candidates against any quantum distinguisher that makes at most $ 2^{n/4} $ (possibly superposition) queries:
\begin{align*}
TNT(x_1,x_2) &:= f_3(x_2 \oplus f_2(x_2 \oplus f_1(x_1)));\\
LRQ(x_1,x_2) &:= f_2(x_2) \oplus f_3(x_2 \oplus f_1(x_1));\\
LRWQ(x_1,x_2) &:= f_3( f_1(x_1) \oplus f_2(x_2)).
\end{align*}
Note that the first construction is a classically secure tweakable block-cipher due to Bao et al., and the third construction was shown to be a quantum-secure tweakable block-cipher by Hosoyamada and Iwata with similar query limits. Of note is our proof framework, an adaptation of Chung et al.'s rigorous formulation of Zhandry's compressed oracle technique in the indistinguishability setup, which could be of independent interest. This framework gives very compact and mostly classical-looking proofs as compared to Hosoyamada-Iwata interpretation of Zhandry's compressed oracle.

2023

ASIACRYPT

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions
Abstract

Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing provably-secure public-key quantum money schemes based on standard cryptographic assumptions has remained an elusive goal. Even proposing plausibly-secure candidate schemes has been a challenge.
These difficulties call for a deeper and systematic study of the structure of public-key quantum money schemes and the assumptions they can be based on. Motivated by this, we present the first black-box separation of quantum money and cryptographic primitives. Specifically, we show that collision-resistant hash functions cannot be used as a black-box to construct public-key quantum money schemes where the banknote verification makes classical queries to the hash function. Our result involves a novel combination of state synthesis techniques from quantum complexity theory and simulation techniques, including Zhandry's compressed oracle technique.

2023

ASIACRYPT

On the (Im)possibility of Time-Lock Puzzles in the Quantum Random Oracle Model
Abstract

Time-lock puzzles wrap a solution s inside a puzzle P in such a way that “solving” P to find s requires significantly more time than generating the pair (s, P), even if the adversary has access to parallel computing; hence it can be thought of as sending a message s to the future. It is known [Mahmoody, Moran, Vadhan, Crypto’11] that when the source of hardness is only a random oracle, then any puzzle generator with n queries can be (efficiently) broken by an adversary in O(n) rounds of queries to the oracle.
In this work, we revisit time-lock puzzles in a quantum world by allowing the parties to use quantum computing and, in particular, access the random oracle in quantum superposition. An interesting setting is when the puzzle generator is efficient and classical, while the solver (who might be an entity developed in the future) is quantum-powered and is supposed to need a long sequential time to succeed. We prove that in this setting there is no construction of time-lock puzzles solely from quantum (accessible) random oracles. In particular, for any n-query classical puzzle generator, our attack only asks O(n) (also classical) queries to the random oracle, even though it does indeed run in quantum polynomial time if the honest puzzle solver needs quantum computing.
Assuming perfect completeness, we also show how to make the above attack run in exactly n rounds while asking a total of m · n queries where m is the query complexity of the puzzle solver. This is indeed tight in the round complexity, as we also prove that a classical puzzle scheme of Mahmoody et al. is also secure against quantum solvers who ask n−1 rounds of queries. In fact, even for the fully classical case, our attack quantitatively improves the total queries of the attack of Mahmoody et al. for the case of perfect completeness from O(mn log n) to mn. Finally, assuming perfect completeness, we present an attack in the “dual” setting in which the puzzle generator is quantum while the solver is classical.
We then ask whether one can extend our classical-query attack to the fully quantum setting, in which both the puzzle generator and the solver could be quantum. We show a barrier for proving such results unconditionally. In particular, we show that if the folklore simulation conjecture, first formally stated by Aaronson and Ambainis [arXiv’2009] is false, then there is indeed a time-lock puzzle in the quantum random oracle model that cannot be broken by classical adversaries. This result improves the previous barrier of Austrin et. al [Crypto’22] about key agreements (that can have interactions in both directions) to time-lock puzzles (that only include unidirectional communication).

2023

ASIACRYPT

Polynomial IOPs for Memory Consistency Checks in Zero-Knowledge Virtual Machines
Abstract

Zero-Knowledge Virtual Machines (ZKVMs) have gained traction in recent years due to their potential applications in a variety of areas, particularly blockchain ecosystems.
Despite tremendous progress on ZKVMs in the industry, no formal definitions or security proofs have been established in the literature.
Due to this lack of formalization, existing protocols exhibit significant discrepancies in terms of problem definitions and performance metrics, making it difficult to analyze and compare these advancements, or to trust the security of the increasingly complex ZKVM implementations.
In this work, we focus on random-access memory, an influential and expensive component of ZKVMs.
Specifically, we investigate the state-of-the-art protocols for validating the correct functioning of memory, which we refer to as the \emph{memory consistency checks}.
Isolating these checks from the rest of the system allows us to formalize their definition and security notion.
Furthermore, we summarize the state-of-the-art constructions using the Polynomial IOP model and formally prove their security.
Observing that the bottleneck of existing designs lies in sorting the entire memory trace, we break away from this paradigm and propose a novel memory consistency check, dubbed $\mathsf{Permem}$.
$\mathsf{Permem}$ bypasses this bottleneck by introducing a technique called the address cycle method, which requires fewer building blocks and---after instantiating the building blocks with state-of-the-art constructions---fewer online polynomial oracles and evaluation queries.
In addition, we propose $\mathsf{gcq}$, a new construction for the lookup argument---a key building block of the memory consistency check, which costs fewer online polynomial oracles than the state-of-the-art construction $\mathsf{cq}$.

2023

ASIACRYPT

Populating the Zoo of Rugged Pseudorandom Permutations
Abstract

A Rugged Pseudorandom Permutation (RPRP) is a variable-input-length tweakable cipher satisfying a security notion that is intermediate between tweakable PRP and tweakable SPRP. It was introduced at CRYPTO 2022 by Degabriele and Karadžić, who additionally showed how to generically convert such a primitive into nonce-based and nonce-hiding AEAD schemes satisfying either misuse-resistance or release-of-unverified-plaintext security as well as Nonce-Set AEAD which has applications in protocols like QUIC and DTLS. Their work shows that RPRPs are powerful and versatile cryptographic primitives. However, the RPRP security notion itself can seem rather contrived, and the motivation behind it is not immediately clear. Moreover, they only provided a single RPRP construction, called UIV, which puts into question the generality of their modular approach and whether other instantiations are even possible. In this work, we address this question positively by presenting new RPRP constructions, thereby validating their modular approach and providing further justification in support of the RPRP security definition. Furthermore, we present a more refined view of their results by showing that strictly weaker RPRP variants, which we introduce, suffice for many of their transformations. From a theoretical perspective, our results show that the well-known three-round Feistel structure achieves stronger security as a permutation than a mere pseudorandom permutation—as was established in the seminal result by Luby and Rackoff. We conclude on a more practical note by showing how to extend the left domain of one RPRP construction for applications that require larger values in order to meet the desired level of security.

2023

ASIACRYPT

Post-Quantum Security of Key Encapsulation Mechanism against CCA Attacks with a Single Decapsulation Query
Abstract

Recently, in post-quantum cryptography migration, it has been shown that an IND-1-CCA-secure key encapsulation mechanism (KEM) is required for replacing an ephemeral Diffie-Hellman (DH) in widely-used protocols, e.g., TLS, Signal, and Noise.
IND-1-CCA security is a notion similar to the traditional IND-CCA security except that the adversary is restricted to one single decapsulation query.
At EUROCRYPT 2022, based on CPA-secure public-key encryption (PKE), Huguenin-Dumittan and Vaudenay presented two IND-1-CCA KEM constructions called $T_{CH}$ and $T_H$, which are much more efficient than the widely-used IND-CCA-secure Fujisaki-Okamoto (FO) KEMs.
The security of $T_{CH}$ was proved in both random oracle model (ROM) and quantum random oracle model (QROM).
However, the QROM proof of $T_{CH}$
relies on an additional ciphertext expansion.
%requires that the ciphertext size of the resulting KEM is twice as large as the one of the underlying PKE.
While, the security of $T_H$ was only proved in the ROM, and the QROM proof is left open.
In this paper, we prove the security of $T_H$ and $T_{RH}$ (an implicit variant of $T_H$) in both ROM and QROM with much tighter reductions than Huguenin-Dumittan and Vaudenay's work.
In particular, our QROM proof will not lead to ciphertext expansion.
Moreover, for $T_{RH}$, $T_H$ and $T_{CH}$, we also show that a $O(1/q)$ ($O(1/q^2)$, resp.) reduction loss is unavoidable in the ROM (QROM, resp.), and thus claim that our ROM proof is optimal in tightness.
Finally, we make a comprehensive comparison among the relative strengths of IND-1-CCA and IND-CCA in the ROM and QROM.

2023

ASIACRYPT

Practical Round-Optimal Blind Signatures in the ROM from Standard Assumptions
Abstract

Blind signatures serve as a foundational tool for privacy-preserving applications and have recently seen renewed interest due to new applications in blockchains and privacy-authentication tokens. With this, constructing practical round-optimal (i.e., signing consists of the minimum two rounds) blind signatures in the random oracle model (ROM) has been an active area of research, where several impossibility results indicate that either the ROM or a trusted setup is inherent.
In this work, we present two round-optimal blind signatures under standard assumptions in the ROM with different approaches: one achieves the smallest sum of the signature and communication sizes, while the other achieves the smallest signature size. Both of our instantiations are based on standard assumptions over asymmetric pairing groups, i.e., CDH, DDH, and/or SXDH. Our first construction is a highly optimized variant of the generic blind signature construction by Fischlin (CRYPTO’06) and has signature and communication sizes 447 B and 303 B, respectively. We progressively weaken the building blocks required by Fischlin
and we result in the first blind signature where the sum of the signature and communication sizes fit below 1 KB based on standard assumptions. Our second construction is a semi-generic construction from a specific class of randomizable signature schemes that admits an all-but-one reduction. The signature size is only 96 B while the communication size is 2.2 KB. This matches the previously known smallest signature size while improving the communication size by several
orders of magnitude. Finally, both of our constructions rely on a (non-black box) fine-grained analysis of the forking lemma that may be of independent interest.

2023

ASIACRYPT

Practically Efficient Private Set Intersection From Trusted Hardware with Side-Channels
Abstract

Private set intersection (PSI) is one of the most important privacy-enhancing technologies with applications such as malware and spam detection, recognition of child pornography, contact discovery, or, more recently, contact tracing. In this paper, we investigate how PSI can be constructed and implemented simply and practically efficient. To this end, a natural possibility is the use of trusted execution environments (TEEs), which are commonly used in place of a trusted third party due to their presumed security guarantees. However, this trust is often not warranted: Today’s TEEs like Intel SGX suffer from a number of side-channels that allow the host to learn secrets of a TEE, unless countermeasures are taken. Furthermore, due to the high complexity and closed-source nature, it cannot be ruled out that a TEE is passively corrupted, i.e. leaks secrets to the manufacturer or a government agency such as the NSA. When constructing a protocol using TEEs, such (potential) vulnerabilities need to be accounted for. Otherwise, all security may be lost. We propose a protocol for two-party PSI whose security holds in a setting where TEEs cannot be fully trusted, e.g. due to the existence of side-channels. In particular, we deal with the possibilities that i) the TEE
is completely transparent for the host, except for very simple secure cryptographic operations or ii) that it leaks all secrets to a third party, e.g. the manufacturer. Even in this challenging setting, our protocol is not only very fast, but also conceptually simple, which is an important feature as more complex protocols tend to be implemented with subtle security faults.
To formally capture this setting, we define variants of the ideal functionality for TEEs due to Pass et al. (EUROCRYPT 2017). Using these functionalities, we prove our protocol’s security, which holds under universal composition. To illustrate the usefulness of our model, we sketch other possible applications like (randomized) oblivious transfer or private computation of the Hamming distance.
Our PSI implementation, which uses Intel SGX as TEE, computes the intersection between two sets with 2^24 128-bit elements in 7.3 seconds. This makes our protocol the fastest PSI protocol to date with respect to single-threaded performance.

2023

ASIACRYPT

Predicate Aggregate Signatures and Applications
Abstract

Motivated by applications in anonymous reputation system and blockchain governance, we initiate the study of predicate aggregate signatures (PAS), which is a new primitive that enables users to sign multiple messages, and these individual signatures can be aggregated by a combiner, preserving the anonymity of the signers. The resulting PAS discloses only a brief description of signers for each message and provides assurance that both the signers and their description satisfy the specified public predicate.
We formally define PAS and give a construction framework to yield a logarithmic size signature, and further reduce the verification time also to logarithmic. We also give several instantiations for several concrete predicates that may be of independent interests.
To showcase its power, we also demonstrate its applications to multiple settings including multi-signatures, aggregate signatures, threshold signatures, (threshold) ring signatures, attribute-based signatures, etc, and advance the state of the art in all of them.

2023

ASIACRYPT

Protostar: Generic Efficient Accumulation/Folding for Special-sound Protocols
Abstract

Accumulation is a simple yet powerful primitive that enables incrementally verifiable computation (IVC) without the need for recursive SNARKs. We provide a generic, efficient accumulation (or folding) scheme for any (2k − 1)-move special-sound protocol with a verifier that checks l degree-d equations. The accumulation verifier only performs k+2 elliptic curve multiplications and k+d+O(1) field/hash operations. Using the compiler from BCLMS21 (Crypto 21), this enables building efficient IVC schemes where the recursive circuit only depends on the number of rounds and the verifier degree of the underlying special-sound protocol but not the proof size or the verifier time. We use our generic accumulation compiler to build Protostar. Protostar is a non-uniform IVC scheme for Plonk that supports high-degree gates and (vector) lookups. The recursive circuit is dominated by 3 group scalar multiplications and a hash of d∗ field elements, where d∗ is the degree of the highest gate. The scheme does not require a trusted setup or pairings, and the prover does not need to compute any FFTs. The prover in each accumulation/IVC step is also only logarithmic in the number of supported circuits and independent of the table size in the lookup.

2023

ASIACRYPT

Pseudorandomness of Decoding, Revisited: Adapting OHCP to Code-Based Cryptography
Abstract

Recent code-based cryptosystems rely, among other things, on the hardness of the decisional decoding problem. If the search version is well understood, both from practical and theoretical standpoints, the decision version has been less studied in the literature, and little is known about its relationships with the search version, especially for structured variants. On the other hand, in the world of Euclidean lattices, the situation is rather different, and many reductions exist, both for unstructured and structured versions of the underlying problems. For the latter versions, a powerful tool called the OHCP framework (for Oracle with Hidden Center Problem), which appears to be very general, has been introduced by Peikert et al. (STOC 2017) and has proved to be very useful as a black box inside reductions.
In this work, we revisit this technique and extract the very essence of this framework, namely the Oracle Comparison Problem (OCP), to show how to recover the support of the error, solving an Oracle with Hidden Support Problem (OHSP), more suitable for code-based cryptography. This yields a new worst-case to average-case search-to-decision reduction for the Decoding Problem, as well as a new average-case to average-case reduction. We then turn to the structured versions and explain why this is not as straightforward as for Euclidean lattices. If we fail to give a search-to-decision reduction for structured codes, we believe that our work opens the way towards new reductions for structured codes, given that the OHCP framework proved to be so powerful in lattice-based cryptography. Furthermore, we also believe that this technique could be extended to codes endowed with other metrics, such as the rank metric, for which no reduction is known.

2023

ASIACRYPT

Quantitative Fault Injection Analysis
Abstract

Active fault injection is a credible threat to real-world digital systems computing on sensitive data. Arguing about security in the presence of faults is non-trivial, and state-of-the-art criteria are overly conservative and lack the ability of fine-grained comparison. However, comparing two alternative implementations for their security is required to find a satisfying compromise between security and performance. In addition, the comparison of alternative fault scenarios can help optimize the implementation of effective countermeasures.
In this work, we use quantitative information flow analysis to establish a vulnerability metric for hardware circuits under fault injection that measures the severity of an attack in terms of information leakage. Potential use cases range from comparing implementations with respect to their vulnerability to specific fault scenarios to optimizing countermeasures. We automate the computation of our metric by integrating it into a state-of-the-art evaluation tool for physical attacks and provide new insights into the security under an active fault attacker.

2023

ASIACRYPT

Quantum Attacks on Hash Constructions with Low Quantum Random Access Memory
Abstract

At ASIACRYPT 2022, Benedikt, Fischlin, and Huppert proposed the quantum herding attacks on iterative hash functions for the first time. Their attack needs exponential quantum random access memory (qRAM), more precisely {$2^{0.43n}$} quantum accessible classical memory (QRACM). As the existence of large qRAM is questionable, Benedikt et al. leave an open question on building low-qRAM quantum herding attacks.
In this paper, we answer this open question by building a quantum herding attack, where the time complexity is slightly increased from Benedikt et al.'s $2^{0.43n}$ to ours $2^{0.46n}$, but {it does not need qRAM anymore (abbreviated as no-qRAM)}. Besides, we also introduce various low-qRAM {or no-qRAM} quantum attacks on hash concatenation combiner, hash XOR combiner, Hash-Twice, and Zipper hash functions.

2023

ASIACRYPT

Quantum Speed-Up for Multidimensional (Zero Correlation) Linear Distinguishers
Abstract

This paper shows how to achieve a quantum speed-up for multidimensional (zero correlation) linear distinguishers.
A previous work by Kaplan et al. has already shown a quantum quadratic speed-up for one-dimensional linear distinguishers.
However, classical linear cryptanalysis often exploits multidimensional approximations to achieve more efficient attacks, and in fact it is highly non-trivial whether Kaplan et al.'s technique can be extended into the multidimensional case.
To remedy this, we investigate a new quantum technique to speed-up multidimensional linear distinguishers.
Firstly, we observe that there is a close relationship between the subroutine of Simon's algorithm and linear correlations via Fourier transform.
Specifically, a slightly modified version of Simon's subroutine, which we call Correlation Extraction Algorithm (CEA), can be used to speed-up multidimensional linear distinguishers.
CEA also leads to a speed-up for multidimensional zero correlation distinguishers, as well as some integral distinguishers through the correspondence of zero correlation and integral properties shown by Bogdanov et al.~and Sun et al.
Furthermore, we observe possibility of a more than quadratic speed-ups for some special types of integral distinguishers when multiple integral properties exist.
Especially, we show a single-query distinguisher on a 4-bit cell SPN cipher with the same integral property as 2.5-round AES.
Our attacks are the first to observe such a speed-up for classical cryptanalytic techniques without relying on hidden periods or shifts.
By replacing the Hadamard transform in CEA with the general quantum Fourier transform, our technique also speeds-up generalized linear distinguishers on an arbitrary finite abelian group.

2023

ASIACRYPT

Ramp hyper-invertible matrices and their applications to MPC protocols
Abstract

Beerliov{\'{a}}{-}Trub{\'{\i}}niov{\'{a}} and Hirt introduced hyper-invertible matrix technique to construct the first perfectly secure MPC protocol in the presence of maximal malicious corruptions $\lfloor \frac{n-1}{3} \rfloor$ with linear communication complexity per multiplication gate\cite{BH08}. This matrix allows MPC protocol to generate correct shares of uniformly random secrets in the presence of malicious adversary. Moreover, the amortized communication complexity of generating each sharing is linear. Due to this prominent feature, the hyper-invertible matrix plays an important role in the construction of MPC protocol and zero-knowledge proof protocol where the randomness needs to be jointly generated. However, the downside of this matrix is that the size of its base field is linear in the size of its matrix. This means if we construct an $n$-party MPC protocol over $\F_q$ via hyper-invertible matrix, $q$ is at least $2n$.
In this paper, we propose the ramp hyper-invertible matrix which can be seen as the generalization of hyper-invertible matrix. Our ramp hyper-invertible matrix can be defined over constant-size field regardless of the size of this matrix. Similar to the arithmetic secret sharing scheme, to apply our ramp hyper-invertible matrix to perfectly secure MPC protocol, the maximum number of corruptions has to be compromised to $\frac{(1-\epsilon)n}{3}$. As a consequence, we present the first perfectly secure MPC protocol in the presence of $\frac{(1-\epsilon)n}{3}$ malicious corruptions with constant communication complexity. Besides presenting the variant of hyper-invertible matrix, we overcome several obstacles in the construction of this MPC protocol. Our arithmetic secret sharing scheme over constant-size field is compatible with the player elimination technique, i.e., it supports the dynamic changes of party number and corrupted party number. Moreover, we rewrite the public reconstruction protocol to support the sharings over constant-size field. Putting these together leads to the constant-size field variant of celebrated MPC protocol in \cite{BH08}.
We note that although it was widely acknowledged that there exists an MPC protocol with constant communication complexity by replacing Shamir secret sharing scheme with arithmetic secret sharing scheme, there is no reference seriously describing such protocol in detail. Our work fills the missing detail by providing MPC primitive for any applications relying on MPC protocol of constant communication complexity. As an application of our perfectly secure MPC protocol which implies perfect robustness in the MPC-in-the-Head framework, we present the constant-rate zero-knowledge proof with $3$ communication rounds. The previous work achieves constant-rate with $5$ communication rounds \cite{IKOS07} due to the statistical robustness of their MPC protocol. Another application of our ramp hyper-invertible matrix is the information-theoretic multi-verifier zero-knowledge for circuit satisfiability\cite{YW22}. We manage to remove the dependence of the size of circuit and security parameter from the share size.

2023

ASIACRYPT

Registered (Inner-Product) Functional Encryption
Abstract

Registered encryption (Garg et al., TCC'18) is an emerging paradigm that tackles the key-escrow problem associated with identity-based encryption by replacing the private-key generator with a much weaker entity known as the key curator. The key curator holds no secret information, and is responsible to:
(i) update the master public key whenever a new user registers its own public key to the system;
(ii) provide helper decryption keys to the users already registered in the system, in order to still enable them to decrypt after new users join the system.
For practical purposes, tasks (i) and (ii) need to be efficient, in the sense that the size of the public parameters, of the master public key, and of the helper decryption keys, as well as the running times for key generation and user registration, and the number of updates, must be small.
In this paper, we generalize the notion of registered encryption to the setting of functional encryption (FE). As our main contribution, we show an efficient construction of registered FE for the special case of (attribute hiding) inner-product predicates, built over asymmetric bilinear groups of prime order. Our scheme supports a large attribute universe and is proven secure in the bilinear generic group model. We also implement our scheme and experimentally demonstrate the efficiency requirements of the registered settings. Our second contribution is a feasibility result where we build registered FE for P/poly based on indistinguishability obfuscation and somewhere statistically binding hash functions.

2023

ASIACRYPT

Registered ABE via Predicate Encodings
Abstract

This paper presents the first generic black-box construction of registered attribute-based encryption (Reg-ABE) via predicate encoding [TCC'14]. The generic scheme is based on $k$-Lin assumption in the prime-order bilinear group and implies the following concrete schemes that improve existing results:
- the first Reg-ABE scheme for span program in the prime-order group; prior work uses composite-order group;
- the first Reg-ABE scheme for zero inner-product predicate from $k$-Lin assumption; prior work relies on generic group model (GGM);
- the first Reg-ABE scheme for arithmetic branching program (ABP) which has not been achieved previously.
Technically, we follow the blueprint of Hohenberger et al. [EUROCRYPT'23] but start from the prime-order dual-system ABE by Chen et al. [EUROCRYPT'15], which transforms a predicate encoding into an ABE. The proof follows the dual-system method in the context of Reg-ABE: we conceptually consider helper keys as secret keys; furthermore, malicious public keys are handled via pairing-based quasi-adaptive non-interactive zero-knowledge argument by Kiltz and Wee [EUROCRYPT'15].

2023

ASIACRYPT

Revisiting Higher-Order Differential-Linear Attacks from an Algebraic Perspective
Abstract

The Higher-order Differential-Linear (HDL) attack was introduced by Biham \textit{et al.} at FSE 2005, where a linear approximation was appended to a Higher-order Differential (HD) transition.
It is a natural generalization of the Differential-Linear (DL) attack.
Due to some practical restrictions, however, HDL cryptanalysis has unfortunately attracted much less attention compared to its DL counterpart since its proposal.
In this paper, we revisit HD/HDL cryptanalysis from an algebraic perspective and provide two novel tools for detecting possible HD/HDL distinguishers, including:
(a) Higher-order Algebraic Transitional Form (HATF) for probabilistic HD/HDL attacks;
(b) Differential Supporting Function (\DSF) for deterministic HD attacks.
In general, the HATF can estimate the biases of $\ell^{th}$-order HDL approximations with complexity $\mathcal{O}(2^{\ell+d2^\ell})$ where $d$ is the algebraic degree of the function studied.
If the function is quadratic, the complexity can be further reduced to $\mathcal{O}(2^{3.8\ell})$.
HATF is therefore very useful in HDL cryptanalysis for ciphers with quadratic round functions, such as \ascon and \xoodyak.
\DSF provides a convenient way to find good linearizations on the input of a permutation, which facilitates the search for HD distinguishers.
Unsurprisingly, HD/HDL attacks have the potential to be more effective than their simpler differential/DL counterparts.
Using HATF, we found many HDL approximations for round-reduced \ascon and \xoodyak initializations, with significantly larger biases than DL ones.
For instance, there are deterministic 2$^{nd}$-order/4$^{th}$-order HDL approximations for \ascon/\xoodyak initializations, respectively (which is believed to be impossible in the simple DL case).
We derived highly biased HDL approximations for 5-round \ascon up to 8$^{th}$ order, which improves the complexity of the distinguishing attack on 5-round \ascon from $2^{16}$ to $2^{12}$ calls.
We also proposed HDL approximations for 6-round \ascon and 5-round \xoodyak (under the single-key model), which couldn't be reached with simple DL so far.
For key recovery, HDL attacks are also more efficient than DL attacks, thanks to the larger biases of HDL approximations.
Additionally, HATF works well for DL (1$^{st}$-order HDL) attacks and some well-known DL biases of \ascon and \xoodyak that could only be obtained experimentally before can now be predicted theoretically.
With \DSF, we propose a new distinguishing attack on 8-round \ascon permutation, with a complexity of $2^{48}$.
Also, we provide a new zero-sum distinguisher for the full 12-round \ascon permutation with $2^{55}$ time/data complexity. We highlight that our cryptanalyses do not threaten the security of \ascon or \xoodyak.

2023

ASIACRYPT

Robust Decentralized Multi-Client Functional Encryption: Motivation, Definition, and Inner-Product Constructions
Abstract

Decentralized Multi-Client Functional Encryption (DMCFE) is a multi-user extension of Functional Encryption (FE) without relying on a trusted third party. However, a fundamental requirement for DMCFE is that the decryptor must collect the partial functional keys and the ciphertexts from all clients. If one client does not generate the partial functional key or the ciphertext, the decryptor cannot obtain any useful information. We found that this strong requirement limits the application of DMCFE in scenarios such as statistical analysis and machine learning.
In this paper, we first introduce a new primitive named Robust Decentralized Multi-Client Functional Encryption (RDMCFE), a notion generalized from DMCFE that aims to tolerate the problem of negative clients leading to nothing for the decryptor, where negative clients represent participants that are unable or unwilling to compute the partial functional key or the ciphertext. Conversely, a client is said to be a positive one if it is able and willing to compute both the partial functional key and the ciphertext. In RDMCFE scheme, the positive client set S is known by each positive client such that the generated partial functional keys help to eliminate the influence of negative clients, and the decryptor can learn the function value corresponding to the sensitive data of all positive clients when the cardinality of the set S is not less than a given threshold. We present such constructions for functionalities corresponding to the evaluation of inner products.
1. We provide a basic RDMCFE construction through the technique of double-masking structure, which is inspired by the work of Bonawitz et al. (CCS 2017). The storage and communication overheads of the construction are small and independent of the length of the vector. However, in the basic construction, for the security guarantee, one set of secret keys can be used to generate partial functional keys for only one function.
2. We show how to design the enhanced construction so that partial functional keys for different functions can be generated with the same set of secret keys, at the cost of increasing storage and communication overheads. Specifically, in the enhanced RDMCFE construction, we protect the mask through a single-input FE scheme and a threshold secret sharing scheme having the additively homomorphic property.

2023

ASIACRYPT

Robust Publicly Verifiable Covert Security: Limited Information Leakage and Guaranteed Correctness with Low Overhead
Abstract

Protocols with \emph{publicly verifiable covert (PVC) security} offer high efficiency and an appealing feature: a covert party may deviate from the protocol, but with a probability (e.g., $90\%$, referred to as the \emph{deterrence factor}), the honest party can identify this deviation and expose it using a publicly verifiable certificate. These protocols are particularly suitable for practical applications involving reputation-conscious parties.
However, in the cases where misbehavior goes undetected (e.g., with a probability of $10\%$), \emph{no security guarantee is provided for the honest party}, potentially resulting in a complete loss of input privacy and output correctness.
In this paper, we tackle this critical problem by presenting a highly effective solution. We introduce and formally define an enhanced notion called \emph{robust PVC security}, such that even if the misbehavior remains undetected, the malicious party can only gain an additional $1$-bit of information about the honest party's input while maintaining the correctness of the output. We propose a novel approach leveraging \emph{dual execution} and \emph{time-lock puzzles} to design a robust PVC-secure two-party protocol with \emph{low overhead} (depending on the deterrence factor). For instance, with a deterrence factor of $90\%$, our robust PVC-secure protocol incurs \emph{only additional ${\sim}10\%$ overhead} compared to the state-of-the-art PVC-secure protocol.
Given the stronger security guarantees with low overhead, our protocol is highly suitable for practical applications of secure two-party computation.

2023

ASIACRYPT

Rotation Key Reduction for Client-Server Systems of Deep Neural Network on Fully Homomorphic Encryption
Abstract

In this paper, we propose a new concept of hierarchical rotation key for homomorphic encryption to reduce the burdens of the clients and the server running on the fully homomorphic encryption schemes such as Cheon-Kim-Kim-Song (CKKS) and Brakerski/Fan-Vercauteran (BFV) schemes. Using this concept, after the client generates and transmits only a small set of rotation keys to the server, the server can generate any required rotation keys from the public key and the smaller set of rotation keys that the client sent. This proposed method significantly reduces the communication cost of the client and the server, and the computation cost of the client. For example, if we implement the standard ResNet-18 network for the ImageNet dataset with the CKKS scheme, the server requires 617 rotation keys. It takes 145.1s for the client with a personal computer to generate whole rotation keys and the total size is 115.7GB. If we use the proposed two-level hierarchical rotation key system, the size of the rotation key set generated and transmitted by the client can be reduced from 115.7GB to 2.91GB (x1/39.8), and the client-side rotation key generation runtime is reduced from 145.1s to 3.74s (x38.8 faster) without any changes in any homomorphic operations to the ciphertexts. If we use the three-level hierarchical rotation key system, the size of the rotation key set generated and transmitted by the client can be further reduced from 1.54GB (x1/75.1), and the client-side rotation key generation runtime is further reduced to 1.93s (x75.2 faster) with a slight increase in the key-switching operation to the ciphertexts and further computation in the offline phase.

2023

ASIACRYPT

SCA-LDPC: A Code-Based Framework for Key-Recovery Side-Channel Attacks on Post-Quantum Encryption Schemes
Abstract

Whereas theoretical attacks on standardized cryptographic primitives rarely lead to actual practical attacks, the situation is different for side-channel attacks. Improvements in the performance of side-channel attacks are of utmost importance.
In this paper, we propose a framework to be used in key-recovery side-channel attacks on CCA-secure post-quantum encryption schemes. The basic idea is to construct chosen ciphertext queries to a plaintext checking oracle that collects information on a set of secret variables in a single query. Then a large number of such queries is considered, each related to a different set of secret variables, and they are modeled as a low-density parity-check code (LDPC code). Secret variables are finally determined through efficient iterative decoding methods, such as belief propagation, using soft information. The utilization of LDPC codes offers efficient decoding, source coding, and error correction benefits. It has been demonstrated that this approach provides significant improvements compared to previous work by reducing the required number of queries, such as the number of traces in a power attack.
The framework is demonstrated and implemented in two different cases. On one hand, we attack implementations of HQC in a timing attack, lowering the number of required traces considerably compared to attacks in previous work. On the other hand, we describe and implement a full attack on a masked implementation of Kyber using power analysis. Using the ChipWhisperer evaluation platform, our real-world attacks recover the long-term secret key of a first-order masked implementation of \textsf{Kyber-768} ~with an average of only 12 power traces.

2023

ASIACRYPT

Scalable Multi-party Private Set Union from Multi-Query Secret-Shared Private Membership Test
Abstract

Multi-party private set union (MPSU) allows \(k(k\geq 3)\) parties, each holding a dataset of known size, to compute the union of their sets without revealing any additional information. Although two-party PSU has made rapid progress in recent years, applying its effective techniques to the multi-party setting would render information leakage and thus cannot be directly extended. Existing MPSU protocols heavily rely on computationally expensive public-key operations or generic secure multi-party computation techniques, which are not scalable.
In this work, we present a new efficient framework of MPSU from multi-party secret-shared shuffle and a newly introduced protocol called multi-query secret-shared private membership test (mq-ssPMT). Our MPSU is mainly based on symmetric-key operations and is secure against any semi-honest adversary that does not corrupt the leader and clients simultaneously. We also propose new frameworks for computing other multi-party private set operations (MPSO), such as the intersection, and the cardinality of the union and the intersection, meeting the same security requirements.
We demonstrate the scalability of our MPSU protocol with an implementation and a comparison with the state-of-the-art MPSU. Experiments show that when computing on datasets of \(2^{10}\) elements, our protocol is \(109\times\) faster than the state-of-the-art MPSU, and the improvement becomes more significant as the set size increases. To the best of our knowledge, ours is the first protocol that reports on large-size experiments. For 7 parties with datasets of \(2^{20}\) elements each, our protocol requires only 46 seconds.

2023

ASIACRYPT

SDitH in the QROM
Abstract

The MPC in the Head (MPCitH) paradigm has recently led to significant improvements for signatures in the code-based setting. In this paper we consider some modifications to a recent twist of MPCitH, called Hypercube-MPCitH, that in the code-based setting provides the currently best known signature sizes. By compressing the Hypercube-MPCitH five-round code-based identification scheme into three-rounds we obtain two main benefits. On the one hand, it allows us to further develop recent techniques to provide a tight security proof in the quantum-accessible random oracle model (QROM), avoiding the catastrophic reduction losses incurred using generic QROM-results for Fiat-Shamir. On the other hand, we can reduce the already low-cost online part of the signature even further. In addition, we propose the use of proof-of-work techniques that allow to reduce the signature size. On the technical side, we develop generalizations of several QROM proof techniques and introduce a variant of the recently proposed extractable QROM.

2023

ASIACRYPT

Sender-Anamorphic Encryption Reformulated: Achieving Robust and Generic Constructions
Abstract

Motivated by the violation of two fundamental assumptions in secure communication - receiver-privacy and sender-freedom - by a certain entity referred to as ``the dictator'', Persiano et al. introduced the concept of Anamorphic Encryption (AME) for public key cryptosystems (EUROCRYPT 2022). Specifically, they presented receiver/sender-AME, directly tailored to scenarios where receiver privacy and sender freedom assumptions are compromised, respectively. In receiver-AME, entities share a double key to communicate in anamorphic fashion, raising concerns about the online distribution of the double key without detection by the dictator. The sender-AME with no shared secret is a potential candidate for key distribution. However, the only such known schemes (i.e., LWE and Dual LWE encryptions) suffer from an intrinsic limitation and cannot achieve reliable distribution.
Here, we reformulate the sender-AME, present the notion of $\ell$-sender-AME and formalize the properties of (strong) security and robustness. Robustness refers to guaranteed delivery of duplicate messages to the intended receiver, ensuring that decrypting normal ciphertexts in an anamorphic way or decrypting anamorphic ciphertexts with an incorrect duplicate secret key results in an explicit abort signal. We first present a simple construction for pseudo-random and robust public key encryption that shares the similar idea of public-key stegosystem by von Ahn and Hopper (EUROCRYPT 2004). Then, inspired by Chen et al.'s malicious algorithm-substitution attack (ASA) on key encapsulation mechanisms (KEM) (ASIACRYPT 2020), we give a generic construction for hybrid PKE with special KEM that encompasses well-known schemes, including ElGamal and Cramer-Shoup cryptosystems.
The constructions of $\ell$-sender-AME motivate us to explore the relations between AME, ASA on PKE, and public-key stegosystem. The results show that a strongly secure $\ell$-sender-AME is such a strong primitive that implies reformulated receiver-AME, public-key stegosystem, and generalized ASA on PKE. By expanding the scope of sender-anamorphic encryption and establishing its robustness, as well as exploring the connections among existing notions, we advance secure communication protocols under challenging operational conditions.

2023

ASIACRYPT

Short Concurrent Covert Authenticated Key Exchange (Short cAKE)
Abstract

Von Ahn, Hopper and Langford introduced the notion of steganographic a.k.a. covert computation, to capture distributed computation where the attackers must not be able to distinguish honest parties from entities emitting random bitstrings. This indistinguishability should hold for the duration of the computation except for what is revealed by the intended outputs of the computed functionality. An important case of covert computation is mutually authenticated key exchange, a.k.a.\ mutual authentication. Mutual authentication is a fundamental primitive often preceding more complex secure protocols used for distributed computation. However, standard authentication implementations are not covert, which allows a network adversary to target or block parties who engage in authentication. Therefore, mutual authentication is one of the premier use cases of covert computation and has numerous real-world applications, e.g., for enabling authentication over steganographic channels in a network controlled by a discriminatory entity.
We improve on the state of the art in covert authentication by presenting a protocol that retains covertness and security under concurrent composition, has minimal message complexity, and reduces protocol bandwidth by an order of magnitude compared to previous constructions. To model the security of our scheme we develop a UC model, which captures the standard features of secure mutual authentication but extends them to covertness. We prove our construction secure in this UC model. We also provide a proof-of-concept implementation of our scheme.

2023

ASIACRYPT

Sigma Protocols from Verifiable Secret Sharing and Their Applications
Abstract

Sigma protocols are one of the most common and efficient zero-knowledge proofs (ZKPs). Over the decades, a large number of Sigma protocols are proposed, yet few works pay attention to the common design principal. In this work, we propose a generic framework of Sigma protocols for algebraic statements from verifiable secret sharing (VSS) schemes. Our framework provides a general and unified approach to understanding Sigma protocols. It not only neatly explains the classic protocols such as Schnorr, Guillou–Quisquater and Okamoto protocols, but also leads to new Sigma protocols that were not previously known.
Furthermore, we show an application of our framework in designing ZKPs for composite statements, which contain both algebraic and non-algebraic statements. We give a generic construction of non-interactive ZKPs for composite statements by combining Sigma protocols from VSS and ZKPs following MPC-in-the-head paradigm in a seamless way via a technique of \textit{witness sharing reusing}. Our construction has advantages of requiring no “glue” proofs for combining algebraic and non-algebraic statements. By instantiating our construction using Ligero++ (Bhadauria et al., CCS 2020) and designing an associated Sigma protocol from VSS, we obtain a concrete ZKP for composite statements which achieves a tradeoff between running time and proof size, thus resolving the open problem left by Backes et al. (PKC 2019).

2023

ASIACRYPT

Simple Threshold (Fully Homomorphic) Encryption From LWE With Polynomial Modulus
Abstract

The learning with errors (LWE) assumption is a powerful tool for building encryption schemes with useful properties, such as plausible resistance to quantum computers, or support for homomorphic computations. Despite this, essentially the only method of achieving threshold decryption in schemes based on LWE requires a modulus that is superpolynomial in the security parameter, leading to a large overhead in ciphertext sizes and computation time. In this work, we propose a (fully homomorphic) encryption scheme that supports a simple t-out-of-n threshold decryption protocol while allowing for a polynomial modulus. The main idea is to use the Rényi divergence (as opposed to the statistical distance as in previous works) as a measure of distribution closeness. This comes with some technical obstacles, due to the difficulty of using the Rényi divergence in decisional security notions such as standard semantic security. We overcome this by constructing a threshold scheme with a weaker notion of one-way security and then showing how to transform any one-way (fully homomorphic) threshold scheme into one guaranteeing indistinguishability-based security.

2023

ASIACRYPT

Solving the Hidden Number Problem for CSIDH and CSURF via Automated Coppersmith
Abstract

We define and analyze the Commutative Isogeny Hidden Number Problem which is the natural analogue of the Hidden Number Problem in the CSIDH and CSURF setting. In short, the task is as follows: Given two supersingular elliptic curves \(E_A\), \(E_B\) and access to an oracle that outputs some of the most significant bits of the \(\ensuremath{\mathsf{CDH}}\) of two curves, an adversary must compute the shared curve \(E_{AB}=\ensuremath{\mathsf{CDH}}(E_A,E_B)\).
We show that we can recover \(E_{AB}\) in polynomial time by using Coppersmith's method as long as the oracle outputs \(\ensuremath{\frac{13}{24}} + \varepsilon \approx 54\%\) (CSIDH) and \(\ensuremath{\frac{31}{41}} + \varepsilon \approx 76\%\) (CSURF) of the most significant bits of the \(\ensuremath{\mathsf{CDH}}\), where $\varepsilon > 0$ is an arbitrarily small constant. To this end, we give a purely combinatorial restatement of Coppersmith's method, effectively concealing the intricate aspects of lattice theory and allowing for near-complete automation. By leveraging this approach, we attain recovery attacks with $\varepsilon$ close to zero within a few minutes of computation.

2023

ASIACRYPT

The Indiﬀerentiability of the Duplex and its Practical Applications
Abstract

The Duplex construction, introduced by Bertoni~\emph{et al.} (SAC 2011), is the Swiss Army knife of permutation-based cryptography. It can be used to realise a variety of cryptographic objects---ranging from hash functions and MACs, to authenticated encryption and symmetric ratchets. Testament to this is the STROBE protocol framework which is a software cryptographic library based solely on the Duplex combined with a rich set of function calls. While prior works have typically focused their attention on specific uses of the Duplex, our focus here is its \emph{indifferentiability}. More specifically, we consider the indifferentiability of the Duplex construction from an \emph{online random oracle}---an idealisation which shares its same interface. As one of our main results we establish the indifferentiability of the Duplex from an online random oracle. However indifferentiability only holds for the standard Duplex construction and we show that the full-state variant of the Duplex cannot meet this notion. Our indifferentiability theorem provides the theoretical justification for the security of the Duplex in a variety of scenarios, amongst others, its use as a general-purpose cryptographic primitive in the STROBE framework. Next we move our attention to AEAD schemes based on the Duplex, namely SpongeWrap, which is the basis for NIST's Lightweight Cryptography standard Ascon. We harness the power of indifferentiability by establishing that SpongeWrap offers security against key-dependent message inputs, related-key attacks, and is also committing.

2023

ASIACRYPT

The Pre-Shared Key Modes of HPKE
Abstract

The Hybrid Public Key Encryption (HPKE) standard was
recently published as RFC 9180 by the Crypto Forum Research Group
(CFRG) of the Internet Research Task Force (IRTF). The RFC specifies
an efficient public key encryption scheme, combining asymmetric and
symmetric cryptographic building blocks.
Out of HPKE’s four modes, two have already been formally analyzed by
Alwen et al. (EUROCRYPT 2021). This work considers the remaining
two modes: HPKE_PSK and HPKE_AuthPSK. Both of them are “pre-shared
key” modes that assume the sender and receiver hold a symmetric pre-
shared key. We capture the schemes with two new primitives which we
call pre-shared key public-key encryption (pskPKE) and pre-shared key
authenticated public-key encryption (pskAPKE). We provide formal secu-
rity models for pskPKE and pskAPKE and prove (via general composition
theorems) that the two modes HPKE_PSK and HPKE_AuthPSK offer active
security (in the sense of insider privacy and outsider authenticity) under
the Gap Diffie-Hellman assumption.
We furthermore explore possible post-quantum secure instantiations of the
HPKE standard and propose new solutions based on lattices and isogenies.
Moreover, we show how HPKE’s basic HPKE_PSK and HPKEAuth_PSK modes
can be used black-box in a simple way to build actively secure post-
quantum/classic-hybrid (authenticated) encryption schemes. Our hybrid
constructions provide a cheap and easy path towards a practical post-
quantum secure drop-in replacement for the basic HPKE modes HPKE_Base
and HPKE_Auth.

2023

ASIACRYPT

The Relationship Between Idealized Models Under Computationally Bounded Adversaries
Abstract

The random oracle, generic group, and generic bilinear map models (ROM, GGM, GBM, respectively) are fundamental heuristics used to justify new computational assumptions and prove the security of efficient cryptosystems. While known to be invalid in some contrived
settings, the heuristics generally seem reasonable for real-world applications.
In this work, we ask: which heuristics are closer to reality? Or conversely, which heuristics are a larger leap? We answer this question through the framework of computational indifferentiability, showing that the ROM is a strictly \milder" heuristic than the GGM, which in turn is strictly
milder than the GBM. While this may seem like the expected outcome, we explain why it does not follow from prior works, and is not the a priori obvious conclusion. In order to prove our results, we develop new ideas for proving computational indifferentiable separations.

2023

ASIACRYPT

Threshold Linear Secret Sharing to the Rescue of MPC-in-the-Head
Abstract

The MPC-in-the-Head paradigm is a popular framework to build zero-knowledge proof systems using techniques from secure multi-party computation (MPC). While this paradigm is not restricted to a particular secret sharing scheme, all the efficient instantiations for small circuits proposed so far rely on additive secret sharing.
In this work, we show how applying a threshold linear secret sharing scheme (threshold LSSS) can be beneficial to the MPC-in-the-Head paradigm. For a general passively-secure MPC protocol model capturing most of the existing MPCitH schemes, we show that our approach improves the soundness of the underlying proof system from 1/N down to 1/binomial(N,\ell), where N is the number of parties and \ell is the privacy threshold of the sharing scheme. While very general, our technique is limited to a number of parties N <= |\F|, where \F is the field underlying the statement, because of the MDS conjecture.
Applying our approach with a low-threshold LSSS also boosts the performance of the proof system by making the MPC emulation cost independent of N for both the prover and the verifier. The gain is particularly significant for the verification time which becomes logarithmic in N (while the prover still has to generate and commit the N input shares).
We further generalize and improve our framework: we show how linearly-homomorphic commitments can get rid of the linear complexity of the prover, we generalize our result to any quasi-threshold LSSS, and we describe an efficient batching technique relying on Shamir's secret sharing.
We finally apply our techniques to specific use-cases. We first propose a variant of the recent SDitH signature scheme achieving new interesting trade-offs. In particular, for a signature size of 10 KB, we obtain a verification time lower than 0.5 ms, which is competitive with SPHINCS+, while achieving much faster signing. We further apply our batching technique to two different contexts: batched SDitH proofs and batched proofs for general arithmetic circuits based on the Limbo proof system. In both cases, we obtain an amortized proof size lower than 1/10 of the baseline scheme when batching a few dozen statements, while the amortized performances are also significantly improved.

2023

ASIACRYPT

Threshold Structure-Preserving Signatures
Abstract

Structure-preserving signatures (SPS) are an important building block for privacy-preserving cryptographic primitives, such as electronic cash, anonymous credentials, and delegatable anonymous credentials. In this work, we introduce the first threshold structure-preserving signature scheme (TSPS). This enables multiple parties to jointly sign a message, resulting in a standard, single-party SPS signature, and can thus be used as a replacement for applications based on SPS.
We begin by defining and constructing SPS for indexed messages, which are messages defined relative to a unique index. We prove its security in the random oracle model under a variant of the generalized Pointcheval-Sanders assumption (PS). Moreover, we generalize this scheme to an indexed multi-message SPS for signing vectors of indexed messages, which we prove secure under the same assumption. We then formally define the notion of a TSPS and propose a construction based on our indexed multi-message SPS. Our TSPS construction is fully non-interactive, meaning that signers simply output partial signatures without communicating with the other signers. Additionally, signatures are short: they consist of 2 group elements and require 2 pairing product equations to verify. We prove the security of our TSPS under the security of our indexed multi-message SPS scheme. Finally, we show that our TSPS may be used as a drop-in replacement for UC-secure Threshold-Issuance Anonymous Credential (TIAC) schemes, such as Coconut, without the overhead of the Fischlin transform.

2023

ASIACRYPT

Tighter Security for Generic Authenticated Key Exchange in the QROM
Abstract

We give a tighter security proof for authenticated key exchange (AKE) protocols that are generically constructed from key encapsulation mechanisms (KEMs) in the quantum random oracle model (QROM). Previous works (Hövelmanns et al., PKC 2020) gave reductions for such a KEM-based AKE protocol in the QROM to the underlying primitives with square-root loss and a security loss in the number of users and total sessions. Our proof is much tighter and does not have square-root loss. Namely, it only loses a factor depending on the number of users, not on the number of sessions.
Our main enabler is a new variant of lossy encryption which we call parameter lossy encryption. In this variant, there are not only lossy public keys, but also lossy system parameters. This allows us to embed a computational assumption into the system parameters, and the lossy public keys are statistically close to the normal public keys. Combining with the Fujisaki-Okamoto transformation, we obtain the first tightly IND-CCA secure KEM in the QROM in a multi-user (without corruption), multi-challenge setting.
Finally, we show that a multi-user, multi-challenge KEM implies a square-root-tight and session-tight AKE protocol in the QROM. By implementing the parameter lossy encryption tightly from lattices, we obtain the first square-root-tight and session-tight AKE from lattices in the QROM.

2023

ASIACRYPT

To attest or not to attest, this is the question – Provable attestation in FIDO2
Abstract

FIDO2 is currently the main initiative for passwordless authentication in web servers. It mandates the use of secure hardware authenticators to protect the authentication protocol's secrets from compromise. However, to ensure that only secure authenticators are being used, web servers need a method to attest their properties.The FIDO2 specifications allow for authenticators and web servers to choose between different attestation modes to prove the characteristics of an authenticator, however the properties of most these modes have not been analysed in the context of FIDO2.
In this work, we analyse the security and privacy properties of FIDO2 when the different attestation modes included in the standard are used, and show that they lack good balance between security, privacy and revocation of corrupted devices. For example, the basic attestation mode prevents remote servers from tracing user's actions across different services while requiring reduced trust assumptions. However in case one device is compromised, all the devices from the same batch (e.g., of the same brand or model) need to be recalled, which can be quite complex (and arguably impractical) in consumer scenarios. As a consequence we suggest a new attestation mode based on the recently proposed TokenWeaver, which provide more convenient mechanisms for revoking a single token while maintaining user privacy.

2023

ASIACRYPT

Too Many Hints - When LLL Breaks LWE
Abstract

All modern lattice-based schemes build on variants of the LWE problem. Information leakage of the LWE secret $\mathbf{s} \in \mathbb{Z}_q^n$ is usually modeled via so-called hints, i.e., inner products of $\mathbf{s}$ with some known vector.
At Crypto`20, Dachman-Soled, Ducas, Gong and Rossi (DDGR) defined among other so-called perfect hints and modular hints. The trailblazing DDGR framework allows to integrate and combine hints successively into lattices, and estimates the resulting LWE security loss.
We introduce a new methodology to integrate and combine an arbitrary number of perfect and modular in a single stroke. As opposed to DDGR's, our methodology is significantly more efficient in constructing lattice bases, and thus easily allows for a large number of hints up to cryptographic dimensions -- a regime that is currently impractical in DDGR's implementation.
The efficiency of our method defines a large LWE parameter regime, in which we can fully carry out attacks faster than DDGR can solely estimate them.
The benefits of our approach allow us to practically determine which number of hints is sufficient to efficiently break LWE-based lattice schemes in practice.
E.g., for mod-$q$ hints, i.e., modular hints defined over $\Z_q$, we reconstruct \Kyber-512 secret keys via LLL reduction (only!) with an amount of $449$ hints.
Our results for perfect hints significantly improve over these numbers, requiring for LWE dimension $n$ roughly $n/2$ perfect hints. E.g., we reconstruct via LLL reduction \Kyber-512 keys with merely $234$ perfect hints.
If we resort to stronger lattice reduction techniques like BKZ, we need even fewer hints.
For mod-$q$ hints our method is extremely efficient, e.g., taking total time for constructing our lattice bases and secret key recovery via LLL of around 20 mins for dimension 512.
For perfect hints in dimension 512, we require around 3 hours.
Our results demonstrate that especially perfect hints are powerful in practice, and stress the necessity to properly protect lattice schemes against leakage.

2023

ASIACRYPT

Towards compressed permutation oracles
Abstract

Compressed oracles (Zhandry, Crypto 2019) are a powerful technique to reason about quantum random oracles, enabling a sort of lazy sampling in the presence of superposition queries. A long-standing open question is whether a similar technique can also be used to reason about random (efficiently invertible) permutations.
In this work, we make a step towards answering this question. We first define the compressed permutation oracle and illustrate its use. While the soundness of this technique (i.e., the indistinguishability from a random permutation) remains a conjecture, we show a curious 2-for-1 theorem: If we use the compressed permutation oracle methodology to show that some construction (e.g., Luby-Rackoff) implements a random permutation (or strong qPRP), then we get the fact that this methodology is actually sound for free.

2023

ASIACRYPT

Two-Round Concurrent 2PC from Sub-Exponential LWE
Abstract

Secure computation is a cornerstone of modern cryptography and a rich body of research is devoted to understanding its round complexity. In this work, we consider two-party computation (2PC) protocols (where both parties receive output) that remain secure in the realistic setting where many instances of the protocol are executed in parallel (concurrent security). We obtain a two-round concurrent-secure 2PC protocol based on a single, standard, post-quantum assumption: The subexponential hardness of the learning-with-errors (LWE) problem. Our protocol is in the plain model, i.e., it has no trusted setup, and it is secure in the super-polynomial simulation framework of Pass (EUROCRYPT 2003). Since two rounds are minimal for (concurrent) 2PC, this work resolves the round complexity of concurrent 2PC from standard assumptions.
As immediate applications, our work establishes feasibility results for interesting cryptographic primitives such as the first two-round password authentication key exchange (PAKE) protocol in the plain model and the first two-round concurrent secure computation protocol for quantum circuits (2PQC).

2023

ASIACRYPT

Unconditionally Secure Multiparty Computation for Symmetric Functions with Low Bottleneck Complexity
Abstract

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) introduced by Boyle et al. (ICALP 2018) to achieve load-balancing. Roughly speaking, it is defined as the maximum communication complexity required by any player within the protocol execution. Since it was shown to be impossible to achieve sublinear bottleneck complexity in the number of players $n$ for all functions, a prior work constructed MPC protocols with low bottleneck complexity for specific functions. However, the previous protocol for symmetric functions needs to assume a computational primitive of garbled circuits and its unconditionally secure variant has exponentially large bottleneck complexity in the depth of an arithmetic formula computing the function, which limits the class of symmetric functions the protocol can compute with sublinear bottleneck complexity in $n$. In this work, we make the following contributions to unconditionally secure MPC protocols for symmetric functions with sublinear bottleneck complexity in $n$.
\begin{itemize}
\item We propose for the first time unconditionally secure MPC protocols computing \textit{any} symmetric function with sublinear bottleneck complexity in $n$. Technically, our first protocol is inspired by the one-time truth-table protocol by Ishai et al. (TCC 2013) but our second and third protocols use a novel technique to express the one-time truth-table as an array of two or higher dimensions and achieve better trade-offs.
\item We propose an unconditionally secure protocol tailored to the AND function with lower bottleneck complexity. It avoids pseudorandom functions used by the previous protocol for the AND function, preserving bottleneck complexity up to a logarithmic factor in $n$.
\item By combining our protocol for the AND function with Bloom filters, we construct an unconditionally secure protocol for private set intersection (PSI), which computes the intersection of players' private sets. This is the first PSI protocol with sublinear bottleneck complexity in $n$ and to the best of our knowledge, there has been no such protocol even under cryptographic assumptions.
\end{itemize}

2023

ASIACRYPT

Unified View for Notions of Bit Security
Abstract

We study the framework of Watanabe and Yasunaga (Asiacrypt 2021) that enables us to evaluate the bit security of cryptographic primitives/games with an operational meaning. First, we observe that their quantitative results preserve even if adversaries are allowed to output the failure symbol in games. With this slight modification, we show that the notion of bit security by Watanabe and Yasunaga is equivalent to that of Micciancio and Walter (Eurocrypt 2018) up to constant bits. Also, we demonstrate that several existing notions of advantages can be captured in a unified way. Based on this equivalence, we show that the reduction algorithm of Hast (J. Cryptology, 2004) gives a tight reduction of the Goldreich-Levin hard-core predicate to the hardness of one-way functions. These two results resolved open problems that remained.
We show that all games we need to care about in their framework are decision games. Namely, for every search game G, there is the corresponding decision game G′ such that G has λ-bit security if and only if G′ has λ-bit security. The game G′ consists of the real and the ideal games, where attacks in the ideal game are never approved. Such games often appear in game-hopping security proofs. The result justifies such security proofs because they lose no security. Finally, we provide a distribution replacement theorem. Suppose a game using distribution Q in a black-box manner is λ-bit secure, and two distributions P and Q are computationally λ-bit secure indistinguishable. In that case, the game where Q is replaced by P is also λ-bit secure.

2023

ASIACRYPT

Universally Composable Auditable Surveillance
Abstract

User privacy is becoming increasingly important in our digital society. Yet, many applications face legal requirements or regulations that prohibit unconditional anonymity guarantees, e.g., in electronic payments where surveillance is mandated to investigate suspected crimes.
As a result, many systems have no effective privacy protections at all, or have backdoors, e.g., stored at the operator side of the system, that can be used by authorities to disclose a user’s private information (e.g., lawful interception). The problem with such backdoors is that they also enable silent mass surveillance within the system. To prevent such misuse, various approaches have been suggested which limit possible abuse or ensure it can be detected. Many works consider auditability of surveillance actions but do not enforce that traces are left when backdoors are retrieved. A notable exception which offers retrospective and silent surveillance is the recent work on misuse-resistant surveillance by Green et al. (EUROCRYPT’21). However, their approach relies on extractable witness encryption, which is a very strong primitive with no known efficient and secure implementations.
In this work, we develop a building block for auditable surveillance. In our protocol, backdoors or escrow secrets of users are protected in multiple ways: (1) Backdoors are short-term and user-specific; (2) they are shared between trustworthy parties to avoid a single point of failure; and (3) backdoor access is given conditionally. Moreover (4) there are audit trails and public statistics for every (granted) backdoor request; and (5) surveillance remains silent, i.e., users do not know they are surveilled. Concretely, we present an abstract UC-functionality which can be used to augment applications with auditable surveillance capabilities. Our realization makes use of threshold encryption to protect user secrets, and is concretely built in a blockchain context with committee-based YOSO MPC. As a consequence, the committee can verify that the conditions for backdoor access are given, e.g., that law enforcement is in possession of a valid surveillance warrant (via a zero-knowledge proof). Moreover, access leaves an audit trail on the ledger, which allows an auditor to retrospectively examine surveillance decisions.
As a toy example, we present an Auditably Sender-Traceable Encryption scheme, a PKE scheme where the sender can be deanonymized by law enforcement. We observe and solve problems posed by retrospective surveillance via a special non-interactive non-committing encryption scheme which allows zero-knowledge proofs over message, sender identity and (escrow) secrets.

2023

ASIACRYPT

Verifiable Decentralized Multi-Client Functional Encryption for Inner Product
Abstract

Joint computation on encrypted data is becoming increasingly crucial with the rise of cloud computing. In recent years, the development of multi-client functional encryption (MCFE) has made it possible to perform joint computation on private inputs, without any interaction. Well-settled solutions for linear functions have become efficient and secure, but there is still a shortcoming: if one user inputs incorrect data, the output of the function might become meaningless for all other users (while still useful for the malicious user). To address this issue, the concept of verifiable functional encryption was introduced by Badrinarayanan et al. at Asiacrypt ’16 (BGJS). However, their solution was impractical because of strong statistical requirements. More recently, Bell et al. introduced a related concept for secure aggregation, with their ACORN solution, but it requires multiple rounds of interactions between users. In this paper,
– we first propose a computational definition of verifiability for MCFE. Our notion covers the computational version of BGJS and extends it to handle any valid inputs defined by predicates. The BGJS notion corresponds to the particular case of a fixed predicate, in our setting;
– we then introduce a new technique called Combine-then-Descend, which relies on the class group. It allows us to construct One-time Decentralized Sum (ODSUM) on verifiable private inputs. ODSUM is the building block for our final protocol of a verifiable decentralized MCFE for inner-product, where the inputs are within a range. Our approach notably enables the efficient identification of malicious users, thereby addressing an unsolved problem in ACORN.

2023

ASIACRYPT

VSS from Distributed ZK Proofs and Applications
Abstract

Non-Interactive Verifiable Secret Sharing (NI-VSS) is a technique for distributing a secret among a group of individuals in a verifiable manner, such that shareholders can verify the validity of their received share and only a specific number of them can access the secret. VSS is a fundamental tool in cryptography and distributed computing. In this paper, we present an extremely efficient NI-VSS scheme using Zero-Knowledge (ZK) proofs on secret shared data. While prior VSS schemes have implicitly used ZK proofs on secret shared data, we specifically use their formal definition recently provided by Boneh et al. in CRYPTO 2019. The proposed NI-VSS scheme uses a quantum random oracle and a quantum computationally hiding commitment scheme in a black-box manner, which ensures its ease of use, especially in post-quantum threshold protocols. Implementation results further solidify its practicality and superiority over current constructions. With the new VSS scheme, for parameter sets $(n, t)=(128, 63)$ and $(2048, 1023)$, a dealer can share a secret in less than $0.02$ and $2.0$ seconds, respectively, and shareholders can verify their shares in less than $0.4$ and $5.0$ milliseconds. Compared to the well-established Pedersen VSS scheme, for the same parameter sets, at the cost of $2.5\times$ higher communication, the new scheme is respectively $22.5\times$ and $3.25\times$ faster in the sharing phase, and notably needs $271\times$ and $479\times$ less time in the verification. Leveraging the new NI-VSS scheme, we revisit several classic and PQ-secure threshold protocols and improve their efficiency. Our revisions led to more efficient versions of both the Pedersen DKG protocol and the GJKR threshold signature scheme. We show similar efficiency enhancements and improved resilience to malicious parties in isogeny-based DKG and threshold signature schemes. We think, due to its remarkable efficiency and ease of use, the new NI-VSS scheme can be a valuable tool for a wide range of threshold protocols.

2023

ASIACRYPT

We Are on the Same Side. Alternative Sieving Strategies for the Number Field Sieve
Abstract

The Number Field Sieve (NFS) is the state-of-the art algorithm for integer
factoring, and sieving is a crucial step in the NFS. It is a very
time-consuming operation, whose goal is to collect many relations. The
ultimate goal is to generate random smooth integers mod $N$ with their prime
decomposition, where smooth is defined on the rational and algebraic sides
according to two prime factor bases.
In modern factorization tool, such as \textsf{Cado-NFS}, sieving is split into
different stages depending on the size of the primes, but defining good
parameters for all stages is based on heuristic and practical arguments. At
the beginning, candidates are sieved by small primes on both sides, and if
they pass the test, they continue to the next stages with bigger primes, up to
the final one where we factor the remaining part using the ECM algorithm. On
the one hand, first stages are fast but many false relations pass them, and we
spend a lot of time with useless relations. On the other hand final stages are
more time demanding but outputs less relations. It is not easy to evaluate the
performance of the best strategy on the overall sieving step since it depends
on the distribution of numbers that results at each stage.
In this article, we try to examine different sieving strategies to speed up
this step since many improvements have been done on all other steps of the
NFS. Based on the relations collected during the RSA-250 factorization and all
parameters, we try to study different strategies to better understand this
step. Many strategies have been defined since the discovery of NFS, and we
provide here an experimental evaluation.

2023

ASIACRYPT

Weak Zero-Knowledge via the Goldreich-Levin Theorem
Abstract

Obtaining three round zero-knowledge from standard cryptographic assumptions has remained a challenging open problem. Meanwhile, there has been exciting progress in realizing useful relaxations such as weak zero-knowledge, strong witness indistinguishability and witness hiding in two or three rounds. In particular, known realizations from generic assumptions obtain:
(1) security against {\em adaptive} verifiers assuming fully homomorphic encryption among other standard assumptions (Bitansky et. al., STOC 2019), and
(2) security against {\em non-adaptive} verifiers in the distributional setting from oblivious transfer (Jain et. al., Crypto 2017).
This work builds three round weak zero-knowledge for NP in the non-adaptive setting from
doubly-enhanced injective trapdoor functions. We obtain this result by developing a new distinguisher-dependent simulation technique that makes crucial use of the Goldreich-Levin list decoding algorithm, and may be of independent interest.

2023

ASIACRYPT

WhatsUpp with Sender Keys? Analysis, Improvements and Security Proofs
Abstract

Developing end-to-end encrypted instant messaging solutions for group conversations is an ongoing challenge that has garnered significant attention from practitioners and the cryptographic community alike. Notably, industry-leading messaging apps such as WhatsApp and Signal Messenger have adopted the Sender Keys protocol, where each group member shares their own symmetric encryption key with others. Despite its widespread adoption, Sender Keys has never been formally modelled in the cryptographic literature, raising the following natural question:
What can be proven about the security of the Sender Keys protocol, and how can we practically mitigate its shortcomings?
In addressing this question, we first introduce a novel security model to suit protocols like Sender Keys, deviating from conventional group key agreement-based abstractions. Our framework allows for a natural integration of two-party messaging within group messaging sessions that may be of independent interest. Leveraging this framework, we conduct the first formal analysis of the Sender Keys protocol, and prove it satisfies a weak notion of security. Towards improving security, we propose a series of efficient modifications to Sender Keys without imposing significant performance overhead. We combine these refinements into a new protocol that we call Sender Keys+, which may be of interest both in theory and practice.

2023

ASIACRYPT

Zero-Knowledge Functional Elementary Databases
Abstract

Zero-knowledge elementary databases (ZK-EDBs) enable a prover to commit a database $D$ of key-value $(x,v)$ pairs and later provide a convincing answer to the query ``send me the value $D(x)$ associated with $x$'' without revealing any extra knowledge (including the size of $D$). After its introduction, several works extended it to allow more expressive queries, but the expressiveness achieved so far is still limited: only a relatively simple queries--range queries over the keys and values-- can be handled by known constructions.
In this paper we introduce a new notion called zero knowledge functional elementary databases (ZK-FEDBs), which allows the most general functional queries. Roughly speaking, for any Boolean circuit $f$, ZK-FEDBs allows the ZK-EDB prover to provide convincing answers to the queries of the form ``send me all records ${(x,v)}$ in ${{D}}$ satisfying $f(x,v)=1$,'' without revealing any extra knowledge (including the size of ${D}$). We present a construction of ZK-FEDBs in the random oracle model and generic group model, whose proof size is only linear in the length of record and the size of query circuit, and is independent of the size of input database $D$.
Our technical constribution is two-fold. Firstly, we introduce a new variant of zero-knowledge sets (ZKS) which supports combined operations on sets. We present a concrete construction that is based on groups with unknown order. Secondly, we develop a tranformation that tranforms the query of Boolean circuit into a query of combined operations on related sets, which may be of independent interest.