Let (N,e) be a public key of the RSA cryptosystem, and d be the corresponding private key. In practice, we usually choose a small e for quick encryption. In this paper, we improve partial private key exposure attacks against RSA with a small public exponent e. The key idea is that under such a setting we can usually obtain more information about the prime factor of N and then by solving a univariate modular polynomial with Coppersmith's method, N can be factored in polynomial time. Compared to previous results, we reduce the number of d's leaked bits needed to mount the attack by log_2 (e) bits. Furthermore, our experiments show that for 1024-bit N, our attack can achieve the theoretical bound on a personal computer, which verified our attack.

YOSO MPC (Gentry et al., Crypto 2021) is a new MPC framework where each participant can speak at most once. This models an adaptive adversary’s ability to watch the network and corrupt or destroy parties it deems significant based on their communication. By using private channels to anonymous receivers (e.g. by encrypting to a public key whose owner is unknown), the communication complexity of YOSO MPC can scale sublinearly with the total number N of available parties, even when the adversary’s corruption threshold is linear in N (e.g. just under N/2). It was previously an open problem whether YOSO MPC can achieve guaranteed output delivery in a constant number of rounds without relying on trusted setup. In this work, we show that this can indeed be accomplished. We demonstrate three different approaches: the first two (which we call YaOSO and YOSO-GLS) use two and three rounds of communication, respectively. Our third approach (which we call YOSO-LHSS) uses O(d) rounds, where d is the multiplicative depth of the circuit being evaluated; however, it can be used to bootstrap any constant-round YOSO protocol that requires setup, by generating that setup within YOSO-LHSS. Though YOSO-LHSS requires more rounds than our first two approaches, it may be more practical, since the zero knowledge proofs it employs are more efficient to instantiate. As a contribution of independent interest, we introduce a verifiable state propagation UC functionality, which allows parties to send private message which are verifiably derived in the “correct” way (according to the protocol in question) to anonymous receivers. This is a natural functionality to build YOSO protocols on top of.

The Module Learning With Errors (MLWE)-based Key Encapsulation Mechanism (KEM) Kyber is NIST's new standard scheme for post-quantum encryption. As a building block, Kyber uses a Chosen Plaintext Attack (CPA)-secure Public Key Encryption (PKE) scheme, referred to as Kyber.CPAPKE. In this paper we study the robustness of Kyber.CPAPKE against key mismatch attacks.

We demonstrate that Kyber's security levels can be compromised if having access to a few mismatch queries of Kyber.CPAPKE, by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in Kyber.CPAPKE.

We further propose an adaptive method to enhance parallel mismatch attacks, initially proposed by Shao et al. at AsiaCCS 2024, thereby significantly reducing query complexity. This method combines the adaptive attack with post-processing via lattice reduction to retrieve the final secret key entries. Our method proves its efficacy by reducing query complexity by 14.6 % for Kyber512 and 7.5 % for Kyber768/Kyber1024.

Furthermore, this approach has the potential to improve multi-value Plaintext-Checking (PC) oracle-based side-channel attacks and fault-injection attacks against Kyber itself.

Isogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of two and a large smooth integer $T$ to divide $p^2-1$ for its prime parameter $p$. We present two new methods that combine previous techniques for finding suitable primes: sieve-and-boost and XGCD-and-boost. We use these methods to find primes for the NIST submission of SQIsign. Furthermore, we show that our methods are flexible and can be adapted to find suitable parameters for other isogeny-based schemes such as AprèsSQI or POKE. For all three schemes, the parameters we present offer the best performance among all parameters proposed in the literature.

Oblivious Pseudorandom Functions (OPRFs) allow a client to evaluate a pseudorandom function (PRF) on her secret input based on a key that is held by a server. In the process, the client only learns the PRF output but not the key, while the server neither learns the input nor the output of the client. The arguably most popular OPRF is due to Naor, Pinkas and Reingold (Eurocrypt 2009). It is based on an Oblivious Exponentiation by the server, with passive security under the Decisional Diffie-Hellman assumption. In this work, we strengthen the security guarantees of the NPR OPRF by protecting it against active attacks of the server. We have implemented our solution and report on the performance. Our main result is a new batch OPRF protocol which is secure against maliciously corrupted servers, but is essentially as efficient as the semi-honest solution. More precisely, the computation (and communication) overhead is a multiplicative factor $o(1)$ as the batch size increases. The obvious solution using zero-knowledge proofs would have a constant factor overhead at best, which can be too expensive for certain deployments. Our protocol relies on a novel version of the DDH problem, which we call the Oblivious Exponentiation Problem (OEP), and we give evidence for its hardness in the Generic Group model. We also present a variant of our maliciously secure protocol that does not rely on the OEP but nevertheless only has overhead $o(1)$ over the known semi-honest protocol. Moreover, we show that our techniques can also be used to efficiently protect threshold blind BLS signing and threshold ElGamal decryption against malicious attackers.

Mixed-Integer Linear Programming (MILP) modeling has become an important tool for both the analysis and the design of symmetric cryptographic primitives. The bit-wise modeling of their nonlinear components, especially the S-boxes, is of particular interest since it allows more informative analysis compared to word-oriented models focusing on counting active S-boxes. At the same time, the size of these models, especially in terms of the number of required inequalities, tends to significantly influence and ultimately limit the applicability of this method to real-world ciphers, especially for larger number of rounds.

It is therefore of great cryptographic significance to study optimal linear inequality descriptions for Boolean functions. The pioneering works of Abdelkhalek et al. (FSE 2017), Boura and Coggia (FSE 2020) and Li and Sun (FSE 2023) provided various heuristic techniques for this computationally hard problem, decomposing it into two algorithmic steps, coined Problem 1 and Problem 2, with the latter being identical to the well-known NP-hard set cover problem, for which there are many heuristic and exact algorithms in the literature.

In this paper, we introduce a novel and efficient branch-and-bound algorithm for generating all minimal, non-redundant candidate inequalities that satisfy a given Boolean function, therefore solving Problem 1 in an optimal manner without relying on heuristics. We furthermore prove that our algorithm correctly computes optimal solutions. Using a number of dedicated optimizations, it provides significantly improved runtimes compared to previous approaches and allows the optimal modeling of the difference distribution tables (DDT) and linear approximation tables (LAT) of many practically used S-boxes. The source code for our algorithm is publicly available as a tool for researchers and practitioners in symmetric cryptography.

In this note we review the technique proposed at ToSC 2018 by Sadeghi et al. for attacks built upon several related-tweakey impossible differential trails. We show that the initial encryption queries are improper and lead the authors to misevaluate a filtering value in the key recovery phase. We identified 4 other papers (from Eurocrypt, DCC, and 2 from ToSC) that follow on the results of Sadeghi et al. and in three of them the flawed technique was reused.

We thus present a careful analysis of these types of attacks and give generic complexity formulas similar to the ones proposed by Boura et al. at Asiacrypt 2014. We apply these to the aforementioned papers and provide patched versions of their attacks. The main consequence is an increase in the memory complexity. We show that in many cases (a notable exception being quantum impossible differentials) it is possible to recover the numeric time estimates of the flawed analysis, and in all cases we were able to build a correct attack reaching the same number of rounds.

Blind signature schemes enable a user to obtain a digital signature on a message from a signer without revealing the message itself. Among the most fundamental examples of such a scheme is blind Schnorr, but recent results show that it does not satisfy the standard notion of security against malicious users, One-More Unforgeability (OMUF), as it is vulnerable to the ROS attack. However, blind Schnorr does satisfy the weaker notion of sequential OMUF, in which only one signing session is open at a time, in the Algebraic Group Model (AGM) + Random Oracle Model (ROM), assuming the hardness of the Discrete Logarithm (DL) problem.

This paper serves as a first step towards characterizing the security of blind Schnorr in the limited concurrency setting. Specifically, we show that blind Schnorr satisfies OMUF when at most two signing sessions can be concurrently open (in the AGM+ROM, assuming DL). Our argument suggests that it is plausible that blind Schnorr satisfies OMUF for up to polylogarithmically many concurrent signing sessions. Our security proof involves interesting techniques from linear algebra and combinatorics.

Side-channel Collision Attacks (SCCA) is a classical method that exploits information dependency leaked during cryptographic operations. Unlike collision attacks that seek instances where two different inputs to a cryptographic algorithm yield identical outputs, SCCAs specifically target the internal state, where identical outputs are more likely. Although SCCA does not rely on the pre-assumption of the leakage model, it explicitly operates on precise trace segments reflecting the target operation, which is challenging to perform when the leakage measurements are noisy. Besides, its attack performance may vary dramatically, as it relies on selecting a reference byte (and its corresponding leakages) to “collide” other bytes. A poor selection would lead to many bytes unrecoverable. These two facts make its real-world application problematic.

This paper addresses these challenges by introducing a novel plaintext-based SCCA. We leverage the bijective relationship between plaintext and secret data, using plaintext as labels to train profiling models to depict leakages from varying operations. By comparing the leakage representations produced by the profiling model instead of the leakage segmentation itself, all secret key differences can be revealed simultaneously without processing leakage traces. Furthermore, we propose a novel error correction scheme to rectify false predictions further. Experimental results show that our approach significantly surpasses the state-of-the-art SCCA in both attack performance and computational complexity (e.g., training time reduced from approximately three hours to five minutes). These findings underscore our method's effectiveness and practicality in real-world attack scenarios.

Most of the previous attacks on Dilithium exploit side-channel information which is leaked during the computation of the polynomial multiplication cs1, where s1 is a small-norm secret and c is a verifier's challenge. In this paper, we present a new attack utilizing leakage during secret key unpacking in the signing algorithm. The unpacking is also used in other post-quantum cryptographic algorithms, including Kyber, because inputs and outputs of their API functions are byte arrays. Exploiting leakage during unpacking is more challenging than exploiting leakage during the computation of cs1 since c varies for each signing, while the unpacked secret key remains constant. Therefore, post-processing is required in the latter case to recover a full secret key. We present two variants of post-processing. In the first one, a half of the coefficients of the secret s1 and the error s2 is recovered by profiled deep learning-assisted power analysis and the rest is derived by solving linear equations based on t = As1 + s2, where A and t are parts of the public key. This case assumes knowledge of the least significant bits of t, t0. The second variant uses lattice reduction to derive s1 without the knowledge of t0. However, it needs a larger portion of s1 to be recovered by power analysis. We evaluate both variants on an ARM Cortex-M4 implementation of Dilithium-2. The experiments show that the attack assuming the knowledge of t0 can recover s1 from a single trace captured from a different from profiling device with a non-negligible probability.

Restricted syndrome decoding problems (R-SDP and R-SDP($G$)) provide an interesting basis for post-quantum cryptography. Indeed, they feature in CROSS, a submission in the ongoing process for standardizing post-quantum signatures.

This work improves our understanding of the security of both problems. Firstly, we propose and implement a novel collision attack on R-SDP($G$) that provides the best attack under realistic restrictions on memory. Secondly, we derive precise complexity estimates for algebraic attacks on R-SDP that are shown to be accurate by our experiments. We note that neither of these improvements threatens the updated parameters of CROSS.

The generic-group model (GGM) and the algebraic-group model (AGM) have been exceptionally successful in proving the security of many classical and modern cryptosystems. These models, however, come with standard-model uninstantiability results, raising the question of whether the schemes analyzed under them can be based on firmer standard-model footing.

We formulate the uber-knowledge (UK) assumption, a standard-model assumption that naturally extends the uber-assumption family to knowledge-type problems. We justify the soundness of UK in both the bilinear GGM and the bilinear AGM. Along the way we extend these models to account for hashing into groups, an adversarial capability that is available in many concrete groups—In contrast to standard assumptions, hashing may affect the validity of knowledge assumptions. These results, in turn, enable a modular approach to security in the GGM and the AGM.

As example applications, we use the UK assumption to prove knowledge soundness of Groth's zero-knowledge SNARK (EUROCRYPT 2016) and of KZG polynomial commitments (ASIACRYPT 2010) in the standard model, where for the former we reuse the existing proof in the AGM without hashing.

The collision-resistant hash function is an early cryptographic primitive that finds extensive use in various applications. Remarkably, the Merkle-Damgård and Merkle tree hash structures possess the collision-resistance preserving property, meaning the hash function remains collision-resistant when the underlying compression function is collision-resistant. This raises the intriguing question of whether reducing the number of underlying compression function calls with the collision-resistance preserving property is possible. In pursuit of addressing these inquiries, we prove that for an ${\ell}n$-to-$sn$-bit collision-resistance preserving hash function designed using $r$ $tn$-to-$n$-bit compression function calls, we must have $r \geq \lceil (\ell-s)/(t-1) \rceil $. Throughout the paper, all operations other than the compression function are assumed to be linear (which we call linear hash mode).

Multi-key fully homomorphic encryption (MKFHE), a generalization of fully homomorphic encryption (FHE), enables a computation over encrypted data under multiple keys. The first MKFHE schemes were based on the NTRU primitive, however these early NTRU based FHE schemes were found to be insecure due to the problem of over-stretched parameters. Recently, in the case of standard (non-multi key) FHE a secure version, called FINAL, of NTRU has been found. In this work we extend FINAL to an MKFHE scheme, this allows us to benefit from some of the performance advantages provided by NTRU based primitives. Thus, our scheme provides competitive performance against current state-of-the-art multi-key TFHE, in particular reducing the computational complexity from quadratic to linear in the number of keys.

We generalize the optimal knowledge extractor for constant-round special sound protocols presented by Wikström (2018) to a knowledge extractor for the corresponding non-interactive Fiat-Shamir proofs in the random oracle model and give an exact analysis of the extraction error and running time.

Relative the interactive case the extraction error and the running time are both asymptotically increased by a multiplicative factor equal to the number of oracle queries made by the prover.

Through carefully chosen notation, novel concepts, and a technical lemma, we effectively recast the extraction problem of the notoriously complex non-interactive case to the interactive case. Thus, our approach may be of independent interest.

The Number Field Sieve and its variants are the best algorithms to solve the discrete logarithm problem in finite fields (except for the weak small characteristic case). The Factory variant accelerates the computation when several prime fields are targeted. This article adapts the Factory variant to non-prime finite fields of medium and large characteristic. A precomputation, solely dependent on an approximate finite field size and an extension degree, allows to efficiently compute discrete logarithms in a constant proportion of the finite fields of the given approximate size and extension degree. We combine this idea with two other variants of NFS, namely the tower and special variant. This combination improves the asymptotic complexity. We also notice that combining our approach with the MNFS variant would be an unnecessary complication as all the potential gain of MNFS is subsumed by our Factory variant anyway. Furthermore, we demonstrate how Chebotarev's density theorem allows to compute the density of finite fields that can be solved with a given precomputation. Finally, we provide experimental data in order to assess the practical reach of our approach.

Salient in many cryptosystems, the exponent-inversion technique began without randomization in the random oracle model (SCIS '03, PKC '04), evolved into the Boneh-Boyen short signature scheme (JoC '08) and exerted a wide influence. Seen as a notable case, Gentry's (EuroCrypt '06) identity-based encryption (IBE) applies exponent inversion on a randomized base in its identity-based trapdoors. Making use of the non-static q-strong Diffie-Hellman assumption, Boneh-Boyen signatures are shown to be unforgeable against q-chosen-message attacks, while a variant q-type decisional assumption is used to establish the security of Gentry-IBE. Challenges remain in proving their security under weaker static assumptions.

Supported by the dual form/system framework (Crypto '09, AsiaCrypt '12), we propose dual form exponent-inversion Boneh-Boyen signatures and Gentry-IBE, with security proven under the symmetric external Diffie-Hellman (SXDH) assumption. Starting from our signature scheme, we extend it into P-signatures (TCC '08), resulting in the first anonymous credential scheme from the SXDH assumption, serving as a competitive alternative to the static-assumption construction of Abe et al. (JoC '16). Moreover, from our Gentry-IBE variant, we propose an accountable-authority IBE scheme also from SXDH, surpassing the fully secure Sahai-Seyalioglu scheme (PKC '11) in efficiency and the generic Kiayias-Tang transform (ESORICS '15) in security. Collectively, we present a suite of results under static assumptions.

In ASIACRYPT 2019, Andreeva et al. introduced a new symmetric key primitive called the forkcipher, designed for lightweight applications handling short messages. A forkcipher is a keyed function with a public tweak, featuring fixed-length input and fixed-length (expanding) output. They also proposed a specific forkcipher, ForkSkinny, based on the tweakable block cipher SKINNY, and its security was evaluated through cryptanalysis. Since then, several efficient AEAD and MAC schemes based on forkciphers have been proposed, catering not only to short messages but also to various purposes such as leakage resilience and cloud security. While forkciphers have proven to be efficient solutions for designing AEAD schemes, the area of forkcipher design remains unexplored, particularly the lack of provably secure forkcipher constructions.

In this work, we propose forkcipher design for various tweak lengths, based on a block cipher as the underlying primitive. We provide proofs of security for these constructions, assuming the underlying block cipher behaves as an ideal block cipher. First, we present a forkcipher, $\widetilde{\textsf{F}}1$, for an $n$-bit tweak and prove its optimal ($n$-bit) security. Next, we propose another construction, $\widetilde{\textsf{F}}2$, for a $2n$-bit tweak, also proving its optimal ($n$-bit) security. Finally, we introduce a construction, $\widetilde{\textsf{F}}r$, for a general $rn$-bit tweak, achieving $n$-bit security.

Broadcast Encryption (BE) allows a sender to send an encrypted message to multiple receivers. In a typical broadcast encryption scenario, the broadcaster decides the set of users who can decrypt a particular ciphertext (denoted as the privileged set). Gritti et al. (IJIS'16) introduced a new primitive called Broadcast Encryption with Dealership (BrED), where the dealer decides the privileged set. A BrED scheme allows a dealer to buy content from the broadcaster and sell it to users. It provides better flexibility in managing a large user base. To date, quite a few different constructions of BrED schemes have been proposed by the research community.

We find that all existing BrED schemes are insecure under the existing security definitions. We demonstrate a concrete attack on all the existing schemes in the purview of the existing security definition. We also find that the security definitions proposed in the state-of-the-art BrED schemes do not capture the real world. We argue about the inadequacy of existing definitions and propose a new security definition that models the real world more closely. Finally, we propose a new BrED construction and prove it to be secure in our newly proposed security model.

Recently, Geraud-Stewart and Naccache proposed two trapdoors based on matrix products. In this paper, we answer the call for cryptanalysis. We explore how using the trace and determinant of a matrix can be used to attack their constructions. We fully break their first construction in a polynomial-time attack. We show an information leak in the second construction using characteristic polynomials, and provide two attacks that decrease the bit security by about half.

Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model.

For more than two decades, pairings have been a fundamental tool for designing elegant cryptosystems, varying from digital signature schemes to more complex privacy-preserving constructions. However, the advancement of quantum computing threatens to undermine public-key cryptography. Concretely, it is widely accepted that a future large-scale quantum computer would be capable to break any public-key cryptosystem used today, rendering today's public-key cryptography obsolete and mandating the transition to quantum-safe cryptographic solutions. This necessity is enforced by numerous recognized government bodies around the world, including NIST which initiated the first open competition in standardizing post-quantum (PQ) cryptographic schemes, focusing primarily on digital signatures and key encapsulation/public-key encryption schemes. Despite the current efforts in standardizing PQ primitives, the landscape of complex, privacy-preserving cryptographic protocols, e.g., zkSNARKs/zkSTARKs, is at an early stage. Existing solutions suffer from various disadvantages in terms of efficiency and compactness and in addition, they need to undergo the required scrutiny to gain the necessary trust in the academic and industrial domains. Therefore, it is believed that the migration to purely quantum-safe cryptography would require an intermediate step where current classically secure protocols and quantum-safe solutions will co-exist. This is enforced by the report of the Commercial National Security Algorithm Suite version 2.0, mandating transition to quantum-safe cryptographic algorithms by 2033 and suggesting to incorporate ECC at 192-bit security in the meantime. To this end, the present paper aims at providing a comprehensive study on pairings at 192-bit security level. We start with an exhaustive review in the literature to search for all possible recommendations of such pairing constructions, from which we extract the most promising candidates in terms of efficiency and security, with respect to the advanced Special TNFS attacks. Our analysis is focused, not only on the pairing computation itself, but on additional operations that are relevant in pairing-based applications, such as hashing to pairing groups, cofactor clearing and subgroup membership testing. We implement all functionalities of the most promising candidates within the RELIC cryptographic toolkit in order to identify the most efficient pairing implementation at 192-bit security and provide extensive experimental results.

Vessels can be recognised by their navigation radar due to the characteristics of the emitted radar signal. This is particularly useful if one wants to build situational awareness without revealing one's own presence. Most countries maintain databases of radar fingerprints but will not readily share these due to national security regulations. Sharing of such information will generally require some form of information exchange agreement.

However, all parties in a coalition benefit from correct identification. We use secure multiparty computation to match a radar signal measurement against secret databases and output plausible matches with their likelihoods. We also provide a demonstrator using MP-SPDZ.

The famous no-cloning principle has been shown recently to enable a number of uncloneable cryptographic primitives, including the copy-protection of certain functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a computation, but that is natively unkeyed: quantum advice. Remarkably, this is an application of the no-cloning principle in a context where the quantum states of interest are not chosen by a random process. We establish unconditional constructions for promise problems admitting uncloneable quantum advice and, assuming the feasibility of quantum copy-protecting certain functions, for languages with uncloneable advice. Along the way, we note that state complexity classes, introduced by Rosenthal and Yuen (ITCS 2022) — which concern the computational difficulty of synthesizing sequences of quantum states — can be naturally generalized to obtain state cloning complexity classes. We make initial observations on these classes, notably obtaining a result analogous to the existence of undecidable problems.

Our proof technique defines and constructs ingenerable sequences of finite bit strings, essentially meaning that they cannot be generated by any uniform circuit family with non-negligible probability. We then prove a generic result showing that the difficulty of accomplishing a computational task on uniformly random inputs implies its difficulty on any fixed, ingenerable sequence. We use this result to derandomize quantum cryptographic games that relate to cloning, and then incorporate a result of Kundu and Tan (arXiv 2022) to obtain uncloneable advice. Applying this two-step process to a monogamy-of-entanglement game yields a promise problem with uncloneable advice, and applying it to the quantum copy-protection of pseudorandom functions with super-logarithmic output lengths yields a language with uncloneable advice.

To address security issues in cloud computing, fully homomorphic encryption (FHE) enables a third party to evaluate functions using ciphertexts that do not leak information to the cloud server. The remaining problems of FHE include high computational costs and limited arithmetic operations, only evaluating additions and multiplications. Arbitrary functions can be evaluated using a precomputed lookup table (LUT), which is one of the solutions for those problems. Previous studies proposed LUT-enabled computation methods 1) with bit-wise FHE and 2) with word-wise FHE. The performance of LUT-enabled computation with bit-wise FHE drops quickly when evaluating BigNum functions because of the complexity being O(s·2^d·m), where m represents the number of inputs, d and s represent the bit lengths of the inputs and outputs, respectively. Thus, LUT-enabled computation with word-wise FHE, which handles a set of bits with one operation, has also been proposed; however, previous studies are limited in evaluating multivariate functions within two inputs and cannot speed up the evaluation when the domain size of the integer exceeds 2N, where N is the number of elements packed into a single ciphertext. In this study, we propose a non-interactive model, in which no decryption is required, to evaluate arbitrary multivariate functions using homomorphic table lookup with word-wise FHE. The proposed LUT-enabled computation method 1) decreases the complexity to O(2^d·m/l), where l is the element size of FHE packing; 2) extends the input and output domain sizes to evaluate multivariate functions over two inputs; and 3) adopts a multidimensional table for enabling multithreading to reduce latency. The experimental results demonstrate that evaluating a 10-bit two-input function and a 5-bit three-input function takes approximately 90.5 and 105.5 s with 16-thread, respectively. Our proposed method achieves 3.2x and 23.1x speedup to evaluate two-bit and three-bit 3-input functions compared with naive LUT-enabled computation with bit-wise FHE.

The Learning with Errors (LWE) problem has become one of the most prominent candidates of post-quantum cryptography, offering promising potential to meet the challenge of quantum computing. From a theoretical perspective, optimizing algorithms to solve LWE is a vital task for the analysis of this cryptographic primitive. In this paper, we propose a fine-grained time/memory trade-off method to analyze c-sum BKW variants for LWE in both classical and quantum models, then offer new complexity bounds for multiple BKW variants determined by modulus q, dimension k, error rate alpha, and stripe size b. Through our analysis, optimal parameters can be efficiently found for different settings, and the minimized complexities are lower than existing results. Furthermore, we enhance the performance of c-sum BKW in the quantum computing model by adopting the quantum Meet-in-the-Middle technique as c-sum solver instead of the naive c-sum technique. Our complexity trade-off formula also applies to the quantum version of BKW, and optimizes the theoretical quantum time and memory costs, which are exponentially lower than existing quantum c-sum BKW variants.

This work introduces several algorithms related to the computation of orientations in endomorphism rings of supersingular elliptic curves. This problem is at the heart of several results regarding the security of oriented-curves in isogeny-based cryptography. Under the Deuring correspondence, it can be expressed purely in terms of quaternion and boils down to representing integers by ternary quadratic forms. Our main contribution is to show that there exist efficient algorithms to solve this problem for quadratic orders of discriminant $n$ up to $O(p^{4/3})$. Our approach improves upon previous results by increasing this bound from $O(p)$ to $O(p^{4/3})$ and removing some heuristics. We introduce several variants of our new algorithm and provide a careful analysis of their asymptotic running time (without heuristic when it is possible). The best proven asymptotic complexity of one of our variants is $O(n^{3/4}/p)$ in average. The best heuristic variant has a complexity of $O(p^{1/3})$ for big enough $n$. We then introduce several results regarding the computation of ideals between oriented orders. The first application of this is a simplification of the known reduction from vectorization to computing the endomorphism ring, removing the assumption on the factorization of the discriminant. As a second application, we relate the problem of computing fixed-degree isogenies between supersingular curves to the problem of computing orientations in endomorphism rings, and we show that for a large range of degree $d$, our new algorithms improve on the state-of-the-art, and in important special cases, the range of degree $d$ for which there exist a polynomial-time algorithm is increased. In the most special case we consider, when both curves are oriented by a small degree endomorphism, we show heuristically that our techniques allow the computation of isogenies of any degree, assuming they exist.

Almost pairwise independence (API) is a quantitative property of a class of functions that is desirable in many cryptographic applications. This property is satisfied by Learning with errors (LWE)-mappings and by special Substitution-Permutation Networks (SPN). API block ciphers are known to be resilient to differential and linear cryptanalysis attacks. Recently, security of protocols against neural network-based attacks became a major trend in cryptographic studies. Therefore, it is relevant to study the hardness of learning a target function from an API class of functions by gradient-based methods.

We propose a theoretical analysis based on the study of the variance of the gradient of a general machine learning objective with respect to a random choice of target function from a class. We prove an upper bound and verify that, indeed, such a variance is extremely small for API classes of functions. This implies the resilience of actual LWE-based primitives against deep learning attacks, and to some extent, the security of SPNs. The hardness of learning reveals itself in the form of the barren plateau phenomenon during the training process, or in other words, in a low information content of the gradient about the target function. Yet, we emphasize that our bounds hold for the case of a regular parameterization of a neural network and the gradient may become informative if a class is mildly pairwise independent and a parameterization is non-regular. We demonstrate our theory in experiments on the learnability of LWE mappings.

We analyze the multi-user (mu) security of a family of nonce-based authentication encryption (nAE) schemes based on a tweakable block cipher (TBC). The starting point of our work is an analysis of the mu security of the SCT-II mode which underlies the nAE scheme Deoxys-II, winner of the CAESAR competition for the defense-in-depth category. We extend this analysis in two directions, as we detail now.

First, we investigate the mu security of several TBC-based variants of the counter encryption mode (including CTRT, the encryption mode used within SCT-II) that differ by the way a nonce, a random value, and a counter are combined as tweak and plaintext inputs to the TBC to produce the keystream blocks that will mask the plaintext blocks. Then, we consider the authentication part of SCT-II and study the mu security of the nonce-based MAC Nonce-as-Tweak (NaT) built from a TBC and an almost universal (AU) hash function. We also observe that the standard construction of an AU hash function from a (T)BC can be proven secure under the assumption that the underlying TBC is unpredictable rather than pseudorandom, allowing much better conjectures on the concrete AU advantage. This allows us to derive the mu security of the family of nAE modes obtained by combining these encryption/MAC building blocks through the NSIV composition method.

Some of these modes require an underlying TBC with a larger tweak length than what is usually available for existing ones. We then show the practicality of our modes by instantiating them with two new TBC constructions, Deoxys-TBC-512 and Deoxys-TBC-640, which can be seen as natural extensions of the Deoxys-TBC family to larger tweak input sizes. Designing such TBCs with unusually large tweaks is prone to pitfalls: Indeed, we show that a large-tweak proposal for SKINNY published at EUROCRYPT 2020 presents an inherent construction flaw. We therefore provide a sound design strategy to construct large-tweak TBCs within the Superposition Tweakey (STK) framework, leading to new Deoxys-TBC and SKINNY variants. We provide software benchmarks indicating that while ensuring a very high security level, the performances of our proposals remain very competitive.

Despite much progress, general-purpose secure multi-party computation (MPC) with active security may still be prohibitively expensive in settings with large input datasets. This particularly applies to the secure evaluation of graph algorithms, where each party holds a subset of a large graph. Recently, Araki et al. (ACM CCS '21) showed that dedicated solutions may provide significantly better efficiency if the input graph is sparse. In particular, they provide an efficient protocol for the secure evaluation of “message passing” algorithms, such as the PageRank algorithm. Their protocol's computation and communication complexity are both $\tilde{O}(M\cdot B)$ instead of the $O(M^2)$ complexity achieved by general-purpose MPC protocols, where $M$ denotes the number of nodes and $B$ the (average) number of incoming edges per node. On the downside, their approach achieves only a relatively weak security notion; $1$-out-of-$3$ malicious security with selective abort.

In this work, we show that PageRank can instead be captured efficiently as a restricted multiplication straight-line (RMS) program, and present a new actively secure MPC protocol tailored to handle RMS programs. In particular, we show that the local knowledge of the participants can be leveraged towards the first maliciously-secure protocol with communication complexity linear in $M$, independently of the sparsity of the graph. We present two variants of our protocol. In our communication-optimized protocol, going from semi-honest to malicious security only introduces a small communication overhead, but results in quadratic computation complexity $O(M^2)$. In our balanced protocol, we still achieve a linear communication complexity $O(M)$, although with worse constants, but a significantly better computational complexity scaling with $O(M\cdot B)$. Additionally, our protocols achieve security with identifiable abort and can tolerate up to $n-1$ corruptions.

Masking is a prominent strategy to protect cryptographic implementations against side-channel analysis. Its popularity arises from the exponential security gains that can be achieved for (approximately) quadratic resource utilization. Many variants of the countermeasure tailored for different optimization goals have been proposed. The common denominator among all of them is the implicit demand for robust and high entropy randomness. Simply assuming that uniformly distributed random bits are available, without taking the cost of their generation into account, leads to a poor understanding of the efficiency vs. security tradeoff of masked implementations. This is especially relevant in case of hardware masking schemes which are known to consume large amounts of random bits per cycle due to parallelism. Currently, there seems to be no consensus on how to most efficiently derive many pseudo-random bits per clock cycle from an initial seed and with properties suitable for masked hardware implementations. In this work, we evaluate a number of building blocks for this purpose and find that hardware-oriented stream ciphers like Trivium and its reduced-security variant Bivium B outperform most competitors when implemented in an unrolled fashion. Unrolled implementations of these primitives enable the flexible generation of many bits per cycle, which is crucial for satisfying the large randomness demands of state-of-the-art masking schemes. According to our analysis, only Linear Feedback Shift Registers (LFSRs), when also unrolled, are capable of producing long non-repetitive sequences of random-looking bits at a higher rate per cycle for the same or lower cost as Trivium and Bivium B. Yet, these instances do not provide black-box security as they generate only linear outputs. We experimentally demonstrate that using multiple output bits from an LFSR in the same masked implementation can violate probing security and even lead to harmful randomness cancellations. Circumventing these problems, and enabling an independent analysis of randomness generation and masking, requires the use of cryptographically stronger primitives like stream ciphers. As a result of our studies, we provide an evidence-based estimate for the cost of securely generating $n$ fresh random bits per cycle. Depending on the desired level of black-box security and operating frequency, this cost can be as low as $20n$ to $30n$ ASIC gate equivalents (GE) or $3n$ to $4n$ FPGA look-up tables (LUTs), where $n$ is the number of random bits required. Our results demonstrate that the cost per bit is (sometimes significantly) lower than estimated in previous works, incentivizing parallelism whenever exploitable. This provides further motivation to potentially move low randomness usage from a primary to a secondary design goal in hardware masking research.

Watermarking pseudorandom functions (PRF) allow an authority to embed an unforgeable and unremovable watermark into a PRF while preserving its functionality. In this work, we extend the work of Kim and Wu [Crypto'19] who gave a simple two-step construction of watermarking PRFs from a class of extractable PRFs satisfying several other properties – first construct a mark-embedding scheme, and then upgrade it to a message-embedding scheme.

While the message-embedding scheme of Kim and Wu is based on complex homomorphic evaluation techniques, we observe that much simpler constructions can be obtained and from a wider range of assumptions, if we forego the strong requirement of security against the watermarking authority. Concretely, we introduce a new notion called extractable PRGs (xPRGs), from which extractable PRFs (without security against authorities) suitable for the Kim-Wu transformations can be simply obtained via the Goldreich-Goldwasser-Micali (GGM) construction. We provide simple constructions of xPRGs from a wide range of assumptions such as hardness of computational Diffie-Hellman (CDH) in the random oracle model, as well as LWE and RSA in the standard model.

Several cryptographic schemes, including lattice-based cryptography and the SHA-2 family of hash functions, involve both integer arithmetic and Boolean logic. Each of these classes of operations, considered separately, can be efficiently implemented under the masking countermeasure when resistance against vertical attacks is required. However, protecting interleaved arithmetic and logic operations is much more expensive, requiring either additional masking conversions to switch between masking schemes, or implementing arithmetic functions as nonlinear operations over a Boolean masking. Both solutions can be achieved by providing masked arithmetic addition over Boolean shares, which is an operation with relatively long latency and usually high area utilization in hardware. A further complication arises when the arithmetic performed by the scheme is over a prime modulus, which is common in lattice-based cryptography. In this work, we propose a first-order masked implementation of arithmetic addition over Boolean shares occupying a very small area, while still having reasonable latency. Our proposal is specifically tuned for efficient addition and subtraction modulo an arbitrary integer, but it can also be configured at runtime for power-of-two arithmetic. To the best of our knowledge, we propose the first such construction whose security is formally proven in the glitch+transition-robust probing model.

Public-key searchable encryption allows keyword-associated tokens to be used to test if a ciphertext contains specific keywords. Due to the low entropies of keywords, the token holder can create ciphertexts from candidate keywords and test them using the token in hand to recover the keywords, known as inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search is a searchable encryption proposed to defend against such attacks. It ensures the sender's private key protects the ciphertexts from the IKGA. PAEKS schemes with reasonable security and practical efficiency remain elusive despite many proposals. This work provides a simple generic PAEKS scheme from non-interactive key exchange (NIKE) and symmetric-key equality-predicate encryption with three new constructions for the latter, respectively from pseudorandom functions (PRFs), the decision bilinear Diffie-Hellman assumption, and the learning-with-errors assumption. Instantiating our generic scheme, we derive several PAEKS schemes from the most well-known assumptions, with some of them achieving full cipher-keyword indistinguishability and full token indistinguishability in the standard model, for the first time. Our instantiated schemes allow practical implementations and outperform the existing PAEKS schemes under the same assumptions.

To be useful and widely accepted, automated contact tracing schemes (also called exposure notification) need to solve two seemingly contradictory problems at the same time: they need to protect the anonymity of honest users while also preventing malicious users from creating false alarms. In this paper, we provide, for the first time, an exposure notification construction that guarantees the same levels of privacy and integrity as existing schemes but with a fully malicious database (notably similar to Auerbach et al. CT-RSA 2021) without special restrictions on the adversary. We construct a new definition so that we can formally prove our construction secure. Our definition ensures the following integrity guarantees: no malicious user can cause exposure warnings in two locations at the same time and that any uploaded exposure notifications must be recent and not previously uploaded. Our construction is efficient, requiring only a single message to be broadcast at contact time no matter how many recipients are nearby. To notify contacts of potential infection, an infected user uploads data with size linear in the number of notifications, similar to other schemes. Linear upload complexity is not trivial with our assumptions and guarantees (a naive scheme would be quadratic). This linear complexity is achieved with a new primitive: zero knowledge subset proofs over commitments which is used by our "no cloning" proof protocol. We also introduce another new primitive: set commitments on equivalence classes, which makes each step of our construction more efficient. Both of these new primitives are of independent interest.

Pattern matching methods are essential in various applications where users must disclose highly sensitive information. Among these applications are genomic data analysis, financial records inspection, and intrusion detection processes, all of which necessitate robust privacy protection mechanisms. Balancing the imperative of protecting the confidentiality of analyzed data with the need for efficient pattern matching presents a significant challenge.

In this paper, we propose an efficient post-quantum secure construction that enables arbitrary pattern matching over encrypted data while ensuring the confidentiality of the data to be analyzed. In addition, we address scenarios where a malicious data sender, intended to send an encrypted content for pattern detection analysis, has the ability to modify the encrypted content. We adapt the data fragmentation technique to handle such a malicious sender. Our construction makes use of a well-suited Homomorphic Encryption packing method in the context of fragmented streams and combines homomorphic operations in a leveled mode (i.e. without bootstrapping) to obtain a very efficient pattern matching detection process.

In contrast to the most efficient state-of-the-art scheme, our construction achieves a significant reduction in the time required for encryption, decryption, and pattern matching on encrypted data. Specifically, our approach decreases the time by factors of $1850$, $10^6$, and $245$, respectively, for matching a single pattern, and by factors of $115$, $10^5$, and $12$, respectively, for matching $2^{10}$ patterns.

We present a solution to the open problem of designing a linear-time, unbiased and timing attack-resistant shuffling algorithm for fixed-weight sampling. Although it can be implemented without timing leakages of secret data in any architecture, we illustrate with ARMv7-M and ARMv8-A implementations; for the latter, we take advantage of architectural features such as NEON and conditional instructions, which are representative of features available on architectures targeting similar systems, such as Intel. Our proposed algorithm improves asymptotically upon the current approach based on constant-time sorting networks ($O(n)$ versus $O(n \log^2 n)$), and an implementation of the new algorithm applied to NTRU is also faster in practice, by a factor of up to $6.91\ (591\%)$ on ARMv8-A cores and $12.89\ (1189\%)$ on the Cortex-M4; it also requires fewer uniform random bits. This translates into performance improvements for NTRU encapsulation, compared to state-of-the-art implementations, of up to 50% on ARMv8-A cores and 72% on the Cortex-M4, and small improvements to key generation (up to 2.7% on ARMv8-A cores and 6.1% on the Cortex-M4), with negligible impact on code size and a slight improvement in RAM usage for the Cortex-M4.

Fischlin's transform (CRYPTO 2005) is an alternative to the Fiat-Shamir transform that enables straight-line extraction when proving knowledge. In this work we focus on the problem of using the Fischlin transform to construct UC-secure zero-knowledge from Sigma protocols, since UC security – that guarantees security under general concurrent composition – requires straight-line (non-rewinding) simulators. We provide a slightly simplified transform that is much easier to understand, and present algorithmic and implementation optimizations that significantly improve the running time. It appears that the main obstacles to the use of Fischlin in practice is its computational cost and implementation complexity (with multiple parameters that need to be chosen). We provide clear guidelines and a simple methodology for choosing parameters, and show that with our optimizations the running-time is far lower than expected. For just one example, on a 2023 MacBook, the cost of proving the knowledge of discrete log with Fischlin is only 0.41ms (on a single core). This is 15 times slower than plain Fiat-Shamir on the same machine, which is a significant multiple but objectively not significant in many applications. We also extend the transform so that it can be applied to batch proofs, and show how this can be much more efficient than individually proving each statement. We hope that this paper will both encourage and help practitioners implement the Fischlin transform where relevant.

Decentralized Multi-Client Functional Encryption (DMCFE) extends the basic functional encryption to multiple clients that do not trust each other. They can independently encrypt the multiple plaintext-inputs to be given for evaluation to the function embedded in the functional decryption key, defined by multiple parameter-inputs. And they keep control on these functions as they all have to contribute to the generation of the functional decryption keys. Tags can be used in the ciphertexts and the keys to specify which inputs can be combined together. As any encryption scheme, DMCFE provides privacy of the plaintexts. But the functions associated to the functional decryption keys might be sensitive too (e.g. a model in machine learning). The function-hiding property has thus been introduced to additionally protect the function evaluated during the decryption process.

In this paper, we provide new proof techniques to analyze a new concrete construction of function-hiding DMCFE for inner products, with strong security guarantees: the adversary can adaptively query multiple challenge ciphertexts and multiple challenge keys, with unbounded repetitions of the same tags in the ciphertext-queries and a fixed polynomially-large number of repetitions of the same tags in the key-queries. Previous constructions were proven secure in the selective setting only.

This paper develops Central Limit arguments for analysing the noise in ciphertexts in two homomorphic encryption schemes that are based on Ring-LWE. The first main contribution of this paper is to present and evaluate an average-case noise analysis for the BGV scheme. Our approach relies on the recent work of Costache et al.(SAC 2023) that gives the approximation of a polynomial product as a multivariate Normal distribution. We show how this result can be applied in the BGV context and evaluate its efficacy. We find this average-case approach can much more closely model the noise growth in BGV implementations than prior approaches, but in some cases it can also underestimate the practical noise growth. Our second main contribution is to develop a Central Limit framework to analyse the noise growth in the homomorphic Ring-LWE cryptosystem of Lyubashevsky, Peikert and Regev (Eurocrypt 2013, full version). Our approach is very general: apart from finite variance, no assumption on the distribution of the noise is required (in particular, the noise need not be subgaussian). We show that our approach leads to tighter bounds for the probability of decryption failure than those of prior work.

Transitioning from classically to quantum secure key agreement protocols may require to exchange fundamental components, for example, exchanging Diffie-Hellman-like key exchange with a key encapsulation mechanism (KEM). Accordingly, the corresponding security proof can no longer rely on the Diffie-Hellman assumption, thus invalidating the security guarantees. As a consequence, the security properties have to be re-proven under a KEM-based security notion.

We initiate the study of the LDACS key agreement protocol (Edition 01.01.00 from 25.04.2023), which is soon-to-be-standardized by the International Civil Aviation Organization. The protocol's cipher suite features Diffie-Hellman as well as a KEM-based key agreement protocol to provide post-quantum security. While the former results in an instantiation of an ISO key agreement inheriting all security properties, the security achieved by the latter is ambiguous. We formalize the computational security using the systematic notions of de Saint Guilhem, Fischlin and Warinshi (CSF '20), and prove the exact security that the KEM-based variant achieves in this model; primarily entity authentication, key secrecy and key authentication. To further strengthen our “pen-and-paper” findings, we model the protocol and its security guarantees using Tamarin, providing an automated proof of the security against a Dolev-Yao attacker.

One of the central questions in cryptology is how efficient generic constructions of cryptographic primitives can be. Gennaro, Gertner, Katz, and Trevisan [SIAM J. of Compt., 2005] studied the lower bounds of the number of invocations of a (trapdoor) one-way permutation in order to construct cryptographic schemes, e.g., pseudorandom number generators, digital signatures, and public-key and symmetric-key encryption.

Recently, quantum machines have been explored to _construct_ cryptographic primitives other than quantum key distribution. This paper studies the efficiency of _quantum_ black-box constructions of cryptographic primitives when the communications are _classical_. Following Gennaro et al., we give the lower bounds of the number of invocations of an underlying quantumly-computable quantum-one-way permutation when the _quantum_ construction of pseudorandom number generator and symmetric-key encryption is weakly black-box. Our results show that the quantum black-box constructions of pseudorandom number generator and symmetric-key encryption do not improve the number of invocations of an underlying quantumly-computable quantum-one-way permutation.

Biscuit is a recent multivariate signature scheme based on the MPC-in-the-Head paradigm. It has been submitted to the NIST competition for additional signature schemes. Signatures are derived from a zero-knowledge proof of knowledge of the solution of a structured polynomial system. This extra structure enables efficient proofs and compact signatures. This short note demonstrates that it also makes these polynomial systems easier to solve than random ones. As a consequence, the original parameters of Biscuit failed to meet the required security levels and had to be upgraded.

X-Wing is a hybrid key-encapsulation mechanism based on X25519 and ML-KEM-768. It is designed to be the sensible choice for most applications. The concrete choice of X25519 and ML-KEM-768 allows X-Wing to achieve improved efficiency compared to using a generic KEM combiner. In this paper, we introduce the X-Wing hybrid KEM construction and provide a proof of security. We show (1) that X-Wing is a classically IND-CCA secure KEM if the strong Diffie-Hellman assumption holds in the X25519 nominal group, and (2) that X-Wing is a post-quantum IND-CCA secure KEM if ML-KEM-768 is itself an IND-CCA secure KEM and SHA3-256 is secure when used as a pseudorandom function. The first result is proved in the ROM, whereas the second one holds in the standard model. Loosely speaking, this means X-Wing is secure if either X25519 or ML-KEM-768 is secure. We stress that these security guarantees and optimizations are only possible due to the concrete choices that were made, and it may not apply in the general case.

In a multiparty signing protocol, also known as a threshold signature scheme, the private signing key is shared amongst a set of parties and only a quorum of those parties can generate a signature. Research on multiparty signing has been growing in popularity recently due to its application to cryptocurrencies. Most work has focused on reducing the number of rounds to two, and as a result: (a) are not fully simulatable in the sense of MPC real/ideal security definitions, and/or (b) are not secure under concurrent composition, and/or (c) utilize non-standard assumptions of different types in their proofs of security. In this paper, we describe a simple three-round multiparty protocol for Schnorr signatures that is secure for any number of corrupted parties; i.e., in the setting of a dishonest majority. The protocol is fully simulatable, secure under concurrent composition, and proven secure in the standard model or random-oracle model (depending on the instantiations of the commitment and zero-knowledge primitives). The protocol realizes an ideal Schnorr signing functionality with perfect security in the ideal commitment and zero-knowledge hybrid model (and thus the only assumptions needed are for realizing these functionalities).

In our presentation, we do not assume that all parties begin with the message to be signed, the identities of the participating parties and a unique common session identifier, since this is often not the case in practice. Rather, the parties achieve consensus on these parameters as the protocol progresses.

Proving whether it is possible to build IND-CCA public-key encryption (PKE) from IND-CPA PKE in a black-box manner is a major open problem in theoretical cryptography. In a significant breakthrough, Gertner, Malkin and Myers showed in 2007 that shielding black-box reductions from IND-CCA to IND-CPA do not exist in the standard model. Shielding means that the decryption algorithm of the IND-CCA scheme does not call the encryption algorithm of the underlying IND-CPA scheme. In other words, it implies that every tentative construction of IND-CCA from IND-CPA must have a re-encryption step when decrypting.

This result was only proven with respect to classical algorithms. In this work we show that it stands in a post-quantum setting. That is, we prove that there is no post-quantum shielding black-box construction of IND-CCA PKE from IND-CPA PKE. In the type of reductions we consider, i.e. post-quantum ones, the constructions are still classical in the sense that the schemes must be computable on classical computers, but the adversaries and the reduction algorithm can be quantum. This suggests that considering quantum notions, which are stronger than their classical counterparts, and allowing for quantum reductions does not make building IND-CCA public-key encryption easier.

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This fundamental problem in query complexity appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider three options for the inversion algorithm: whether it can get quantum advice about the permutation, whether the query algorithm can restrict the distribution with which the challenge input is sampled, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the permutation inversion problem and establish lower bounds for them. Our results show that, perhaps surprisingly, the permutation inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse—provided it cannot query the challenge itself.

We prove that isogenies between Drinfeld F[x]-modules over a finite field can be computed in polynomial time. This breaks Drinfeld analogs of isogeny-based cryptosystems.

In recent years, quantum technology has been rapidly developed. As security analyses for symmetric ciphers continue to emerge, many require an evaluation of the resources needed for the quantum circuit implementation of the encryption algorithm. In this regard, we propose the quantum circuit decision problem, which requires us to determine whether there exists a quantum circuit for a given permutation f using M ancilla qubits and no more than K quantum gates within the circuit depth D. Firstly, we investigate heuristic algorithms and classical SAT-based models in previous works, revealing their limitations in solving the problem. Hence, we innovatively propose an improved SAT-based model incorporating three metrics of quantum circuits. The model enables us to find the optimal quantum circuit of an arbitrary 3 or 4-bit S-box under a given optimization goal based on SAT solvers, which has proved the optimality of circuits constructed by the tool, LIGHTER-R. Then, by combining different criteria in the model, we find more compact quantum circuit implementations of S-boxes such as RECTANGLE and GIFT. For GIFT S-box, our model provides the optimal quantum circuit that only requires 8 gates with a depth of 31. Furthermore, our model can be generalized to linear layers and improve the previous SAT-based model proposed by Huang et al. in ASIACRYPT 2022 by adding the criteria on the number of qubits and the circuit depth.

The LowMC family of block ciphers was proposed by Albrecht et al. in Eurocrypt 2015, specifically targeting adoption in FHE and MPC applications due to its low multiplicative complexity. The construction operates a 3-bit quadratic S-box as the sole non-linear transformation in the algorithm. In contrast, both the linear layer and round key generation are achieved through multiplications of full rank matrices over GF(2). The cipher is instantiable using a diverse set of default configurations, some of which have partial non-linear layers i.e., in which the S-boxes are not applied over the entire internal state of the cipher.

The significance of cryptanalysing LowMC was elevated by its inclusion into the NIST PQC digital signature scheme PICNIC in which a successful key recovery using a single plaintext/ciphertext pair is akin to retrieving the secret signing key. The current state-of-the-art attack in this setting is due to Dinur at Eurocrypt 2021, in which a novel way of enumerating roots of a Boolean system of equation is morphed into a key-recovery procedure that undercuts an ordinary exhaustive search in terms of time complexity for the variants of the cipher up to five rounds.

In this work, we demonstrate that this technique can efficiently be enriched with a specific linearization strategy that reduces the algebraic degree of the non-linear layer as put forward by Banik et al. at IACR ToSC 2020(4). This amalgamation yields new attacks on certain instances of LowMC up to seven rounds.

We revisit the question of what the definition of bit security should be, previously answered by Micciancio-Walter (Eurocrypt 2018) and Watanabe-Yasunaga (Asiacrypt 2021). Our new definition is simple, but (i) captures both search and decision primitives in a single framework like Micciancio-Walter, and (ii) has a firm operational meaning like Watanabe-Yasunaga. It also matches intuitive expectations and can be well-formulated regarding Hellinger distance. To support and justify the new definition, we prove several classic security reductions with respect to our bit security. We also provide pathological examples that indicate the ill-definedness of bit security defined in Micciancio-Walter and Watanabe-Yasunaga.

Predicate encryption (PE) is a type of public-key encryption that captures many useful primitives such as attribute-based encryption (ABE). Although much progress has been made to generically achieve security against chosen-plaintext attacks (CPA) efficiently, in practice, we also require security against chosen-ciphertext attacks (CCA). Because achieving CCA-security on a case-by-case basis is a complicated task, several generic conversion methods have been proposed, which typically target different subclasses of PE such as ciphertext-policy ABE. As is common, such conversion methods may sacrifice some efficiency. Notably, for ciphertext-policy ABE, all proposed generic transformations incur a significant decryption overhead. Furthermore, depending on the setting in which PE is used, we may also want to require that messages are signed. To do this, predicate signature schemes can be used. However, such schemes provide a strong notion of privacy for the signer, which may be stronger than necessary for some practical settings at the cost of efficiency.

In this work, we propose the notion of predicate extension, which transforms the predicate used in a PE scheme to include one additional attribute, in both the keys and the ciphertexts. Using predicate extension, we can generically obtain CCA-security and signatures from a CPA-secure PE scheme. For the CCA-security transform, we observe that predicate extension implies a two-step approach to achieving CCA-security. This insight broadens the applicability of existing transforms for specific subclasses of PE to cover all PE. We also propose a new transform that incurs slightly less overhead than existing transforms. Furthermore, we show that predicate extension allows us to create a new type of signatures, which we call PE-based signatures. PE-based signatures are weaker than typical predicate signatures in the sense that they do not provide privacy for the signer. Nevertheless, such signatures may be more suitable for some practical settings owing to their efficiency or reduced interactivity. Lastly, to show that predicate extensions may facilitate a more efficient way to achieve CCA-security generically than existing methods, we propose a novel predicate-extension transformation for a large class of pairing-based PE, covered by the pair and predicate encodings frameworks. In particular, this yields the most efficient generic CCA-conversion for ciphertext-policy ABE.

Fully Homomorphic Encryption (FHE) is a prevalent cryptographic primitive that allows for computation on encrypted data. In various cryptographic protocols, this enables outsourcing computation to a third party while retaining the privacy of the inputs to the computation. However, these schemes make an honest-but-curious assumption about the adversary. Previous work has tried to remove this assumption by combining FHE with Verifiable Computation (VC). Recent work has increased the flexibility of this approach by introducing integrity checks for homomorphic computations over rings. However, efficient FHE for circuits of large multiplicative depth also requires non-ring computations called maintenance operations, i.e. modswitching and keyswitching, which cannot be efficiently verified by existing constructions. We propose the first efficiently verifiable FHE scheme that allows for arbitrary depth homomorphic circuits by utilizing the double-CRT representation in which FHE schemes are typically computed, and using lattice-based SNARKs to prove components of this computation separately, including the maintenance operations. Therefore, our construction can theoretically handle bootstrapping operations. We also present the first implementation of a verifiable computation on encrypted data for a computation that contains multiple ciphertext-ciphertext multiplications. Concretely, we verify the homomorphic computation of an approximate neural network containing three layers and >100 ciphertexts in less than 1 second while maintaining reasonable prover costs.

The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.

Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.

In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage.

We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded.

Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have to read the entire input). In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold.

We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest.

As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for $\mathsf{NP}$.

There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89).

However, the distribution of quantum public keys is a challenging task. Therefore, the main question that motivates our work is if quantum PKE from OWF is possible if we have classical public keys. Such protocols are impossible if ciphertexts are also classical, given the impossibility result of Austrin et al.(CRYPTO'22) of quantum enhanced key-agreement (KA) with classical communication.

In this paper, we focus on black-box separation for PKE with classical public key and quantum ciphertext from OWF under the polynomial compatibility conjecture, first introduced in Austrin et al.. More precisely, we show the separation when the decryption algorithm of the PKE does not query the OWF. We prove our result by extending the techniques of Austrin et al. and we show an attack for KA in an extended classical communication model where the last message in the protocol can be a quantum state.