International Association
for Cryptologic Research

Masking has become a widely applied and heavily researched method to protect cryptographic implementations against SCA attacks. The success of masking is primarily attributed to its strong theoretical foundation enabling it to formally prove security by modeling physical properties through so-called probing models. Specifically, the robust $d$-probing model enables us to prove the security for arbitrarily masked hardware circuits, manually or with the assistance of automated tools, even when considering the imperfect nature of physical hardware, including the occurrence of physical defaults such as glitches. However, the generic strategy employed by the robust $d$-probing model comes with a downside: It tends to over-conservatively model the information leakage caused by glitches meaning that the robust $d$-probing model considers glitches that can never occur in practice. This implies that in theory, an adversary could gain more information than she would obtain in practice. From a designer's perspective, this entails that (1) securely designed hardware circuits may need to be withdrawn due to potential insecurity under the robust $d$-probing model and (2) designs that satisfy the security requirements of the robust $d$-probing model may incur unnecessary overhead, such as increased circuit size or latency. In this work, we refine the formal treatment of glitches within the robust $d$-probing model to address glitches more accurately within a formal adversary model. Unlike the robust $d$-probing model, our approach considers glitches based on the operations performed and the data processed, ensuring that only manifesting glitches are accounted for. As a result, we introduce the RR $d$-probing model, a formal adversary model maintaining the same level of security as the robust $d$-probing model but without the overly conservative treatment of glitches. Leveraging our new model, we prove the security of \ac{LMDPL} gadgets, a class of physically secure gadgets reported as insecure based on the robust $d$-probing model. We provide manual proofs and automated security evaluations employing an updated version of PROLEAD capable of verifying the security of masked circuits under our new model.

A compiler introduced by Kalai et al. (STOC'23) converts any nonlocal game into an interactive protocol with a single computationally-bounded prover. Although the compiler is known to be sound in the case of classical provers, as well as complete in the quantum case, quantum soundness has so far only been established for special classes of games. In this work, we establish a quantum soundness result for all compiled two-player nonlocal games. In particular, we prove that the quantum commuting operator value of the underlying nonlocal game is an upper bound on the quantum value of the compiled game. Our result employs techniques from operator algebras in a computational and cryptographic setting to establish information-theoretic objects in the asymptotic limit of the security parameter. It further relies on a sequential characterization of quantum commuting operator correlations which may be of independent interest.

MIFARE Classic smart cards, developed and licensed by NXP, are widely used but have been subjected to numerous attacks over the years. Despite the introduction of new versions, these cards have remained vulnerable, even in card-only scenarios. In 2020, the FM11RF08S, a new variant of MIFARE Classic, was released by the leading Chinese manufacturer of unlicensed "MIFARE compatible" chips. This variant features specific countermeasures designed to thwart all known card-only attacks and is gradually gaining market share worldwide. In this paper, we present several attacks and unexpected findings regarding the FM11RF08S. Through empirical research, we discovered a hardware backdoor and successfully cracked its key. This backdoor enables any entity with knowledge of it to compromise all user-defined keys on these cards without prior knowledge, simply by accessing the card for a few minutes. Additionally, our investigation into older cards uncovered another hardware backdoor key that was common to several manufacturers.

For secure multi-party computation in the line of the secret-sharing based SPDZ protocol, actively secure multiplications consume correlated randomness in the form of authenticated Beaver triples, which need to be generated in advance. Although it is a well-studied problem, the generation of Beaver triples is still a bottleneck in practice. In the two-party setting, the best solution with low communication overhead is the protocol by Boyle et al. (Crypto 2020), which is derived from the recent primitive of Pseudorandom Correlation Generators (PCGs) (Crypto 2019). Their protocol requires less than 2 MB of communication to generate about 100 MB of Beaver triples (per party). In this work, we improve their protocol in terms of communication (7%), computation (20% for its interactive phase), and the amount of correlated randomness consumed by internal secure two-party computations (11% storage). To achieve our improvements, we propose a novel actively secure protocol for the efficient generation of (authenticated) secret-shared scaled unit vectors, which in general are the main building blocks of current PCG protocols.

Zero-knowledge proofs allow one party to prove the truth of a statement without disclosing any extra information. Recent years have seen great improvements in zero-knowledge proofs. Among them, zero-knowledge SNARKs are notable for their compact and efficiently-verifiable proofs but face challenges with high prover costs for large-scale applications. To accelerate proof generation, Pianist (Liu et al, S&P 2024) proposes to distribute the proof generation process across multiple machines, and achieves a significant reduction in overall prover time. However, Pianist inherits the quasi-linear computational complexity from its underlying SNARK proof system Plonk, limiting its scalability and efficiency with large circuits. In this paper, we introduce HyperPianist, a fully distributed proof system with linear-time prover complexity and logarithmic communication cost among distributed machines. Starting from deVirgo (Cheng et al., CCS 2024), we study their distributed multivariate SumCheck protocol and achieve logarithmic communication cost by using an additively homomorphic multivariate polynomial commitment scheme in the distributed setting. Given the distributed SumCheck protocol, we then adapt HyperPlonk (Chen et al., EuroptCrypt 2023), a proof system based on multivariate polynomials, to the distributed setting without extra overhead for witness re-distribution. In addition, we propose a more efficient construction of lookup arguments based on Lasso (Setty et al., Eurocrypt 2024), and adapt it to the distributed setting to enhance HyperPianist and obtain HyperPianist+.

We study the linear code equivalence problem (LEP) for linear $[n,k]$-codes over finite fields $\mathbb{F}_q$. Recently, Chou, Persichetti and Santini gave an elegant heuristic algorithm that solves LEP over large finite fields (with $q = \Omega(n)$) in time $2^{\frac{1}{2}\operatorname{H}\left(\frac{k}{n}\right)n}$, where $\operatorname{H}(\cdot)$ denotes the binary entropy function. However, for small finite fields, their algorithm can be significantly slower. In particular, for fields of constant size $q = \mathcal{O}(1)$, its runtime increases by an exponential factor $2^{\Theta(n)}$. We present an improved and provably correct version of their algorithm, which achieves the desired runtime of $2^{\frac{1}{2}\operatorname{H}\left(\frac{k}{n}\right)n}$ for all finite fields of size $q \geq 7$. For a wide range of parameters, this improves over the runtime of all previously known algorithms by an exponential factor.

The recent VOLE-based interactive zero-knowledge (VOLE-ZK) protocols along with non-interactive zero-knowledge (NIZK) proofs based on MPC-in-the-Head (MPCitH) and VOLE-in-the-Head (VOLEitH) extensively utilize the commitment schemes, which adopt a circular correlation robust (CCR) hash function as the core primitive. Nevertheless, the state-of-the-art CCR hash construction by Guo et al. (S&P'20), building from random permutations, can only provide 128-bit security, when it is instantiated from AES. This brings about a gap between AES-based CCR hash function and high security (beyond 128-bit security). In this paper, we fill this gap by constructing a new CCR hash function from AES, supporting three security levels (i.e., 128, 192 and 256). Using the AES-based CCR hash function, we present an all-but-one vector commitment (AVC) scheme, which constitutes a computationally intensive part of the NIZK proofs from MPCitH and VOLEitH, where these NIZK proofs can in turn be transformed into the promising post-quantum signature candidates. Furthermore, we obtain an efficient VOLE-ZK protocol with security levels higher than 128 from the CCR hash function. Our benchmark results show that the AES-based CCR hash function has a comparable performance with CCR hash functions based on Rijndael with larger block sizes, which is not standardized and has a limited application range. In the AVC context, the expensive commitment component instantiated with our AES-based CCR hash function improves the running time by a factor of $7 \sim 30 \times$, compared to the SHA3-based instantiation used in the recent post-quantum signature algorithm FAEST.

\scarf, an ultra low-latency tweakable block cipher, is the first cipher designed for cache randomization. The block cipher design is significantly different from the other common tweakable block ciphers; with a block size of only 10 bits, and yet the input key size is a whopping $240$ bits. Notably, the majority of the round key in its round function is absorbed into the data path through AND operations, rather than the typical XOR operations. In this paper, we present a key-recovery attack on a round-reduced version of SCARF with 4 + 4 rounds under the single-tweak setting. Our attack is essentially a Meet-in-the-Middle (MitM) attack, where the matching phase is represented by a system of linear equations. Unlike the cryptanalysis conducted by the designers, our attack is effective under both security requirements they have outlined. The data complexity of our attack is $2^{10}$ plaintexts, with a time complexity of approximately $2^{60.63}$ 4-round of SCARF encryptions. It is important to note that our attack does not threaten the overall security of SCARF.

This study addresses the challenge of strengthening cryptographic security measures in the face of evolving cyber threats. The aim is to apply Kleene's Theorem and automata theory to improve the modeling and analysis of cybersecurity scenarios, focusing on the CyberMoraba game. Representing the game's strategic moves as regular expressions and mapping them onto finite automata provides a solid framework for understanding the interactions between attackers and defenders. This approach helps in identifying optimal strategies and predicting potential outcomes, which contributes to the development of stronger cryptographic security protocols. The research advances the theoretical use of automata theory in cybersecurity while offering practical insights into enhancing defense mechanisms against complex cyber attacks. This work connects theoretical computer science with practical cybersecurity, demonstrating the importance of automata theory in cryptology.

We study the problem of generating public unbiased randomness in a distributed manner within the recent You Only Speak Once (YOSO) framework for stateless multiparty computation, introduced by Gentry et al. in CRYPTO 2021.

Such protocols are resilient to adaptive denial-of-service attacks and are, by their stateless nature, especially attractive in permissionless environments.

While most works in the YOSO setting focus on independent random corruptions, we consider YOSO protocols with worst-case corruptions, a model introduced by Nielsen et al. in CRYPTO 2022.

Prior work on YOSO public randomness generation with worst-case corruptions designed information-theoretic protocols for $t$ corruptions with either $n=6t+1$ or $n=5t$ roles, depending on the adversarial network model.

However, a major drawback of these protocols is that their communication and computational complexities scale exponentially with $t$.

In this work, we complement prior inefficient results by presenting and analyzing simple and efficient protocols for YOSO public randomness generation secure against worst-case corruptions in the computational setting.

Our first protocol is based on publicly verifiable secret sharing and uses $n=3t+2$ roles.

Since this first protocol requires setup and somewhat heavy cryptographic machinery, we also provide a second lighter protocol based on ElGamal commitments and verifiable secret sharing which uses $n=5t+4$ or $n=4t+4$ roles depending on the underlying network model. We demonstrate the practicality of our second protocol by showing experimental evaluations, significantly improving over prior proposed solutions for worst-case corruptions, especially in terms of transmitted data size.

The formal verification of architectural strength in terms of computational complexity is achieved through reduction of the Non-Commutative Grothendieck problem in the form of a quadratic lattice. This multivariate form relies on equivalences derived from a k-clique problem within a multigraph. The proposed scheme reduces the k-clique problem as an input function, resulting in the generation of a quadratic used as parameters for the lattice. By Grothendieck’s inequality, the satisfiability of lattice constraints in terms of NP-Hard and NP-Complete bounds is provably congruent to a closest vector problem in the lattice. The base vectors of the resulting lattice are treated as a holomorphic vector bundle. From the resulting bilinear matrices, the tight hardness reduction of the closest vector problem as the shortest vector problem is introduced within the system. The derivation of the closest vector problem requires that the lattice is necessarily generated by a <0|1>-Matrix expressed as a quadratic. This vector bundle is denoted as the unit ball with congruent topology to the Riemann sphere, symbolized as ?. For the Grothendieck constraints, the relative vector norms necessarily result in satisfaction of NP-Hard requirements for shortest vector problems in the lattice.

Topology-hiding broadcast (THB) enables parties communicating over an incomplete network to broadcast messages while hiding the network topology from within a given class of graphs. Although broadcast is a privacy-free task, it is known that THB for certain graph classes necessitates computational assumptions, even against "honest but curious" adversaries, and even given a single corrupted party. Recent works have tried to understand when THB can be obtained with information-theoretic (IT) security (without cryptography or setup assumptions) as a function of properties of the corresponding graph class.

We revisit this question through a case study of the class of wheel graphs and their subgraphs. The $n$'th wheel graph is established by connecting $n$ nodes who form a cycle with another "center" node, thus providing a natural extension that captures and enriches previously studied graph classes in the setting of IT-THB.

We present a series of new findings in this line. We fully characterize feasibility of IT-THB for any class of subgraphs of the wheel, each possessing an embedded star (i.e., a well-defined center connected to all other nodes). Our characterization provides evidence that IT-THB feasibility may correlate with a more fine-grained degree structure---as opposed to pure connectivity---of the corresponding graphs. We provide positive results achieving perfect IT-THB for new graph classes, including ones where the number of nodes is unknown. Further, we provide the first feasibility of IT-THB on non-degenerate graph-classes with $t>1$ corruptions, for the class of friendship graphs (Erdos, Renyi, Sos '66).

This paper surveys interactions between choices of elliptic curves and the security of elliptic-curve cryptography. Attacks considered include not just discrete-logarithm computations but also attacks exploiting common implementation pitfalls.

Lookup arguments have recently attracted a lot of developments due to their applications in the constructions of succinct non-interactive arguments of knowledge (SNARKs). A closely related topic is subsequence arguments in which one can prove that string $\mathbf{s}$ is a subsequence of another string $\mathbf{t}$, i.e., deleting some characters in $\mathbf{t}$ can achieve $\mathbf{s}$. A dual notion, namely, non-subsequence arguments, is to prove that $\mathbf{s}$ is not a subsequence of $\mathbf{t}$. These problems have a lot of important applications in DNA sequence analysis, internet of things, blockchains, natural language processing, speech recognition, etc. However, despite their applications, they are not well-studied in cryptography, especially succinct arguments for non-subsequences with efficient proving time and sublinear verification time.

In this work, we propose the first succinct non-subsequence argument. Our solution applies the sumcheck protocol and is instantiable by any multivariate polynomial commitment schemes (PCSs). We achieve an efficient prover whose running time is linear in the size of sequences $\mathbf{s}$, $\mathbf{t}$ and their respective alphabet $\Sigma$. Our proof is succinct and the verifier time is sublinear assuming the employed PCS has succinct commitments and sublinear verification time. When instantiating with Sona PCS (EUROCRYPT'24), we achieve proof size $\mathcal{O}(\log_2|\mathbf{s}| + \log_2|\mathbf{t}|+\log_2|\Sigma|)$, prover time $\mathcal{O}(|\mathbf{s}|+|\mathbf{t}|+|\Sigma|)$ and verifier time $\mathcal{O}(\sqrt{|\mathbf{s}|}+\sqrt{|\mathbf{t}|}+\sqrt{|\Sigma|})$.

Extending our technique, we can achieve a batch subsequence argument for proving in batch $k$ interleaving subsequence and non-subsequence arguments without proof size suffering a linear blow-up in $k$.

Let $N=pq$ be the product of two balanced prime numbers $p$ and $q$. In 2002, Elkamchouchi, Elshenawy and Shaban introduced an RSA-like cryptosystem that uses the key equation $ed - k (p^2-1)(q^2-1) = 1$, instead of the classical RSA key equation $ed - k (p-1)(q-1) = 1$. Another variant of RSA, presented in 2017 by Murru and Saettone, uses the key equation $ed - k (p^2+p+1)(q^2+q+1) = 1$. Despite the authors' claims of enhanced security, both schemes remain vulnerable to adaptations of common RSA attacks. Let $n$ be an integer. This paper proposes two families of RSA-like encryption schemes: one employs the key equation $ed - k (p^n-1)(q^n-1) = 1$ for $n > 0$, while the other uses $ed - k [(p^n-1)(q^n-1)]/[(p-1)(q-1)] = 1$ for $n > 1$. Note that we remove the conventional assumption of primes having equal bit sizes. In this scenario, we show that regardless of the choice of $n$, continued fraction-based attacks can still recover the secret exponent. Additionally, this work fills a gap in the literature by establishing an equivalent of Wiener's attack when the primes do not have the same bit size.

Verifiable Timed Signatures (VTS) are cryptographic constructs that enable obtaining a signature at a specific time in the future and provide evidence that the signature is legitimate. This framework particularly finds utility in applications such as payment channel networks, multiparty signing operations, or multiparty computation, especially within blockchain architectures. Currently, VTS schemes are based on signature algorithms such as BLS signature, Schnorr signature, and ECDSA. These signature algorithms are considered insecure against quantum attacks due to the effect of Shor's Algorithm on the discrete logarithm problem. We present a new VTS scheme called VT-Dilithium based on CRYSTALS-Dilithium Digital Signature Algorithm that has been selected as NIST's quantum-resistant digital signature standard and is considered secure against both classical and quantum attacks. Integrating Dilithium into the VTS scheme is more challenging problem due to its complex mathematical operations (i.e. polynomial multiplications, rounding operations) and large module parameters such as polynomials, polynomial vectors, and matrices. This work aims to provide a comprehensive exposition of the VT-Dilithium scheme.

We present a key-recovery attack on a variant of the Seasign signature scheme presented by [Kim24], which attempts to avoid rejection sampling by presampling vectors $\mathbf{f}$ such that the $\mathbf{f}-\mathbf{e}$ is contained in an acceptable bound, where $\mathbf{e}$ is the secret key. We show that this choice leads to a bias of these vectors such that, in a small number of signatures, the secret key can either be completely recovered or its keyspace substantially reduced. In particular, on average, given $20$ signatures, with parameter set II of their paper, the attack reduces the private key to 128 possibilities

Privacy preserving systems often need to allow anonymity while requiring accountability. For anonymous clients, depending on application, this may mean banning/revoking their accounts, docking their reputation, or updating their state in some complex access control scheme. Frequently, these operations happen asynchronously when some violation, e.g., a forum post, is found well after the offending action occurred. Malicious clients, naturally, wish to evade this asynchronous negative feedback. Considering privacy-preserving analogues of modern access control and reputation schemes raises a more fundamental technical challenge with far broader applications: how do we allow multiple parties to interact with private state stored by an anonymous client while ensuring state integrity and supporting oblivious updates?

We propose zk-promises, a framework which supports Turing-complete state machines with arbitrary asynchronous callbacks. In zk-promises, client state is stored in a zk-object. Updates to the zk-object, represented as a cryptographic commitment to the new, modified object, require a zkSNARK that ensures integrity and atomicity while providing confidentiality. Clients can modify and prove their state by calling valid methods (e.g, to show they are authorized to post) and can give callbacks to third parties (e.g., to later hold them accountable). Through careful protocol design, we ensure clients who advance their state-machine are forced to ingest callbacks that are called by a third party.

zk-promises allows us to build a privacy-preserving account model. State that would normally be stored on a trusted server can be privately outsourced to the client while preserving the server's ability to update the account. To demonstrate the feasibility of our approach, we build an anonymous reputation system with better than state-of-the-art performance and features, supporting asynchronous reputation updates, banning, and reputation-dependent rate limiting to better protect against Sybil attacks.

Many applications rely on accumulators and authenticated dictionaries, from timestamping certificate transparency and memory checking to blockchains and privacy-preserving decentralized electronic money, while Merkle tree and its variants are efficient for arbitrary element membership proofs, non-membership proofs, i.e., universal accumulators, and key-based membership proofs may require trees up to 256 levels for 128 bits of security, assuming binary tree, which makes it inefficient in practice, particularly in the context of zero-knowledge proofs.

Building on the hardness of multi-collision we introduce a novel (non-)membership, optionally key-value, accumulator with up to 2x smaller tree depth while preserving the same security level, as well as multiple application-specific versions with even shallower trees, up to 6x smaller depth, that rely on the low-entropy source. Moreover, solving for special case of adversarial attacks we introduce key index variants which might be a stepping stone for an entropy-free accumulator.

Notably, unlike other constructions, this work, although may, doesn't depend on the dynamic depth of the tree which is simpler and more suitable for constant-size ZKP circuits, while ensuring a substantially smaller upper bound on depth.

Efficient in practice construction in the adversarial context, e.g. blockchain, where the tree manager doesn't need to be trusted, i.e., operations can be carried out by an untrusted party and verified by anyone, is the primary goal. Example instantiations are considered, where special treatment is given to the application of representing serial numbers, aka nullifiers. Nevertheless, the constructions are self-sufficient and can be used in other contexts, without blockchain and/or zero-knowledge proofs, including non-adversarial contexts.

Furthermore, our findings might be of independent interest for other use cases, such as hash tables, databases and other data structures.

In the multi-user with corruptions (muc) setting there are $n\geq 1$ users, and the goal is to prove that, even in the face of an adversary that adaptively corrupts users to expose their keys, un-corrupted users retain security. This can be considered for many primitives including signatures and encryption. Proofs of muc security, while possible, generally suffer a factor n loss in tightness, which can be large. This paper gives new proofs where this factor is reduced to the number c of corruptions, which in practice is much smaller than n. We refer to this as corruption-parametrized muc (cp-muc) security. We give a general result showing it for a class of games that we call local. We apply this to get cp-muc security for signature schemes (including ones in standards and in TLS 1.3) and some forms of public-key and symmetric encryption. Then we give dedicated cp-muc security proofs for some important schemes whose underlying games are not local, including the Hashed ElGamal and Fujisaki-Okamoto KEMs and authenticated key exchange. Finally, we give negative results to show optimality of our bounds.