Remote power analysis is a novel threat to information systems. Under this attack model, the adversary does not require direct physical access to the platform or specialized sensing equipment. Most of the literature in this field deals with advanced acquisition methods and adversarial models. In contrast, side-channel analysis techniques for remote attacks have not been sufficiently explored. We bridge this gap by taking a look at the characteristics of the data recovered from remote power analysis. We use these insights to propose a novel selection rule for correlation-based attacks that boosts success confidence. This improvement comes from the observation that the samples in a power trace are not independent. We show that adjacent samples can also provide useful information by proposing a post-processing step that capitalizes on these additional leakages. In contrast to previous work, the proposed technique does not rely on the selection of points of interest within the power traces. We further investigate the characteristics of "remote" power traces and their effect on the proposed selection rule through experiments with real (TDC, ChipWhisperer) and synthetic data sets. To assess the advantage of the proposed improvement, we also introduce novel performance metrics that divert from known-key evaluation techniques.

𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 is a widely deployed perceptual hash function used for the detection of illicit content such as Child Sexual Abuse Material (CSAM). This paper presents the first mathematical description of 𝐴𝑙𝑙𝑒𝑔𝑒𝑑 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴, a new function which has identical outputs to that of 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 for a large database of test images. From this description, several design weaknesses are identified: the algorithm is piece-wise linear and differentiable, the hash value only depends on the sum of the RGB values of each pixel, and it is trivial to find images with hash value equal to all zeroes. The paper further demonstrates that gradient-based optimization techniques and quadratic programming can exploit the mathematical weaknesses of 𝐴𝑙𝑙𝑒𝑔𝑒𝑑 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 and 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 to produce visually appealing exact collisions and second preimages; for near-collisions and near-second-preimages the image quality can be further improved. The same techniques can be used to recover the rough shapes of an image from its hash value, disproving the claim from the designer that 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 is irreversible. Finally, it is also shown that it is easy to produce high-quality perceptually identical images with a hash value that is far from the original image allowing to avoid detection. We have implemented our attacks on a large set of varied images and we have tested them on both 𝐴𝑙𝑙𝑒𝑔𝑒𝑑 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 and 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴. Our attacks have success rates close or equal to 100% and run in seconds or minutes on a personal laptop; they present a substantial improvement over earlier work that requires hours on parallel machines and that results only in near-collisions. We believe that with additional optimization of the parameters, the image quality and/or the attack performance can be further improved. Our work demonstrates that 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 is unreliable for the detection of illicit content: it is easy to incriminate someone by sending them false content with a hash value close to illicit content (a false positive) and to avoid detection of illicit content with minimal modifications to an image (a false negative). False positives and leakage of information are particularly problematic in a Client Side Scanning (CSS) scenario as envisaged by several countries, where large hash databases would be stored on every user device and billions of images would be hashed with 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴 every day. Overall, our research cast serious doubts on the suitability of 𝑃ℎ𝑜𝑡𝑜𝐷𝑁𝐴for the large-scale detection of illicit content.

We present an exponential-time key recovery attack on the public-key encryption scheme using matrix codes proposed by Aragon et al. at Asiacrypt 2024. The secret key is a Gabidulin code expanded using an $\mathbb{F}_q$-basis of $\mathbb{F}_{q^m}$ to obtain a matrix code, which is then hidden by appending random rows and columns and by left- and right-multiplication with invertible matrices. Our attack does not rely on the Gabidulin structure and hence applies to most $\mathbb{F}_{q^m}$-linear codes hidden by their transform. Its complexity is better than the previously best-known distinguisher and significantly better than the naive key recovery algorithm. Our attack breaks some of their proposed parameters. For example, a parameter set targeting 192-bit security is reduced to about 161 bits, and a 256-bit set to about 223 bits.

In this work, we present new cryptanalytic attacks on recently proposed, theory-inspired constructions of weak pseudorandom functions (weak-PRFs). We demonstrate attacks on several such designs, showing that the initial security arguments require significant refinement. Methodologically, our approach relies on novel observations about the structure of cyclic matrices, applications of Wagner's generalized birthday technique, and conversion into polynomial systems over $\mathbb{F}_3$. These findings highlight the need for a more careful analysis of those weak-PRF candidates

At CRYPTO 2009, Heninger and Shacham presented a branch-and-prune algorithm for reconstructing an RSA private key given a random fraction of its private components. This method has been widely adopted in side-channel attacks, and its complexity is closely related to the specific leakage pattern encountered. In this work, we propose a new leakage model that enables efficient key reconstruction by exploiting a vulnerability in the modular exponentiation invoked by OpenSSL's implementation of Miller-Rabin primality test. This vulnerability reveals the least significant $b$ bits of each window. Through our proposed model, these bits form new leakage patterns, which we term aligned and misaligned. In particular, the misaligned case includes previously undocumented scenarios where full key recovery is achievable without branching. Then we analyze the global and local behavior of key reconstruction under these patterns. Our evaluation demonstrates that they yield more efficient key reconstruction and maintain this advantage even in the presence of additional erasures. Moreover, in specific scenarios, successful reconstruction remains practical even if the bits obtained are less than 50\%. Finally, we conducted a series of experiments to confirm the practicality of our work, successfully recovering the lower 4 bits from each 6-bit window and demonstrating efficient key reconstruction under our model.

LESS is a digital signature scheme that is currently in the second round of the National Institute of Standards and Technology’s (NIST’s) ongoing call for standardization of additional post-quantum signature schemes. Recently, the ZKfault attack by Mondal et al. (Asiacrypt 2024) showed several attack surfaces on the first version of LESS (LESS-v1) that can be exploited using different fault attacks. However, the designers of LESS have updated the scheme in the second round to improve efficiency and signature size. The fault attacks in ZKfault are not directly applicable to this new version of LESS (LESS-v2). The physical security of LESS-v2 is still unexplored. In this work, we analyze the new structure of the LESS-v2 signature scheme and propose a method for universal forgery. One crucial observation is that, for LESS-v2, an adversary does not require the full signing key, but some other secret-related information, namely, a permutation of secret monomial matrices. We assume an adversary can use execution interruption techniques, such as fault attacks, to recover this extra information. We have analyzed multiple such attack surfaces in the design of LESS-v2, and using fault injection, we can recover secret-related information. We showed the average number of required faults for two particular fault models to recover the secret equivalent component and observed that, for most parameters, we need only 1 faulted signature, and at most 1088. Our attacks rely on simple and standard fault models. We demonstrated these using both simulation and a simple experimental setup.

ML-DSA (formerly CRYSTALS-Dilithium), the primary NIST post-quantum signature standard, relies on rejection sampling to ensure that released signatures are statistically independent of the secret key. Recent work by Liu et al. and Damm et al. showed that this protection breaks down as soon as an attacker obtains even a single bit of the generated masking randomness per signature, enabling key recovery via linear regression over the resulting noisy linear system. However, this regression approach requires the attacker to collect a large number of such leaky signatures—up to 2.4 million so-called informative relations for ML-DSA-65—thereby limiting the attack’s practical applicability. We dramatically reduce this cost by reformulating the key recovery as a constraint-satisfaction problem solvable by local optimization. Our approach rests on two contributions. First, we construct a verification routine that checks candidate subkeys using only the collected leakage relations, i.e. without knowledge of the remaining secret-key components or relying on computation-intensive reductions. Second, building on theoretical insights from this verification method, we design a multi-tier hill-climbing algorithm that iteratively refines candidates by minimizing a scoring function. In the exact leakage setting, our attack recovers ML-DSA subkeys from as few as 5 000 to 35 000 informative relations across all parameter sets and leakage bit indices the attack is applicable for, constituting a reduction by a factor of 37–68× over the previous state of the art. We further extend the attack to a noisy leakage model, where the leaked bit is flipped independently with error probability p. We demonstrate experimentally that key recovery remains feasible even at noise rates as high as 45%, again with substantially fewer leakage information than prior work.

Can we hope to provide provable security against model extraction attacks? As a step towards a theoretical study of this question, we unify and abstract a wide range of "observational" model extraction defenses (OMEDs) --- roughly, those that attempt to detect model extraction by analyzing the distribution over the adversary's queries. To accompany the abstract OMED, we define the notion of complete OMEDs --- when benign clients can freely interact with the model --- and sound OMEDs --- when adversarial clients are caught and prevented from reverse engineering the model. Our formalism facilitates a simple argument for obtaining provable security against model extraction by complete and sound OMEDs, using (average-case) hardness assumptions for PAC-learning, in a way that abstracts current techniques in the prior literature. The main result of this work establishes a partial computational incompleteness theorem for the OMED: any efficient OMED for a machine learning model computable by a polynomial size decision tree that satisfies a basic form of completeness cannot satisfy soundness, unless the subexponential Learning Parity with Noise (LPN) assumption does not hold. To prove the incompleteness theorem, we introduce a class of model extraction attacks called natural Covert Learning attacks based on a connection to the Covert Learning model of Canetti and Karchmer (TCC '21), and show that such attacks circumvent any defense within our abstract mechanism in a black-box, nonadaptive way. As a further technical contribution, we extend the Covert Learning algorithm of Canetti and Karchmer to work over any "concise" product distribution (albeit for juntas of a logarithmic number of variables rather than polynomial size decision trees), by showing that the technique of learning with a distributional inverter of Binnendyk et al. (ALT '22) remains viable in the Covert Learning setting.

PRISM is an isogeny-based cryptographic framework that relies on the hardness of computing a large prime-degree isogeny from a supersingular elliptic curve with an unknown endomorphism ring. It includes both an identification scheme PRISM-id and a signature scheme PRISM-sig. In this work, we present two attacks on PRISM-id. First, we analyze the probability that a randomly sampled prime $q$ in PRISM-id results in a $q$-torsion subgroup defined over a small extension field, and we show that this probability is higher than claimed in the original proposal. Exploiting this observation, we construct classical forgery attacks on PRISM-id. The first attack addresses the scenario in which the attacker cannot reject a challenge. It succeeds with probability $\tilde{\Theta}(2^{-(\lambda + \log\lambda)(1-\varepsilon)})$ and runs in expected time $\tilde{O}(\max\{2^{3\lambda\varepsilon}, 2^{\lambda(\varepsilon + 1/2)}\})$ for any positive real number $\varepsilon < 1/3$. Setting $\varepsilon = 1/4$ yields success probability $\tilde{\Theta}(2^{-3(\lambda + \log\lambda)/4})$ and expected time complexity $\tilde{O}(2^{3\lambda/4})$. The second forgery attack covers the scenario in which the attacker is allowed to reject challenges. It always succeeds and runs in expected time $\tilde{O}(2^{6\lambda/7})$. Finally, we describe an attack against the underlying hardness assumption of PRISM-id that runs in expected time $\tilde{O}(2^{\lambda/2})$. Note that our results do not affect the security of PRISM-sig.

The selection of shift polynomials is a pivotal yet challenging step in Coppersmith's method for computing modular roots of multivariate polynomials. We propose a novel, determinant-based strategy for generating these polynomials, thereby presenting an improved variant of Coppersmith's method tailored for certain multivariate modular equations. Our approach is first validated on solving the Modular Inversion Hidden Number Problem (MIHNP) and predicting the Inversive Congruential Generator (ICG), where it is shown to outperform prior methods both in theory and in practice. Furthermore, when applied to the Modular Inversion Double Hidden Numbers Problem (MIDHNP), our analysis reveals that MIDHNP is not harder than MIHNP, thereby disproving a conjecture by Boneh et al. (Asiacrypt 2001).

Poseidon[GKR+19 ] and its successor Poseidon2[GKS23] are arithmetization-oriented permutations proposed for hashing inside algebraic proof systems. While there is extensive prior work on cryptanalysis of reduced-round Poseidon/Poseidon2 and theoretical and practical weaknesses of the Fiat-Shamir transform, these two attacks are typically studied in isolation. This work asks whether combining them i.e., instantiating Fiat-Shamir with Poseidon can enable new attacks. We design and implement multiple candidate attacks that encode verifier checks together with reduced-round Poseidon-based challenge derivation as explicit polynomial systems, targeting settings such as Sigma protocols and FRI-like degree enforcement. We evaluate these approaches using Gr¨obner bases. We use this model to derive Gr¨obner-basis attack formulations aimed at constructing verifier-accepting transcripts that violate the intended low-degree bound, and we report the computational bottlenecks encountered in representative parameter regimes. We also document additional explored directions, including retry-style challenge biasing and reduced-round investigations, in order to clarify which attacks appear more or less promising. Across our implementations, we do not obtain meaningful forgeries: even with heavily reduced Poseidon parameters, Gr¨obner-basis computations do not find solutions for random instances of the constructed systems. Our results provide negative evidence for several natural algebraic attack routes on Poseidon-based Fiat-Shamir instantiations, and help clarify which known Fiat-Shamir weaknesses do and do not transfer to well-structured, fully transcript-bound deployments.

The Unbalanced Oil and Vinegar (UOV) construction has been a central framework in multivariate cryptography since its appearance in 1999. In fact, four schemes in the second round of NISTs additional call for signatures are UOV-based. For efficiency considerations, most of these schemes are defined over a field of characteristic 2. This has as a side effect that the polar forms of the UOV public maps are not only symmetric, but also alternating. In this work, we propose a new key-recovery attack on UOV over fields of characteristic 2 that exploits this alternating property. We interpret the polar forms of the UOV public map as elements of the exterior algebra. Moreover, we show that these forms exhibit a structure that is dependent on the secret oil space. Using the Plücker embedding, we also express the dual of the secret oil space as an element of the exterior algebra. Utilizing the structure of the public maps, we can formulate relations on this secret element in this algebra. Finally, we demonstrate that the secret oil space can be recovered using sparse linear algebra techniques. This new attack has a lower time complexity than previous methods and reduces the security of $\texttt{uov-Ip}$, $\texttt{uov-III}$, and $\texttt{uov-V}$, by 4, 11, and 20 bits respectively. In addition, the attack is applicable to MAYO$_2$ and reduces its security by 28 bits.

The multistep solving strategy consists in a divide-and-conquer approach: when a multivariate polynomial system is computationally infeasible to solve directly, one variable is assigned over the elements of the base finite field, and the procedure is recursively applied to the resulting simplified systems. In a previous work by the same authors (among others), this approach proved effective in the algebraic cryptanalysis of the Trivium cipher. In this paper, we present a new formulation of the corresponding algorithm based on a Depth-First Search strategy, along with a novel complexity analysis leveraging tree structures. We also introduce the notion of an ``oracle function'', which is intended to determine whether evaluating a new variable is required to simplify the current polynomial system. This notion allows us to unify all previously proposed variants of the multistep strategy, including the classical hybrid approach, by appropriately selecting the oracle function. Finally, we employ the multistep solving strategy in the cryptanalysis of the NSA's recently introduced low-latency block cipher Aradi, achieving a first full-round algebraic attack that exposes structural features in its symbolic model.

Domain-informed deep learning integrates specialized knowledge into deep neural networks through modifications to inputs, architectures, loss functions, or training processes. Such approach is usually employed to improve model performance in low/noisy data regime via domain-specific priors. Side-channel analysis is such a domain and even though straight deep learning has become a powerful tool for profiled side-channel, it still struggles on more complex datasets because of weak signals distributed across many datapoints. Initial attempts at integrating specific knowledge into models have been extremely successful to pushing boundaries of what can be achieved with deep learning. For example, integrating knowledge about the masking scheme in Masure et al provides significant improvements in decreasing the profiling complexity. Marquet et Oswald went further by leveraging redundant features across multiple tasks, such as shared randomness or common masking flow. In this work, we continue the discussion by using belief propagation on a larger graph to guide the learning. We introduce a multi-task learning model that explicitly integrates a factor graph reflecting the algebraic dependencies among intermediates in the computations of Kyber's inverse Number Theoretic Transform (iNTT). Such framework allow the model to learn a joint representation of the related tasks that is mutually beneficial. For the first time, we show that one can perform a belief propagation during training even when one does not have access to the internal randomness, on the masked shares, potentially improving greatly the performances of the attack.

The protection of executable code in embedded systems requires efficient mechanisms that ensure confidentiality and integrity. Belkheyar et al. recently proposed the Authenticated Code Encryption (ACE) framework, with ChiLow-(32 + $\tau$) as the first instantiation of ACE2 at EUROCRYPT 2025. The design of ChiLow-(32 + $\tau$) is based on a 32-bit tweakable block cipher with a quadratic nonlinear layer, known as ChiChi (denoted by $\chi\!\!\chi$), and a nested tweak key schedule optimized for secure code execution under strict query limits. In this work, we study the resistance of ChiLow to integral cryptanalysis. We identify new integral distinguishers in both the single-tweak and related-tweak models. Using these results and a nested strategy to recover all round tweaks, we present a key-recovery attack on 7 out of 8 rounds of ChiLow. The central contribution of our work is that it resolves the challenge of deriving the master key from the recovered round tweaks, an open problem highlighted by the designers and in a recent cryptanalysis by Peng et al. The attack on 7 rounds requires $2^{6.32}$ chosen ciphertexts, has a time complexity of about $2^{121.75}$ encryptions, and requires negligible memory.

The studies by Gohr et al. at Crypto 2019 and subsequent related works have demonstrated that neural networks can offer new insights for cryptanalysis. Building on this insight, we leverage neural networks to learn features closely associated with integral properties and use neural network-derived distinguishers as a benchmark for the automatic search. This approach not only confirms the value of deep learning in feature discovery but also shows that neural-guided insights can improve the performance of classical cryptanalytic methods. Neural networks motivate the development of a more effective framework for identifying integral distinguishers. Comparative results show that existing automated methods, limited by search efficiency and the large search space, often fail to locate optimal distinguishers. In contrast, neural networks can directly identify high-quality integral distinguishers and reveal associated non-random structural features that are typically missed by traditional approaches. Based on these neural-network results, we refine the meet-in-the-middle search framework, thereby improving the trade-off between accuracy and computational cost. Notably, under the assumption of full-state key XOR with independent round keys, the refined framework achieves the known theoretical upper bound for key-independent integral distinguishers on non-standard SKINNY. Integral distinguishers identified by neural networks, whose underlying non-random features are successfully interpreted through Boolean function analysis, are translated into classical forms, enhancing integral key-recovery attacks. In particular, we propose a 16-round key-recovery attack on SKINNY-n-n based on a general integral key-recovery approach, improving the best-known result by two rounds under the single-tweakey setting. Furthermore, we present key-recovery attacks on 18-round SKINNY-n-2n and 20-round SKINNY-n-3n using integral distinguishers under the single-tweakey setting for the first time.

The wide adoption of deep neural networks (DNNs) raises the question of how can we equip them with a desired cryptographic functionality (e.g, to decrypt an encrypted input, to verify that this input is authorized, or to embed a secret backdoor which alters the DNN's normal operation). The problem is that cryptographic primitives are typically designed to run on digital computers that use Boolean gates to map sequences of bits to sequences of bits, whereas DNNs are a special type of analog computer that uses linear mappings and ReLUs to map vectors of real numbers to vectors of real numbers. This discrepancy between the discrete and continuous computational models raises two fundamental questions: How can we implement standard cryptographic primitives as DNNs, and whether DNN implementations of secure cryptosystems remain secure in the new setting, in which an attacker can ask the DNN to process a message whose ``bits'' are arbitrary real numbers. In this paper we lay the foundations of this new area of research, defining the meaning of correctness and security for implementations of cryptographic primitives as ReLU-based DNNs. We then show that the natural implementations of block ciphers as DNNs can be broken in linear time by using such nonstandard inputs (this attack was experimentally tested in the case of full round AES-128, and had 100% success rate). Finally, we develop a new method for implementing any desired cryptographic functionality as a standard ReLU-based DNN in a provably secure and correct way. Our novel protective technique has very low overhead (a constant number of additional layers and a linear number of additional neurons), and is completely practical.

This work presents the first third-party cryptanalysis of \textsf{Blink}, a recent tweakable block cipher built on the Three-Hash Framework with a long-key design. Leveraging the idea of Superbox, we develop a lightweight theoretical model capturing the value correlations, weak-key conditions, fixed-key probabilities and the local clustering behaviors inside a \textsf{Blink} Superbox when the value spaces are affine. This model is intended as a concrete, easy-to-follow specialization of existing generic frameworks adapted to the structure of \textsf{Blink}. We then build a simple pattern-based automatic tool to search for weak tweak-key differentials. The main results are as follows: For \textsf{Blink-64} with 448-bit key size, we obtain a 10-round distinguisher with probability $2^{-50.42}$ for up to $2^{442}$ weak keys (equivalently $2^{-6}$ of the full key space); For \textsf{Blink-128} with 1024-bit key size, we obtain a 10-round distinguisher with probability $2^{-68.83}$ for up to $2^{1010}$ weak keys (equivalently $2^{-14}$ of the full key space), which can be extended to a 12-round multiple differential distinguisher with probability $2^{-96.83}$. Based on the weak tweak-key distinguisher, we further mount a 13-round key recovery attack on \textsf{Blink-64}, recovering the full 448-bit master key with time complexity $2^{114.02}$ and $2^{56}$ chosen plaintexts. All these distinguishers and key recovery attacks work within the data and time bounds claimed by the designers. And our analysis remains consistent with the security of the full-round design of \textsf{Blink}, while offering additional insight into the edge-case behaviors arising from the tweak-key interaction in \textsf{Blink}, and could be potentially informative for future refinements of tweakable block cipher constructions.

We define and analyze the Leveled Isogeny Problem with Hints (LIPH), which is a generalization of the Isogeny Problem with Level Structure first introduced by De Feo, Fuoutsa and Panny at EUROCRYPT'24. In a LIPH instance we are tasked to recover a secret isogeny \(\varphi\) given masked torsion point images \(M\cdot(\varphi(P),\varphi(Q))^\top\) for some \((P,Q)\) of order \(N\) and unknown \(M\in GL_2(N)\). Additionally, we are provided a \emph{hint} on \( M \), revealing some bits of its entries. Instances of LIPH occur naturally in the case of modern isogeny-based key exchanges that use masked torsion points as part of their public key, when additionally some parts of the masking matrix \( M \) are revealed due to, for instance, a side-channel attack. We provide efficient algorithms that solve various instances of LIPH, leading to efficient \emph{partial key recovery attacks} in practice. More specifically, we present Coppersmith-type attacks that are able to recover an M-SIDH/POK\'E secret key given \(50\%\) (resp. \(86\%\)) of the most-significant bits of an entry of \( M \), and a FESTA secret key given the 67\% of the most-significant bits of \( M \). In the case of FESTA we also present a tailored combinatorial attack running in subexponential time $O(2^{\sqrt{n}})$ with probability of $84\%$ when $50\%$ of the bits of $M$ leak at random.

Cryptographic group actions provide a basis for simple post-quantum generalizations of many cryptographic protocols based on the discrete logarithm problem (DLP). However, many advanced group action-based protocols do not solely rely on the core group action problem (the so called vectorization problem), but also on variants of this problem, to either improve efficiency or enable new functionalities. For example, the security of the CSI-SharK threshold signature protocol relies on the hardness of the Vectorization Problem with Shifted Inputs where (in DLP formalism) the adversary not only receives g and g^x, but also g^(x^c) for multiple known values of c. A natural open question is whether the additional data allows adversaries to solve the underlying problem more efficiently. We revisit the concrete quantum security of this problem. We start from a quantum multiple hidden shift algorithm of Childs and van Dam, which to the best of our knowledge was never applied in cryptography before. We describe and analyze a variant of this algorithm, and we specify and analyze all its subroutines to provide concrete complexity estimates. We then apply our analysis to the CSI-SharK protocol. In prior analyses based on Kuperberg’s algorithms, group action evaluations contributed to a significant part of the overall T-gate cost. For CSI-SharK’s suggested parameters, our new approach requires significantly fewer calls to the group action evaluation subroutine, leading to significant complexity improvements overall. We describe two instances of our approach, one minimizing the T-gate complexity, and the other one keeping qubit requirements small, both of them resulting in significant complexity improvements over previous works. More generally, we quantify the quantum security degradation resulting from additional published data in the CSI-SharK protocol.

First, we correct certain omissions in the literature on the complexity analysis of Crossbred and give a full analysis of this algorithm. Secondly, we propose a criterion to reduce the number of polynomials generated in the preprocessing step for a set of admissible parameters $D$, $d$ and $k$, whenever this step of the algorithm produces more polynomials than necessary. We conclude by applying this criterion to the security of MQOM.

Amutha and Perumal recently proposed a two-party key exchange protocol based on \(\alpha\)-\(v\)-\(w\)-duo circulant matrices over the max-plus semiring, claiming resistance to known tropical attacks and suitability for IoT environments. This paper presents a complete cryptanalysis of this protocol. We uncover a fundamental structural weakness: the construction imposes an affine parameterization on the secret matrices, reducing each matrix to a single integer parameter. Consequently, the public messages become simple shifts of a publicly computable matrix, and the session key reduces to a constant shift of another public matrix. An eavesdropper can recover the shared secret in constant time after a one-time precomputation. The attack is deterministic, succeeds with probability 1, and requires only passive observation. We verify the attack on the authors' own example.

In this paper, we introduce a novel framework for meet-in-the-middle (MITM) attacks on ARX designs, termed \textit{dual-syncopation} MITM attack, which formalizes a compact, rule-based language for tracking deterministic and non-deterministic information for two independent propagations through ARX operations. The language provides an uniform abstraction for previous techniques, e.g., initial structure, partial matching, partial-fixing, and naturally supports automation. With the language, we additionally encode new technical insights that is not covered in literature and build an efficient automatic search tool for MITM attacks on ARX designs that can be fully optimized within hours. As a result, we obtain the first preimage attacks on 46- and 47-step SHA-256, extending the previous record of 45 steps by two steps. For SHA-512, we present the first preimage attack on 51 steps, extending the prior record of 50 steps by one step. In addition, we provide a collection of improved preimage attacks on 43-, 44-, and 45-step SHA-256; 46-, 47-, 48-, 49-, and 50-step SHA-512; as well as full-step MD5. The proposed attacks can be converted to free-start collision attacks with the technique proposed by Li, Isobe, and Shibutani at FSE 2012. Our results mark the first improvements on theoretical attacks on SHA-2 in a decade and push the boundary of cryptanalysis of ARX designs.

In 2006 de Graaf et al. devised a Lie-algebra-based strategy for finding a linear transformation $T \in PGL_{N+1}(\mathbb{Q})$ connecting two linearly equivalent projective varieties $X, X' \subseteq \mathbb{P}^N$ over $\mathbb{Q}$. The method succeeds for several families of "classical" varieties such as Veronese varieties, which have large automorphism groups. In this paper, we study the Lie algebra method over finite fields, which comes with new technicalities when compared to $\mathbb{Q}$ due to, e.g., the characteristic being positive. Concretely, we make the method work for Veronese varieties of dimension $r \geq 2$ and (heuristically) for secant varieties of Grassmannians of planes. This leads to classical polynomial-time attacks against two candidate-post-quantum key exchange protocols based on disguised Veronese surfaces and threefolds, which were recently proposed by Alzati et al., as well as a digital signature scheme based on secant varieties of Grassmannians of planes due to Di Tullio and Gyawali. We provide an implementation in Magma.

Goldreich's pseudorandom generators (PRGs) with constant locality admit highly parallel implementations, yet the concrete security of instantiations based on the $\mathsf{XOR}\text{-}\mathsf{THR}$ predicate has remained unclear. In this work, we present novel seed recovery attacks on Goldreich's PRGs instantiated on $\mathsf{XOR}\text{-}\mathsf{THR}$ predicates with $m=n^s$, where $m$ and $n$ are the length of output and input, respectively. By partitioning the output bits into groups according to common input bits, high-biased noisy equations can be derived for the group whose common input bits are all 1s (or all 0s). Leveraging two solvers tailored to these equations, we achieve the seed recovery attacks, which needs roughly $2^{n(1-\log_2{(1 + \frac{2s}{\sqrt{2\pi (b-s)}})})}$ calls to Gaussian elimination when the input length of the $\mathsf{THR}$ predicate $b\geq (n-s)^{1/s}+s-1$ with small stretch $s$. Applying our attack to the $\mathsf{XOR}\text{-}\mathsf{MAJ}$ challenges in STOC 2016 yields complexity \(2^{\,n\!\left(1-\log_{2}\!\left(1+\sqrt{\frac{s}{18\pi}}\right)\right)} \le 2^{0.82n}\), i.e., at least a \(2^{0.18n}\) speedup over exhaustive search for any stretch \(s>1\). We also deploy our attack on an instance used in the construction of silent oblivious transfer protocols (Eurocrypt 2024) with \(n = 256\). This attack is capable of breaking the instance using approximately \(2^{31.3}\) calls to Gaussian elimination over 244 variables. We successfully implemented the attack on a cluster of 14 CPU cores, recovering the seed in 71 hours, demonstrating the attack's efficiency. Beyond PRGs, with appropriate adaptations our method extends to FiLIP stream ciphers instantiated with \mathsf{THR}-related predicates. Our evaluation indicates that most FiLIP instances do not meet their claimed security. For instance, the configuration \(\mathsf{XOR}_{100}\text{-}\mathsf{THR}_{11,22}\text{-}\mathsf{THR}_{11,22}\) is broken in about \(2^{59}\) calls to Gaussian elimination over 357 variables despite a 397-bit key and a claimed 80-bit security level.

We propose a novel algorithm to solve underdetermined systems of multivariate quadratic (MQ) equations over finite fields. In modern MQ signature schemes such as MAYO, QR-UOV and SNOVA finding solutions to such systems is equivalent to signature forgery. The current benchmark for estimating forgery bit complexity is Hashimoto’s algorithm which transforms the original underdetermined MQ system $P$ into a more tractable system $\tilde{P}$. A hybrid combination of solving $\tilde{P}$ via Gröbner basis and exhaustive search eventually solves $P$. We introduce a novel transformation that pushes the hybrid approach to its extreme. Specifically, we reduce the underdetermined MQ system to a sequence of quadratic equations in a single variable at the cost of a larger exhaustive search. As a consequence, signature forgery no longer relies on the hardness of MQ solving but becomes pure guessing via exhaustive search. This in turn implies that signature forgery is significantly more vulnerable against quantum attacks via Grover search. We provide accurate estimates for the classical and quantum bit complexity of forging signatures for MAYO, QR-UOV and SNOVA using our novel algorithm. We reduce the quantum security of all security levels of MAYO, QR-UOV and SNOVA.

In a recent preprint, Grigoriev, Monico, and Shpilrain proposed a digital signature protocol based on the use of matrices over the tropical integer semiring. We show some design flaws of the proposed scheme, together with an efficient attack to forge signatures for an arbitrary message, and a key-recovery attack when given access to a list of honest signatures.

We present new algebraic attacks on Poseidon2 and Poseidon2b. We exploit the specific structure of the matrices that define the linear layers in the hash function which allows us to improve round-skipping for the constrained-input constrained-output CICO problem. The security of many circuit-friendly hash functions has been measured by their resistance against attacks on the CICO problem. However, we show how to boost our round-skipping attack when directly modelling algebraic preimage attacks of Poseidon2(b) in compression and sponge mode. To the best of our knowledge, our attack provides the first examples where finding preimages is easier than solving the corresponding CICO problem in Poseidon2(b). Furthermore, we describe the first algebraic collision attack that outperforms its algebraic preimage counterpart. We improve over state-of-the-art algebraic attacks for a range of parameters, e.g. for one recommended $128$-bit parameter set we improve over previous state-of-the-art algebraic collision attacks by a factor of $2^{106}$. However, due to the algebraic security margin this does not mean the primitive falls short of its claimed security level. Finally, we discuss how our attacks can be mitigated without affecting the efficiency of Poseidon2(b).

This paper focuses on quantum key-recovery attacks on block ciphers. Previous works on quantum differential and truncated differential attacks like [Kaplan et al., ToSC 2016] have shown that classical algorithms for key-recovery, typically based on generating differential pairs and sieving them, can be accelerated by up to a quadratic speedup using variants of quantum search, quantum amplitude amplification, and quantum collision-finding. In this paper, we introduce a new quantum truncated differential key-recovery attack, which leverages the quantum convolution algorithm introduced in [Schrottenloher, CRYPTO 2022] and previously used in linear cryptanalysis. We adapt this algorithm to the case of differential cryptanalysis, by rewriting the probability of a differential of an $n$-bit cipher as a convolution of functions with $2n$-bit input. We then construct a quantum state whose amplitudes encode the probability of the differential for different key guesses, and use this as the starting point of a quantum search. In some cases (although not on practical ciphers so far), the speedup is better than quadratic compared to classical attacks. We also extend the framework to related-key differential attacks. We give applications to a 9-round attack on QARMAv2-64 adapted from [Ahmadian et al., DCC 2024] and a 12-round related-key attack on AES-256 from [Boura et al., CRYPTO 2023], which show improvement over classical attacks and over Kaplan et al.'s strategy when taking into account the amount of memory and the type of quantum memory used (as our attack requires only quantum-accessible classical memory).

The Fiat-Shamir transform is one of the most widely applied methods for secure signature construction. Fiat-Shamir starts with an interactive zero-knowledge identification protocol and transforms this via a hash function into a non-interactive signature. The protocol's zero-knowledge property ensures that a signature does not leak information on its secret key $\mathbf s$, which is achieved by blinding $\vec s$ via proper randomness $\mathbf y$. Most prominent Fiat-Shamir examples are EC-DSA signatures and the new post-quantum standard ML-DSA (aka Dilithium). In practice, EC-DSA signatures have experienced fatal attacks via leakage of a few bits of the randomness $\mathbf y$ per signature. Similar attacks now emerge for lattice-based signatures, such as ML-DSA . We build on, improve and generalize the pioneering leakage attack on ML-DSA by Liu, Zhou, Sun, Wang, Zhang, and Ming. Using a transformation to Integer LWE (ILWE), their attack can recover a 256-dimensional subkey of ML-DSA-44 from leakage in a single bit of $\mathbf{y}$ per signature, in any bit position $j \geq 6$. However, the number of required signatures grows exponentially as $4^j$. In this work, we show that not all leaky signatures carry information about the secret subkey. We introduce the notion of informative signature relations. This notion allows us to define a preprocessing step, called filter-and-shift that leads to ILWE instances that require a smaller sample amount. Unlike the standard ILWE transformation, filter-and-shift exploits the smallness of secret keys, and therefore might be of independent cryptanalytic interest. In comparison to Liu et al., for $j=6$ we require only a quarter of the signatures and reduce the exponential growth to $2^j$. In addition, we show that the secret subkey can be recovered even with a leak bit corrupted by a large amount of noise, in theory up to the maximum of $50\%$. Experimentally, we still recover the secret with $43\%$ noise, where we need $170$ times as many signatures as in the noise-free setting. The attack applies more generally to all Fiat-Shamir-type lattice-based signatures. For a signature scheme based on module LWE over an $\ell$-dimensional module, the attack uses a 1-bit leak per signature to efficiently recover a $\frac{1}{\ell}$-fraction of the secret key. In the ring LWE setting, which can be seen as module LWE with $\ell = 1$, the attack recovers the whole key.

Neural network model extraction has recently emerged as an important security concern, as adversaries attempt to recover a network’s parameters via black-box queries. Carlini et al. proposed in CRYPTO’20 a model extraction approach inspired by differential cryptanalysis, consisting of two steps: signature extraction, which extracts the absolute values of network weights layer by layer, and sign extraction, which determines the signs of these signatures. However, in practice this signature-extraction method is limited to very shallow networks only, and the proposed sign-extraction method is exponential in time. Recently, Canales-Martínez et al. (Eurocrypt’24) proposed a polynomial-time sign-extraction method, but it assumes the corresponding signatures have already been successfully extracted and can fail on so-called low-confidence neurons. In this work, we first revisit and refine the signature extraction process by systematically identifying and addressing for the first time critical limitations of Carlini et al.'s signature-extraction method. These limitations include rank deficiency and noise propagation from deeper layers. To overcome these challenges, we propose efficient algorithmic solutions for each of the identified issues, greatly improving the capabilities of signature extraction. Our approach permits the extraction of much deeper networks than previously possible. In addition, we propose new methods to improve numerical precision in signature extraction, and enhance the sign extraction part by combining two polynomial methods to avoid exponential exhaustive search in the case of low-confidence neurons. This leads to the very first end-to-end model extraction method that runs in polynomial time. We validate our attack through extensive experiments on ReLU-based neural networks, demonstrating significant improvements in extraction depth. For instance, our attack extracts consistently at least eight layers of neural networks trained on either the MNIST or CIFAR-10 datasets, while previous works could barely extract the first three layers of networks of similar width. Our results represent a crucial step toward practical attacks on larger and more complex neural network architectures.

In this paper we introduce a new attack on the multivariate encryption scheme HFERP, a big field scheme including an extra variable set, additional equations of the UOV or Rainbow shape as well as addi- tional random polynomials. Our attack brings several parameter sets well below their claimed security levels. The attack combines novel methods applicable to multivariate schemes with multiple equation types with in- sights from the Simple Attack that broke Rainbow in early 2022, though interestingly the technique is applied in an orthogonal way. In addition to this attack, we apply support minors techniques on a MinRank instance drawing coefficients from the big field, which was effective against other multivariate big field schemes. This work demonstrates that there exist previously unknown impacts of the above works well beyond the scope in which they were derived.

In response to the quantum threat, new post-quantum cryptographic algorithms will soon be deployed to replace existing public-key schemes. MAYO is a quantum-resistant digital signature scheme whose small keys and signatures make it suitable for widespread adoption, including on embedded platforms with limited security resources. This paper demonstrates two single-trace side-channel attacks on a MAYO implementation in ARM Cortex-M4 that recover a secret key with probabilities of 99.9% and 91.6%, respectively. Both attacks use deep learning-assisted power analysis exploiting information leakage during modular multiplication to reveal a vector in the oil space. This vector is then extended to a full secret key using algebraic techniques.

This paper presents a comprehensive approach to the cryptanalysis of block ciphers using Mixed Integer Linear Programming (MILP). By formulating the cipher’s components including substitution boxes, linear layers, and key schedules as systems of linear inequalities, MILP enables the automated discovery of optimal cryptanalytic characteristics. Our methodology is demonstrate the MILP modelling through the analysis of the ITUbee cipher under three attack models: differential, linear, and related-key differential cryptanalysis. This work highlights the potential of MILP as a robust, generalizable tool for evaluating cipher security and guiding the design of resilient cryptographic primitives.

Non profiled side-channel attacks aim at exploiting leakage traces from a targeted embedded system to extract secret information, without a priori knowledge on the true leakage model of the device. To automate and simplify attacks, deep learning techniques have thus been introduced in the side-channel community. Most of the works published have mainly explored the use of discriminative models in the profiled or non profiled context. However, the lack of interpretability and explainability of these models constitutes a major limitation for security laboratory. Indeed, the lack of theoretical results regarding the choice of neural network architectures or the selection of appropriate loss functions poses significant challenges for evaluators seeking to construct a relevant and suitable model for the targeted leakage traces. To address the aforementioned limitations, we propose in this work a novel conditional generative model, specifically designed to carry out non profiled attacks, which is fully interpretable and explainable. To do so, we develop a novel model that fits to the non profiled context. To guarantee the interpretability and explainability of our model, we provide theoretical results to justify both its architecture, and a new loss function for its optimization process. We further propose a key recovery strategy based on our model that requires no leakage model assumptions. As a consequence, our work represents thus the first interpretable and generic (i.e. no a priori knowledge on the leakage model is required) non profiled deep learning-based side-channel attacks. Moreover, to emphasise the benefits of our new model in comparison with conventional linear regression based attack (LRA), we also provide a theoretical comparative analysis on the deterministic part estimation for different Gaussian noise configurations. Finally, we experimentally validate and compare the attack performances of our model with LRA and state-of-the-art discriminative-models-based non profiled attacks using simulations and various publicly available datasets.

Although studied for several years now, parameter extraction of Deep Neural Networks (DNNs) has seen the major advances only in recent years. Carlini et al. (Crypto 2020) and Canales-Martínez et al. (Eurocrypt 2024) showed how to extract the parameters of ReLU-based DNNs efficiently (polynomial time and polynomial number of queries, as a function on the number of neurons) in the raw-output setting, i.e., when the attacker has access to the raw output of the DNN. On the other hand, the more realistic hard-label setting gives the attacker access only to the most likely label after the DNN's raw output has been processed. Recently, Carlini et al. (Eurocrypt 2025) presented an efficient parameter extraction attack in the hard-label setting applicable to DNNs having a large number of parameters. The work in Eurocrypt 2025 recovers the parameters of all layers except the output layer. The techniques presented there are not applicable to this layer due to its lack of ReLUs. In this work, we fill this gap and present a technique that allows recovery of the output layer. Additionally, we show parameter extraction methods that are more efficient when the DNN has contractive layers, i.e., when the number of neurons decreases in those layers. We successfully apply our methods to some networks trained on the CIFAR-10 dataset. Asymptotically, our methods have polynomial complexity in time and number of queries. Thus, a complete extraction attack combining the techniques by Carlini et al. and ours remains with polynomial complexity. Moreover, real execution time is decreased when attacking DNNs with the required contractive architecture.

Spoed is an authenticated encryption scheme based on compression functions. We show that Spoed fails to achieve its claimed security guarantees with respect to both integrity and confidentiality. In particular, we present a universal forgery attack that succeeds with probability one using only a single encryption query and a single decryption query. The attack exploits a structural weakness in the feedback mechanism of Spoed, allowing internal inputs of the underlying pseudorandom function to coincide during verification. We further show that the same weakness enables efficient plaintext-recovery attacks, permitting recovery of almost the entire plaintext with at most two decryption queries, depending on the associated-data length. We explain why the original security proof of Spoed fails, and identify the mismatch between the collision events used in the H-coefficient analysis and the schemes actual behavior. Finally, we propose a minimally modified variant, fSpoed, and prove that it achieves the originally claimed security bounds under standard assumptions.

Key recovery for impossible differential (ID) cryptanalysis has seen few systematic advancements in nearly a decade, while the recent resurgence of impossible boomerang (IB) attacks has produced several powerful but disparate strategies. This, combined with the high complexity of existing tools for finding IB distinguishers, highlights the need for a unified optimization framework. In this paper, we address these gaps by introducing the Impossible Upper and Lower Boomerang Connectivity Tables (iUBCT/iLBCT), new lightweight tools for finding two-round contradictions. We then modernize key recovery by providing the first formal analysis of probabilistic extensions and by adapting the generic key guessing framework from rectangle cryptanalysis, which enables a systematic search for attacks with optimal complexities, particularly for memory. These techniques are integrated into a new Mixed-Integer Linear Programming (MILP)-based tool, leading to a suite of improved attacks on SKINNY, SKINNYee, Midori, and Deoxys-BC. Our results include the first 30-round attack on SKINNYee, extending the state of the art by one round. For other targets, our framework yields attacks with substantial memory and time reductions. In particular, we reduce the complexity of the best previous ID attack on SKINNY-128-384 by factors of up to $2^{131}$ (memory) and $2^{9}$ (time), and the best previous IB attack on Deoxys-BC-384 by factors of up to $2^{56}$ (memory) and $2^{25}$ (time). Many of these results provide new time-memory-data trade-offs, often achieving complexity reductions at the cost of moderately increased data requirements.

Deep neural networks (DNNs) are today’s central machine learning engines, yet their parameters represent valuable intellectual prop- erty exposed to extraction through black-box queries. While existing cryptanalytic attacks have primarily targeted ReLU-based architectures, this work extends model-stealing techniques to a broad class of non-linear activation functions, including GELU, SiLU, SELU, Sigmoid, and oth- ers. We present the first universal black-box attack capable of recovering both weights and biases from networks whose activations converge to lin- ear behavior outside narrow non-linear regions. Our method generalizes prior geometric approaches by leveraging higher-order derivatives and ad- jacent linear zone analysis, bypassing the need for non-differentiability. We show that, for several activations, neuron signatures can be recov- ered more easily than in the ReLU case, and we further demonstrate that activation functions themselves can be identified when not publicly known. Our results broaden the scope of cryptanalytic model extraction, revealing that the secrecy of activation functions or smoothness of nonlin- earities does not provide effective protection against black-box recovery attacks.

We study lattice constructions arising from Coppersmith’s method combined with the Unravelled Linearization technique introduced by Herrmann and May (ASIACRYPT~2009) for solving structured polynomial equations, which can yield improved asymptotic bounds. This work contributes in two aspects, theoretical and practical. Theoretical contribution: While Unravelled Linearization, introduced can lead to improved asymptotic bounds, computing these bounds is technically delicate. Previous works typically assume that the lattice dimension is a polynomial function of the scaling parameter $m$ and therefore rely on Lagrange interpolation to derive asymptotic bounds. We show that this assumption does not hold in general. In particular, the interpolation approach used in Herrmann and May (ASIACRYPT~2009) and in \texttt{cuso} (EUROCRYPT~2025) may yield incorrect results: in the former case, the exponant in the determinate may be a quasi-polynomial instead of polynomial, while in the latter it becomes polynomial only beyond a certain threshold. To address this issue, we present a rigorous analysis based on Ehrhart theory for computing asymptotic bounds. As applications, we improve five cryptanalytic results, including attacks on linear congruential generators, quadratic generators, the subset-sum pseudorandom generator, and a recent partial-key attack on isogenies in the P\`oke setting. In the latter case, we reduce the required leakage of most significant bits from $85.29\%$ to $79.81\%$, and further to $79.08\%$ in certain special cases. Practical contribution: Asymptotic bounds alone are insufficient for practical attacks, since one must also determine an appropriate lattice dimension. To avoid trivial guessing of the lattice dimension from small to large, we introduce an estimator, $\mathsf{DimOracle}$, based on Ehrhart theory. Our approach simultaneously estimates the lattice dimension and determinant via the associated Ehrhart (quasi-)polynomials. Due to Barvinok’s algorithm, any fixed number of leading coefficients of these (quasi-)polynomial can be computed in polynomial time by reducing the problem to volume computations of faces of the Newton polytope. Using these coefficients, $\mathsf{DimOracle}$ provides accurate predictions of the required lattice size in practice. We implement $\mathsf{DimOracle}$ and demonstrate its effectiveness through experimental results.

One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. We show that this problem is related to the problem of finding a good splitting of a principally polarized superspecial abelian surface. We provide formal security reductions, as well as a proof-of-concept implementation of an algorithm to compute endomorphisms of elliptic curves by solving the splitting problem.

As a NIST-standardized hash function, SHA-256 has been extensively analyzed in the context of collision attacks. Although Mendel et al. introduced the first 31-step collision attack at EUROCRYPT 2013, the number of attacked steps has not been increased for more than a decade. After a thorough review of existing attacks, we identify that progressing beyond 31 steps necessitates new local collisions in the message expansion. To date, such local collisions have been manually constructed, which is both time-consuming and technically challenging. Besides, even the latest automated models for searching signed differential trails fail to accurately account for the bit conditions imposed by Boolean functions, potentially overlooking high-quality trails. In this paper, we enhance the existing framework by overcoming these two limitations. Firstly, an automated tool that can efficiently identify high-quality local collisions is given following the main idea of EUROCRYPT 2013. Secondly, two new models of Boolean functions that can accurately capture bit conditions are introduced. Leveraging these improvements, we finally reach the first 37-step collision attack on SHA-256, extending the number of attacked steps by six, and this is the first such advancement in 12 years.

In november 2024, the Ethereum foundation (EF) issued a bounty program with challenges on Poseidon and Poseidon2. The goal of these challenges is to find CICO solutions on different round-reduced instances of Poseidon and Poseidon2, defined on different prime fields. We denote the four main instances Poseidon-256, Poseidon2-64, Poseidon2-31m and Poseidon2-31k. In the challenges, the goal is to solve CICO-1 for Poseidon-256 and Poseidon-64, and CICO-2 for Poseidon-31m and Poseidon-31k. We found CICO solutions to the first 3 proposed instances of Poseidon2-31m and Poseidon2-31k, along with solutions for the first two Poseidon-256 instances. These solutions have been confirmed to be correct and eligible for bounty by the Ethereum fundation, except for the first instance of Poseidon-256, which was claimed by another team before us. In order to solve the instances of Poseidon2-31m and Poseidon2-31k, we used a new resultant-based approach, whereas our attacks on Poseidon-256 only relies on already-known univariate root finding.

Developers implementing elliptic curve cryptography (ECC) face a wide range of implementation choices created by decades of research into elliptic curves. The literature on elliptic curves offers a plethora of curve models, scalar multipliers, and addition formulas, but this comes with the price of enabling attacks to also use the rich structure of these techniques. Navigating through this area is not an easy task and developers often obscure their choices, especially in black-box hardware implementations. Since side-channel attackers rely on the knowledge of the implementation details, reverse engineering becomes a crucial part of attacks. This work presents ECTester -- a tool for testing black-box ECC implementations. Through various test suites, ECTester observes the behavior of the target implementation against known attacks but also non-standard inputs and elliptic curve parameters. We analyze popular ECC libraries and smartcards and show that some libraries and most smartcards do not check the order of the input points and improperly handle the infinity point. Based on these observations, we design new techniques for reverse engineering scalar randomization countermeasures that are able to distinguish between group scalar randomization, additive, multiplicative or Euclidean splitting. Our techniques do not require side-channel measurements; they only require the ability to set custom domain parameters, and are able to extract not only the size but also the exact value of the random mask used. Using the techniques, we successfully reverse-engineered the countermeasures on 13 cryptographic smartcards from 5 major manufacturers -- all but one we tested on. Finally, we discuss what mitigations can be applied to prevent such reverse engineering, and whether it is possible at all.

Side-channel analysis (SCA) can recover secret keys by exploiting physical leakages emitted during cryptographic computations. Most SCA techniques, however, require knowledge of the plaintext or ciphertext corresponding to each measured trace, which may be unavailable in realistic adversarial settings. Blind side-channel analysis (Blind SCA), first introduced in 2014, relaxes this requirement, but existing work has mainly targeted S-box nonlinearities. We present a systematic study of blind SCA targeting modular addition, the core nonlinear operation in ARX-based block ciphers, by leveraging key-dependent statistical characteristics arising from carry propagation. We introduce MALeak, a framework that models analysis targets as generalized key-dependent functions involving modular addition. We validate key recovery in simulation under varying noise levels and instantiate MALeak for HIGHT and SPECK by deriving cipher-specific attack procedures. We further evaluate the MALeak instantiations for HIGHT and SPECK on real power traces collected from an STM32F415 microcontroller (ARM Cortex-M4). Our results show that, given suitable points of interest (PoIs), MALeak can recover secret keys of ARX-based block ciphers without access to the corresponding plaintext or ciphertext.

Inspired by a recent paper from Shanghai Jiao Tong University and China Telecom Quantum Information Technology Group [1]—which demonstrated a full break of the KAZ algorithm family submitted to Malaysia’s MySEAL 2.0 standardization—we focus specifically on its signature component. Within the same core theoretical framework, we have observed a subtle inaccuracy in the formula given in the original work. While this does not prevent the final private-key recovery via lattice reduction, it leads to incorrect derivation of the intermediate sensitive signature data e₁ and e₂. Building on this observation, we propose a refined lattice construction that successfully reproduces the original attack while eliminating the need for an additional step: computing the greatest common divisor (GCD) between the signature component S₂ and the modulus ϕ(N). This new construction is equally capable of recovering the private key using two signatures.

Kyber a.k.a ML-KEM is a quantum-safe Key Encapsulation Mechanism, that has been standardized by NIST under FIPS-203 and will definitely in the coming years be implemented in several commercial products. Following fors instance this report https://radar.cloudflare.com/adoption-and-usage?dateRange=52w, one can notice that since the end of 2024, the post-quantum encrypted share of the HTTPS request traffics has been increasing and is about to reach 50% now. However, the resilience of implementations against side channel attacks is still an open and practical concern. One of the drawbacks of the ongoing side channel analysis research related to PQC schemes is the availability of open-source datasets. Luckily some open-source datasets start popping up. For instance, the one recently published by Rezaeezade et al. in the paper 2025/811. This dataset captures power consumption during a pair-pointwise multiplication occurring in the course of ML-KEM decapsulation process and involving the decapsulation (sub)key and ciphertexts. In this paper we present both a profiled (template) and an unprofiled (CPA) side channel attacks targeting that pair-pointwise multiplication, which yield, in both cases, a complete recovery of the decapsulation secret (sub)key.

The success of deep learning in cryptanalysis has been largely demonstrated empirically, yet it lacks a foundational theoretical framework to explain its performance. We bridge this gap by establishing a formal learning-theoretic framework for symmetric cryptanalysis. Specifically, we introduce the Coin-Tossing (CoTo) model to abstract the process of constructing distinguishers and propose a unified algebraic representation, the Conjunctive Parity Form (CPF), to capture a broad class of traditional distinguishers without needing domain-specific details. Within this framework, we prove that any concept in the CPF class is learnable in sub-exponential time in the setting of symmetric cryptanalysis. Guided by insights from our complexity analysis, we demonstrate preprocessing the data with a flexible output generating function can simplify the learning task for neural networks. This approach leads to a state-of-the-art practical result: the first improvement on the deep learning-based distinguisher for $S{\scriptsize PECK}32/64$ since 2019, where we enhance accuracy and extend the attack from 8 to a record 9 rounds.

Originally introduced as a machine learning problem in 1991, model extraction was explicitly cast as a cryptanalytic challenge at CRYPTO 2020 and has since gained increasing prominence in this context. While early work focused on ReLU-based neural networks, recent studies have investigated model extraction in the raw-output setting for PReLU-based models. However, research on other activation functions remains largely unexplored. In modern deep learning, activation functions beyond ReLU are widely used, thereby creating a need for extraction techniques that can accommodate a wider variety of activation functions. This paper broadens the scope of model extraction by introducing a systematic framework for parameter recovery that is specifically tailored to different categories of activation functions. In addition to ReLU and PReLU, we investigate several other activation functions, including Leaky ReLU, HardTanh, ELU, and the Step function. To the best of our knowledge, this is the first study to explore model extraction for these activation functions and for PReLU-based models in the hard-label setting. We provide a detailed theoretical analysis of the properties of each activation function, propose novel attack strategies, and offer new theoretical insights. The effectiveness of our approach is demonstrated through model extraction attacks in both the raw-output and hard-label settings. Moreover, we discuss the security implications of activation functions for neural network design and explore how composite or mixed activation functions may enhance security. This work provides valuable insights into model extraction and introduces a flexible framework that may have meaningful implications for both the cryptographic and machine learning communities.

The Rank Decoding Problem (R-DP) has gained a lot of attention due to the competitive KEM proposals ROLLO and RQC, as well as the more recent signature scheme RYDE, the latter being a second-round candidate in the ongoing NIST post-quantum standardization process. While previous attacks on the R-DP are based on combinatorial methods, the seminal work of [Bardet et al., 2020] has shown the potential of attacks that use algebraic modelings, breaking the proposed parameters of ROLLO and RQC. These algebraic attacks model the R-DP as a large system of equations. For most parameter ranges, this system is underdetermined; hence, the algebraic attack first needs to perform several guessing steps to obtain a reduced instance for which the system of equations is overdetermined. These steps, in essence, guess a supersupport of the unknown error support, making this attack a hybrid approach between combinatorial and algebraic solvers. In this paper, we present a novel type of guessing step based on searching a subsupport of the error support. While supersupport guessing only reduces the length and dimension of the code, subsupport guessing instead reduces the length and the rank weight of the sought-after error vector. This introduces an additional method for instance reduction compatible with supersupport guessing. Both types of guessing step can be performed sequentially in hybrid attacks, and their numbers can be optimized to outperform current hybrid attacks. We provide experimentally supported comparisons of the attack complexities with and without the novel guessing technique. We measure the impact of our new hybrid attack on the RYDE parameters; for the NIST security category 5 parameters, we decrease the hybrid MaxMinors attack complexity from 301 bits to 272 bits, outperforming all other known rank decoders and tightening the margin above the 256 threshold. For the other security levels, we decrease the complexities to be on par with the best performing combinatorial decoders.

We present practical attacks that completely break all four cryptographic schemes submitted to Malaysia's MySEAL 2.0 standardization initiative: the KAZ-KA key agreement scheme, the KAZ-KEM key encapsulation mechanism, the KAZ-SIGN v1.6.4, and KAZ-SIGN v2.0 digital signature schemes. KAZ-KA, KAZ-KEM, and KAZ-SIGN v2.0 operate over $\mathbb{Z}_N$ where $N$ is a primorial, the product of consecutive small primes. This design choice makes the group order $\varphi(N)$ extremely smooth, enabling efficient attacks. For KAZ-KA and KAZ-KEM, we recover the private key by enumerating candidates modulo each small prime factor and solving discrete logarithms in small groups. For KAZ-SIGN v2.0, we exploit the linear structure of signatures to formulate a hidden number problem instance, which we solve using lattice reduction with only two signatures. For KAZ-SIGN v1.6.4, we demonstrate universal signature forgery attacks using only the public key by exploiting its verification algorithm, without requiring the private key. All attacks are implemented and executed in under one second on a standard consumer laptop (a MacBook) across all suggested security levels (128, 192, and 256 bits). These results conclusively prove that the analyzed schemes are fundamentally insecure and unsuitable for any deployment or migration.

This paper introduces a generalized cryptanalytic framework for RSA and its variants, systematizing existing attacks while revealing a wide class of structural weaknesses independent of the private exponent's size. While traditional analyses exploit the key equation $ed \equiv 1 \pmod{(p-1)(q-1)}$ or its extensions like $ed \equiv 1 \pmod{(p^n-1)(q^n-1)}$ for a given RSA modulus $N=pq$ and its public exponent $e$, we unify these approaches by investigating the more general algebraic property defined by the congruence $eu \equiv 1 \pmod{(p^n-a)(q^n-b)}$, where $a$, $b$, and $u$ are unknown small integer parameters. Using Coppersmith's method with unravelled linearization, we demonstrate that the modulus $N$ can be factored in polynomial time if such a relation exists for parameters within a new, rigorously derived bound. Our framework not only unifies and generalizes several well-known attacks (retrieving their bounds as special cases when $a=b=1$) but also significantly expands the set of weak keys. We show that an RSA instance secure against all previous small private exponent attacks may still be broken if its public key possesses this hidden algebraic structure. This work serves as a comprehensive security analysis, highlighting a new family of weak keys that future cryptographic designs should avoid.

Is module-lattice reduction better than unstructured lattice reduction? This question was highlighted as 'Q8' in the Kyber NIST standardization submission (Avanzi et al., 2021), as potentially affecting the concrete security of Kyber and other module-lattice-based schemes. Foundational works on module-lattice reduction (Lee, Pellet-Mary, Stehlé, and Wallet, ASIACRYPT 2019; Mukherjee and Stephens-Davidowitz, CRYPTO 2020) confirmed the existence of such module variants of LLL and block-reduction algorithms, but focus only on provable worst-case asymptotic behavior. In this work, we present a concrete average-case analysis of module-lattice reduction. Specifically, we address the question of the expected slope after running module-BKZ, and pinpoint the discriminant $\Delta_K$ of the number field at hand as the main quantity driving this slope. We convert this back into a gain or loss on the blocksize $\beta$: module-BKZ in a number field $K$ of degree $d$ requires an SVP oracle of dimension $\beta + \log(|\Delta_K| / d^d)\beta /(d\log \beta) + o(\beta / \log \beta)$ to reach the same slope as unstructured BKZ with blocksize $\beta$. This asymptotic summary hides further terms that we predict concretely using experimentally verified heuristics. Incidentally, we provide the first open-source implementation of module-BKZ for some cyclotomic fields. For power-of-two cyclotomic fields, we have $|\Delta_K| = d^d$, and conclude that module-BKZ requires a blocksize larger than its unstructured counterpart by $d-1+o(1)$. On the contrary, for all other cyclotomic fields we have $|\Delta_K| < d^d$, so module-BKZ provides a sublinear $\Theta(\beta/\log \beta)$ gain on the required blocksize, yielding a subexponential speedup of $\exp(\Theta(\beta/\log \beta))$.

We will improve the best known lower bound of the $r$-th order nonlinearity of Boolean function for $r > 2$ via algebraic immunity

The Fujisaki-Okamoto transform is a popular solution to design post- quantum public key encryption schemes, or key encapsulation mechanisms. In order to ensure security against chosen-ciphertext attacks, it checks the validity of ciphertexts by re-encrypting decrypted messages. This operation in turn leads to severe side- channel weaknesses, because the re-encrypted messages can be made key-dependent. Hence, distinguishing them thanks to leakage is sufficient to extract (long-term) secret key information. As a result, recent works suggested to ensure the validity of ciphertexts by other means than re-encryption. For now, the main candidate for this purpose, integrated in the Polka encryption scheme (PKC 2023) and analyzed more generically by Hövelmanns et al. (EUROCRYPT 2025), is to use continuous norm checks through the decryption process. In this paper, we evaluate the extent to which replacing the FO-transform by such norm checks helps resistance against leakage. Negatively, we exhibit new attack vectors that were not anticipated in previous (heuristic) analyzes. Positively, we observe that the removal of the FO-transform nevertheless reduces the attack surface and we identify possible tracks to further minimize it. Overall, our results therefore shed light on the challenge of designing post-quantum public-key encryption schemes, or key encapsulation mechanisms, that can be efficiently protected against side-channel attacks. We hope they can inform theory about leakage sources that could be better taken over by design, to develop new schemes allowing a scarcer use of implementation-level countermeasures.

In this work, we present a practical fault-injection attack against the current Unbalanced Oil and Vinegar signature scheme non-deterministic implementation that enables complete secret key recovery from a single faulty signature, given one prior fault-free signature. By applying fault injection to disrupt the mixing of the vinegar and oil components during signature generation, the secret key can be recovered directly from the faulty signature. We validate the attack experimentally on a real device using an electromagnetic fault injection setup, establishing the required glitch in practice rather than through simulation. Our experimental results indicate that a single execution of the attack achieves a success rate exceeding 90%. Furthermore, we demonstrate the real-world feasibility of the attack by transferring the attack parameters to an architecturally equivalent target, requiring only minor recalibration. To the best of our knowledge, this is the first work to demonstrate an electromagnetic fault-injection attack in the context of multivariate-based signature schemes. Additionally, we discuss possible countermeasures to protect implementations of UOV-based schemes against such physical attacks.

In the McEliece public-key encryption scheme, a private key is almost always not determined uniquely by its associated public key. We highlight a structural characterization of equivalent private keys that reduces the cost estimate for a simple private-key search using the support-splitting algorithm (SSA) by a polynomial but practically very substantial factor. In addition, we show how to apply the attack to extended codes in order to further improve the performance of the attack. (All of these techniques appear to be known to experts, but not all details have previously been laid out in the literature.) In addition to spelling out the — thus far — missing details underlying these attack strategies, we provide an optimized software implementation of the SSA for this kind of key search and demonstrate its capabilities in practice by solving a key-recovery challenge with a naïve a‑priori cost estimate of $2^{91}$ bit operations in just ${\approx}\,1470$ core days, testing ${\approx}\,7700$ private-key candidates per core and second in the process. We stress that the speedup from those equivalences on private keys and from our implementation techniques is merely polynomial and does not indicate any weakness in realistic instantiations of the McEliece cryptosystem, whose parameter choices are primarily constrained by decoding attacks rather than ludicrously more expensive key-recovery attacks.

The butterfly structures were introduced by Perrin et al. as a generalization of the Dillon's APN permutation operated in 6 bits. It was proved by several authors independently that such butterflies are differentially 4-uniform and have best known nonlinearity among functions over $\mathbb{F}_{2^{2k}}$. In [LLHQ21, LHXZ22] authors provided sufficient coefficient conditions such that the closed butterfly is a permutation and they further prove that such functions have boomerang uniformity 4 and are linear equivalent to Gold functions. In this paper, we adopt techniques from [DZ23] and [GK] to classify closed butterfly structures satisfying more general conditions in terms of EA-equivalence and CCZ-equivalence.

In this work, we present two fault attacks against MPCitH-based signature schemes: we present a key recovery attack and a signature forgery attack, both of which only need a single successful fault injection to succeed. We analyze all five MPCitH-based schemes which are currently analyzed in round 2 of NIST's additional signature standardization process: Mirath, MQOM, PERK, RYDE, and SDitH. Our analysis shows that all five schemes are vulnerable to at least one of the attacks. We validate the practicality of our attacks using the ChipWhisperer setup and discuss countermeasures to prevent the attacks.

Neural network model extraction attacks pose a serious threat to the intellectual property of deep learning models. While most prior work focuses on Fully Connected Networks (FCNs), effective extraction of Convolutional Neural Networks (CNNs) remains underexplored, particularly in the hard-label setting. In this work, we propose the first systematic method for the recovery of complete CNN parameters in such conditions. By reformulating convolutional layers as sparse Block Toeplitz with Toeplitz Blocks (BTTB) matrices, we extend the model extraction attack method from FCNs to CNNs. The proposed method supports both one- and two-dimensional CNNs, handling scenarios with multiple kernels, multi-channel structures, and average pooling. To enhance computational efficiency and scalability, a kernel-centric clustering algorithm is proposed to exploit kernel parameter sharing, and a Singular Value Decomposition (SVD)-based acceleration strategy is adopted to address the computational cost of large sample sets. Moreover, we perform experiments to demonstrate that our method accurately and efficiently extracts CNN parameters, including multi-channel, multi-kernel and average-pooling layers, with a worst-case relative error of $2^{-17.75}$ and up to $2^{9.26}$ speedup, and recover large models LeNet-5 within practical runtime.

Efficiently masking multiplications in software is a long standing and extensively studied problem. A variety of gadgets have been proposed to perform these multiplications, each offering different trade-offs between efficiency and security. However, almost all existing solutions rely on arithmetic masking, in which multiplications cannot be naturally protected. In this work, we introduce two novel gadgets, named A2S and S2A, that enable conversions between arithmetic masking and Shamir’s Secret Sharing (SSS)-based masking. With this approach, multiplications can be performed naturally and securely in a sharewise manner. We prove that our gadgets achieve SNI security, which provides security guarantees and straightforward composability. Moreover, we demonstrate that composing them with multiplication yields PINI security. We then provide a detailed complexity analysis and discuss the contexts where our gadgets are most relevant. As a case study, we apply them to the MQOM post-quantum signature scheme, a candidate in the second round of the NIST additional post-quantum digital signature standardization process. When computing the sensitive multiplications in MQOM, for masking order t = 1, our approach reduces the number of multiplications, additions, and randomness requirements by 31%, 71%, and 60%, respectively, compared to the state of the art, while incurring only small additional memory overhead. We further show that these gains not only hold but actually increase as the masking order grows. Our results demonstrate that arithmetic-to-SSS conversions provide an effective and scalable path toward efficient masked implementations, making them particularly attractive for postquantum cryptography.

This work extends the methodology of the Class Elimination Attack (CEA) and the Reference Identities (RI/GRI) used in cryptanalysis for its application to block ciphers like AES and complex SPN variants. Probabilistic results concerning the partitioned key space are generalized to algebraic structures defined over finite fields $ \mathbb{F}_{2^n} $, linking them to the cipher's diffusion and confusion properties. Theorems establishing upper bounds for the expected number of classes to explore as a function of the diffusion capacity are proposed, and a parameterized complexity analysis is provided. The results offer a theoretical framework for evaluating the resistance of symmetric ciphers against attacks based on genetic algorithms and partition optimization.

ARADI is a low-latency block cipher introduced by the U.S. National Security Agency (NSA), targeting secure and efficient memory encryption. However, unlike most academic cipher proposals, the design rationale behind ARADI has not been made public, leaving its security to be only assessed through independent analysis. In this work, we present improved key-recovery attacks on up to 12 out of 16 rounds of ARADI in the single-key setting — advancing the best known attacks by two rounds. Our techniques build upon the ZeroSum distinguisher framework and leverage the Fast Hadamard Transform (FHT). A central insight in our attacks is that the linear layer of ARADI exhibits weak diffusion. This structural property allows partial decryption with only a subset of the round keys, significantly reducing the key-guessing space.

Since 2009, the cryptographic community has its eyes fixed on automatic tools based on solvers to help the cryptanalysts trying to attack symmetric cryptographic schemes. Among those automatic tools, TAGADA is dedicated to search for a particular kind of cryptanalysis called differential cryptanalysis. It is of major importance for the cryptographic community to have automatic tools dedicated to the analysis of security of symmetric key primitives to be convince about what symmetric key schemes should be used and what symmetric key schemes should not be used. In this paper, we will see how to extend TAGADA from differential cryptanalysis to boomerang cryptanalysis which is an important kind of attacks in symmetric key cryptography. We will also compare our tool with the two existing ones dedicated to boomerang distinguishers proposed by Hadipour et al. and Derbez et al.

To enhance the diversity of basic hard problems underlying post-quantum cryptography (PQC) schemes, NIST launched an additional call for PQC signatures in 2023. Among numerous candidate schemes, several code-based ones, which have successfully advanced to the second round, are constructed by applying the Fiat--Shamir transform to the parallel repetition of a (relatively low soundness) commit-and-prove sigma protocol similar to the Stern identification scheme. In Fiat--Shamir-based signatures, it is well-known that key material will be leaked if an attacker can somehow obtain what amounts, in the sigma protocol, to the responses to different challenges with respect to the same commitment. This idea is for example at the basis of a famous differential fault attack against deterministic Fiat--Shamir-based signatures like EdDSA. It is usually difficult to mount a fault injection attack based on that principle against a properly randomized Fiat--Shamir-based scheme however (at least with single faults): since commitment collisions are ruled out, it typically involves obtaining the responses to multiple challenges with respect to the same commitment within a single execution of the signature, which is often impossible by construction (e.g., because the extra information will not fit in a single signature, or because it is hard to force the computation of both responses). Due to the comparative inefficiency of signatures based on Stern-like protocols with parallel repetition, candidate constructions are led to use clever compression techniques to reduce signature size, in a way that increases the attack surface for physical attacks. In this paper, we demonstrate this against the LESS signature scheme, which uses so-called GGM trees for signature compression. We propose a simple fault attack on the construction of a binary array used to build the GGM tree, and show that a small number of faulty signatures suffice for full key recovery. We provide a thorough mathematical model of the attack as well as extensive experimental validation with glitch attacks on a ChipWhisperer board, showing that, depending on the target parameter set and the precise fault model we consider, full key recovery can very often be achieved with just one or two faulty signatures, and never more than a couple hundred even in the least favorable scenario for the attacker.

We introduce an efficient SAT-based space partitioning technique that enables systematic exploration of large search spaces in cryptanalysis. The approach divides complex search spaces into manageable subsets through combinatorial necklace generation, allowing precise tracking of explored regions while maintaining search completeness. We demonstrate the technique's effectiveness through extensive cryptanalysis of Ascon-Hash256. For differential-based collision attacks, we conduct an exhaustive search of 2-round collision trails, proving that no collision trail with weight less than 156 exists. Through detailed complexity analysis and parameter optimization, we present an improved 2-round collision attack with complexity $2^{61.79}$. We also discover new Semi-Free-Start (SFS) collision trails that enable practical attacks on both 3-round and 4-round Ascon-Hash256, especially improving the best known 4-round SFS trail from weight 295 to 250. Furthermore, applying the technique to Meet-in-the-Middle structure search yields improved attacks on 3-round Ascon-Hash256. We reduce the collision attack complexity from $2^{116.74}$ to $2^{114.13}$ with memory complexity $2^{112}$ (improved from $2^{116}$), and the preimage attack complexity from $2^{162.80}$ to $2^{160.75}$ with memory complexity $2^{160}$ (improved from $2^{162}$).

In this work we study quantitative existence results for genus-$2$ curves over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank at least $1$ or $2$, ordering the curves by the naive height of their integral Weierstrass models. We use geometric techniques to show that asymptotically the Jacobians of almost all integral models with two rational points at infinity have rank $r \geq 1$. Since there are $\asymp X^{\frac{13}{2}}$ such models among the $X^7$ curves $y^2=f(x)$ of height $\leq X$, this yields a lower bound of logarithmic density $13/14$ for the subset of rank $r \geq 1$. We further present a large explicit subfamily where Jacobians have ranks $r \geq 2$, yielding an unconditional logarithmic density of at least $5/7$. Independently, we give a construction of genus-$2$ curves with split Jacobian and rank $2$, producing a subfamily of logarithmic density at least $ 2/21$. Finally, we analyze quadratic and biquadratic twist families in the split-Jacobian setting, obtaining a positive proportion of rank-$2$ twists. These results have implications for Regev's quantum algorithm in hyperelliptic curve cryptography.

Nym is a reputation- and incentive-enhanced anonymous communications network that utilizes staking, performance monitoring, and rewards to encourage high-quality contributions. In this work, we analyze the reputation mechanism used in Nym’s Mixnet and NymVPN service. Using a combination of source code analysis, data collection from Nym mainnet, and network simulations with a custom simulator, we demonstrate active attacks that may allow a moderately resourced adversary to gain control of a fraction of Nym Mixnet’s active set. This condition may enable connection de-anonymization attacks. In particular, we show that the mechanism Nym uses to measure node performance is vulnerable to a form of “framing” attack that allows a small number of low-stake nodes to damage the score of high-reputation active nodes. We then consider and discuss various mitigations. This work highlights the challenge of nodes’ reliability measurement in reputation-enhanced networks, where the entry of low-reputation nodes is required for network survivability but also grants attackers a platform to launch attacks against the network.

Searchable Encryption (SE) has shown a lot of promise towards enabling secure and efficient queries over encrypted data. In order to achieve this efficiency, SE inevitably leaks some information, and a big open question is how dangerous this leakage is. While prior reconstruction attacks have demonstrated effectiveness in one-dimensional settings, extending them to high-dimensional datasets remains challenging. Existing methods either demand excessive query information (e.g. an attacker that has observed all possible responses) or produce low-quality reconstructions in sparse databases. In this work, we present REMIN, a new leakage-abuse attack against SE schemes in multi-dimensional settings, based on access and search pattern leakage from range queries. Our approach leverages unsupervised representation learning to transform query co-occurrence frequencies into geometric signals, allowing the attacker to infer relative spatial relationships between records. This enables accurate and scalable reconstruction of high-dimensional datasets under minimal leakage. We begin with a passive adversary that persistently observes all encrypted queries and responses, and later extend our analysis to an more active attacker capable of poisoning the dataset. Furthermore, we introduce REMIN-P, a practical variant of the attack that incorporates a poisoning strategy. By injecting a small number of auxiliary anchor points REMIN-P significantly improves reconstruction quality, particularly in sparse or boundary regions. We evaluate our attacks extensively on both synthetic and real-world structured datasets. Compared to state-of-the-art reconstruction attacks, our reconstruction attack achieves up to 50% reduction in mean squared error (MSE), all while maintaining fast and scalable runtime. Our poisoning attack can further reduce MSE by an additional 50% on average, depending on the poisoning strategy.

Ongoing efforts to transition to post-quantum public-key cryptosystems have created the need for algorithms with a variety of performance characteristics and security assumptions. Among the candidates in NIST's post-quantum standardisation process for additional digital signatures is FAEST, a Vector Oblivious Linear Evaluation in-the-Head (VOLEitH)-based scheme, whose security relies on the one-wayness of the Advanced Encryption Standard (AES). The VOLEitH paradigm enables competitive performance and signature sizes under conservative security assumptions. However, since it was introduced recently, in 2023, its resistance to physical attacks has not yet been analysed. In this paper, we present the first security analysis of VOLEitH-based signature schemes in the context of side-channel and fault injection attacks. We demonstrate four practical attacks on a masked implementation of FAEST in ARM Cortex-M4 capable of recovering the full secret key with high probability (greater than 0.87) from a single signature. These attacks exploit vulnerabilities of components specific to VOLEitH schemes and FAEST, such as the parallel all-but-one vector commitments, the VOLE generation, and the AES proof generation. Finally, we propose countermeasures to mitigate these attacks and enhance the physical security of VOLEitH-based signature schemes.

The Rank Syndrome Decoding (RSD) problem forms the foundation of many post-quantum cryptographic schemes. Its inherent hardness, with best known algorithms for common parameter regimes running in time exponential in $n^2$ (for $n$ being the code length), enables compact parameter choices and efficient constructions. Several RSD-based submissions to the first NIST PQC process in 2017 were, however, invalidated by algebraic attacks, raising fundamental concerns about the security of RSD-based designs. In this work, we revisit the parameters of prominent rank-based constructions and analyze the rationales that guided their selection, as well as their security against modern attacks. We provide a unified complexity analysis of all major RSD algorithms, including combinatorial, algebraic, and hybrid approaches, under a common cost model. All estimates are made publicly available through a dedicated open source module. Furthermore, we present the first asymptotic analysis of these algorithms, yielding deep insights into the relations between different procedures. We show that all studied algorithms converge to one of three distinct asymptotic runtime exponents. We then provide an asymptotic baseline in terms of the worst-case decoding exponent. In particular, we find that for an extension degree equal to the code length, the best known algorithms achieve a complexity of $2^{0.1481n^2 + o(n^2)}$, attained simultaneously by algebraic and combinatorial approaches. Overall, our results reinforce confidence in the RSD assumption and the design rationales of modern RSD-based schemes such as RYDE.

Searchable symmetric encryption (SSE) enables queries over symmetrically encrypted databases. To achieve practical efficiency, SSE schemes incur a certain amount of leakage; however, this leads to the possibility of leakage cryptanalysis, i.e., cryptanalytic attacks that exploit the leakage from the target SSE scheme to subvert its data and query privacy guarantees. Leakage cryptanalysis has been widely studied in the context of SSE schemes supporting either keyword queries or range queries, often with devastating consequences. However, little or no attention has been paid to cryptanalysing substring SSE schemes, i.e., SSE schemes supporting arbitrary substring queries over encrypted data. This is despite their relevance to many real-world applications, e.g., in the context of securely querying outsourced genomic databases. In this paper, we present the first leakage cryptanalysis of three prominent substring-SSE schemes due to Chase and Shen (PoPETS '15), Faber et al. (ESORICS '15), and Hahn et al. (SIGMOD 2018). We propose novel, inference-based query reconstruction attacks on each of these schemes that exploit their respective leakage profiles. We implement our attacks and experimentally validate their success rates and efficiency over real-world datasets. Our attacks achieve high query reconstruction rate with practical efficiency, and scale smoothly to large datasets. Notably, our attack success attack rate is the highest against the scheme due to Hahn et al. (SIGMOD 2018), which is the most recent of the three schemes. This demonstrates that, as far as substring SSE is concerned, newer schemes are not necessarily "more secure". To the best of our knowledge, ours are the first and only query reconstruction attacks on (and the first systematic leakage cryptanalysis of) any substring-SSE scheme to date. Query reconstruction against substring SSE schemes is inherently harder to achieve than against traditional SSE schemes for keyword search, as the query space for substring SSE is significantly larger. In fact, while the vast majority of known attacks against SSE schemes for keyword search restrict the query space to the most-frequent keywords, our attacks achieve decent query recovery rates without any such restriction on the queried substrings. Our work carries a wider message for designers of SSE schemes: it is not sufficient to merely identify the leakage profile of any new scheme; rather, it is incumbent on designers to cryptanalyze that leakage profile and show that is not consequential in the face of state-of-the-art attacks. The novel attack techniques in our paper provide a starting point for such analysis for substring SSE schemes.

Side-channel analysis (SCA) has emerged as a critical field in securing hardware implementations against potential vulnerabilities. With the advent of artificial intelligence(AI), neural network-based approaches have proven to be among the most useful techniques for profiled SCA. Despite the success of NN-assisted SCA, a critical challenge remains, namely understanding predictive uncertainty. NNs are often uncertain in their predictions, leading to incorrect key guesses with high probabilities, corresponding to a higher rank associated with the correct key. This uncertainty stems from multiple factors, including measurement errors, randomness in physical quantities, and variability in NN training. Understanding whether this uncertainty arises from inherent data characteristics or can be mitigated through better training is crucial. Additionally, if data uncertainty dominates, identifying specific trace features responsible for misclassification becomes essential. We propose a novel approach to estimating uncertainty in NN-based SCA by leveraging Renyi entropy, which offers a generalized framework for capturing various forms of uncertainty. This metric allows us to quantify uncertainty in NN predictions and explain its impact on key recovery. We decompose uncertainty into epistemic (model-related) and aleatoric (data-related) components. Given the challenge of estimating probability distributions in high-dimensional spaces, we use matrix-based Renyi α-entropy and α-divergence to better approximate leakage distributions, addressing the limitations of KL divergence in SCA. We also explore the sources of uncertainty, e.g., resynchronization, randomized keys, as well as hyperparameters related to NN training. To identify which time instances (features in traces) contribute most to uncertainty, we also integrate SHAP explanations with our framework, overcoming the limitations of conventional sensitivity analysis. Lastly, we show that predictive uncertainty strongly correlates with standard SCA metrics like rank, offering a complementary measure for evaluating attack complexity. Our theoretical findings are backed by extensive experiments on available datasets and NN models.

Side-channel attacks exploiting Plaintext-Checking (PC) and Decryption Failure (DF) oracles are a pressing threat to deployed post-quantum cryptography. These oracles can be instantiated from tangible leakage sources like timing, power, and microarchitectural behaviors, making them a practical concern for leading schemes based on lattices, codes, and isogenies. In this paper, we revisit chosen-ciphertext side-channel attacks that leverage the DF oracle on ML-KEM. While DF oracles are often considered inefficient compared to their binary PC counterparts in lattice-based schemes, we demonstrate that their full potential has been largely unrealized. We introduce a novel attack framework that combines adaptive query generation with belief propagation for Low-Density Parity-Check (LDPC) codes. Our methodology crafts carefully balanced parity checks over multiple secret coefficients, maximizing the Shannon information extracted from each oracle query, even in the presence of significant noise. This approach dramatically reduces the number of queries required for a full key recovery, achieving near-optimal efficiency by approaching the theoretical Shannon information bound. For ML-KEM-768 with an oracle accuracy of 95%, our attack requires only 2950 queries (a 1.35 ratio to the Shannon lower bound), establishing that a well-designed DF attack can surpass the efficiency of state-of-the-art binary PC attacks. To validate the practical impact of our findings, we apply our framework to the recent GoFetch attack, showing significant gains in this real-world, microarchitectural side-channel scenario. Our method reduces the required measurement traces by over an order of magnitude and eliminates the need for computationally expensive post-processing, enabling a full key recovery on higher-security schemes previously considered intractable.

Hash functions and extendable output functions are some of the most fundamental building blocks in cryptography. They are often used to build commitment schemes where a committer binds themselves to some value that is also hidden from the verifier until the opening is sent. Such commitment schemes are commonly used to build signature schemes, e.g., Ed25519 via Schnorr signatures, or non-interactive zero-knowledge proofs. We specifically analyze the binding security when Ascon-Hash256 or Ascon-XOF128 is used inside of Ed25519, which is closely related to finding second preimages. While there is ample prior work on Ascon-XOF128 and Ascon-Hash256, none of it applies in this setting either because it analyzes short outputs of 64 or 128 bits or because the complexity is above the security claim and generic attack of 128 bits. We show how to exploit the setting of finding a forgery for Ed25519. We find that this setting is quite challenging due to the large 320-bit internal state combined with the 128-bit security level. We propose a second-preimage attack for 1-round Ascon-Hash256 with a complexity of $2^{64}$ Gaussian eliminations and a random-prefix-preimage attack (also known as Nostradamus attack) for 1-round Ascon-Hash256, for the Ed25519 setting, with complexity $2^{29.7}$ Gaussian eliminations.

The ongoing transition to post-quantum cryptography has led to a surge of research in side-channel countermeasures tailored to these schemes. A prominent method to prove security in the context of side-channel analysis is the utilization of the well-established t-probing model. However, recent studies by Hermelink et al. at CCS 2024 demonstrate a simple and practical attack on a provably secure implementation of the Fujisaki-Okamoto transform. In this paper, we present an unsupervised single-trace side-channel attack on a tenth-order masked implementation of fixed-weight polynomial sampling. Notably, this masking scheme has also been proven to be secure in the t-probing model. Both attacks reveal a mismatch between the correct, well-understood theory of the t-probing model and its practical application – the security proofs are valid, yet the attacks still succeed at high noise levels. Therefore, we take a closer look at the underlying causes and the assumptions made for transferring t-probing security to practice. In particular, we investigate the amount of noise required for this transfer. We find that, depending on the design decisions, the additional noise required can be substantial and difficult to achieve. Consequently, we examine the factors that impact the required amount of additional noise and which need to be considered for practically secure implementations. In particular, non-uniformly distributed shares – a setting that is increasingly encountered in post-quantum cryptographic algorithms – can lead to an increased noise requirement, and thus could reduce the security level of the masked implementation. Our analysis allows us to provide practical guidelines for masking scheme designers, thereby facilitating the development of theoretically and practically secure designs.

Side-channel attacks following a classical differential power analysis (DPA) style are well understood, along with the effect the mask- ing countermeasure has on them. However, simple attacks (SPA) where the target variable does not vary thanks to a known value, such as the plaintext, are less studied. In this paper, we investigate how the masking countermeasure affects the success rate of simple attacks. To this end, we provide theoretical, simulated, and practical experiments. Interestingly, we will see that masking can allow us to asymptotically recover more information on the secret than in the case of an unprotected implemen- tation, depending on the masking type. We will see that this is true for masking encodings that add non-linearity with respect to the leakages, such as arithmetic masking, while it is not for Boolean masking. We be- lieve this context provides interesting results, as the average information of arithmetic encoding is proven less informative than the Boolean one.

A partial key exposure attack is a key recovery attack where an adversary obtains a priori partial knowledge of the secret key, e.g., through side-channel leakage. While for a long time post-quantum cryptosystems, unlike RSA, have been believed to be resistant to such attacks, recent results by Esser, May, Verbel, and Wen (CRYPTO ’22), and by Kirshanova and May (SCN ’22), have refuted this belief. In this work, we focus on partial key exposure attacks in the context of rank-metric-based schemes, particularly targeting the RYDE, MIRA, and MiRitH digital signatures schemes, which are active candidates in the NIST post-quantum cryptography standardization process. We demonstrate that, similar to the RSA case, the secret key in RYDE can be recovered from a constant fraction of its bits. Specifically, for NIST category I parameters, our attacks remain efficient even when less than 25% of the key material is leaked. Interestingly, our attacks lead to a natural improvement of the best generic attack on RYDE without partial knowledge, reducing security levels by up to 9 bits. For MIRA and MiRitH our attacks remain efficient as long as roughly 57%-60% of the secret key material is leaked. Additionally, we initiate the study of partial exposure of the witness in constructions following the popular MPCitH (MPC-in-the-Head) paradigm. We show a generic reduction from recovering RYDE and MIRA’s witness to the MinRank problem, which again leads to efficient key recovery from constant fractions of the secret witness in both cases.

We show that a simple eavesdropper listening in on classical communication between potentially entangled quantum parties will eventually be able to impersonate any of the parties. Furthermore, the attack is efficient if one-way puzzles do not exist. As a direct consequence, one-way puzzles are implied by reusable authentication schemes over classical channels with quantum pre-shared secrets that are potentially evolving. As an additional application, we show that any quantum money scheme that can be verified through only classical queries to any oracle cannot be information-theoretically secure. This significantly generalizes the prior work by Ananth, Hu, and Yuen (ASIACRYPT'23) where they showed the same but only for the specific case of random oracles. Therefore, verifying black-box constructions of quantum money inherently requires coherently evaluating the underlying cryptographic tools, which may be difficult for near-term quantum devices.

This paper focuses on the optimization of the number of logical qubits in quantum algorithms for factoring and computing discrete logarithms in $\mathbb{Z}_N^*$. These algorithms contain an exponentiation circuit modulo $N$, which is responsible for most of their cost, both in qubits and operations. In this paper, we show that using only $o(\log N)$ work qubits, one can obtain the least significant bits of the modular exponentiation output. We combine this result with May and Schlieper's truncation technique (ToSC 2022) and the Eker{\aa}-H{\aa}stad variant of Shor's algorithm (PQCrypto 2017) to solve the discrete logarithm problem in $\mathbb{Z}_N^*$ using only $d + o(\log N)$ qubits, where $d$ is the bit-size of the logarithm. Consequently we can factor $n$-bit RSA moduli using $n/2 + o(n)$ qubits, while current envisioned implementations require about $2n$ qubits. Our algorithm uses a Residue Number System and succeeds with a parametrizable probability. Being completely classical, we have implemented and tested it. For RSA factorization, we can reach a gate count $\mathcal{O}(n^3)$ for a depth $\mathcal{O}(n^2 \log^3 n)$, which then has to be multiplied by $\mathcal{O}(\log n)$ (the number of measurement results required by Eker{\aa}-H{\aa}stad). To factor an RSA-2048 instance, we estimate that 1730 logical qubits and $2^{36}$ Toffoli gates will suffice for a single run, and the algorithm needs on average 40 runs. To solve a discrete logarithm instance of 224 bits (112-bit classical security) in a safe-prime group of 2048 bits, we estimate that 684 logical qubits would suffice, and 20 runs with $2^{32}$ Toffoli gates each.

The stream cipher ChaCha is one of the most widely used ciphers in the real world, such as in TLS, SSH and so on. In this paper, we study the security of ChaCha via differential cryptanalysis based on probabilistic neutral bits (PNBs). We introduce the syncopation technique for the PNB-based approximation in the backward direction, which significantly amplifies its correlation by utilizing the property of ARX structure. In virtue of this technique, we present a new and efficient method for finding a good set of PNBs, and then a refined framework of key-recovery attack is formalized for round-reduced ChaCha. Further, we generalize the PNB-based approximation by a concept called probabilistic neutral expressions (PNEs). In the PNE-based framework, a new key guessing strategy is presented along with the carry-preserving technique. The new techniques allow us to break 7.5 rounds of 256-bit ChaCha, as well as to bring faster attacks on 7 rounds of 256-bit ChaCha. In addition, to the best of our knowledge, we present the first related-key attack on 256-bit ChaCha8 which is one out of three original ciphers in the ChaCha family. Regarding 128-bit ChaCha, our techniques permit us to defeat 7 rounds when excluding the last rotation.

We show that the secret sharing scheme [Cryptogr. Commun. 16(1): 3-20 (2024)] cannot be put into practice. (1) It confused the elements in a residue class ring modulo a prime $p$ with the points in an elliptic curve group over the finite field $F_p$. (2) It confused the underlying elliptic curve with the Lagrange interpolating curve, and falsely requires the interpolating polynomial to map a point on the elliptic curve to another point on the same elliptic curve. (3) It misuses the bit-wise XOR operator for the operands with unequal bit-length, which results in the exposure of any participant's share, and the loss of confidentiality.

Sequences over the residue ring of integers modulo $m$ generated by linear feedback shift registers (LFSRs) exhibit ring-level linearity and bit-level nonlinearity, making such kind of LFSRs (denoted as $\mathbb{Z}/(m)$-LFSRs) a key component of stream ciphers. Beyond fundamental cryptographic properties, the unpredictability of truncated $\mathbb{Z}/(m)$-LFSRs has attracted considerable attention as a critical security consideration in the design of stream cipher components. This paper investigates the unpredictability of truncated Fibonacci $\mathbb{Z}/(m)$-LFSRs under various scenarios. First, we provide a practical heuristic estimation for the values of two key parameters based on lattice theory, thereby avoiding previous blind search. This estimation is subsequently applied to determine the number of truncated digits required in different scenarios. Next, we develop a lattice-based method for finding annihilating polynomials over $\mathbb{Z}/(m)$ by the high-order truncated digits when the modulus $m$ is known but coefficients are unknown, filling a methodological gap for this specific case. Finally, we demonstrate that when both the modulus $m$ and coefficients are unknown but $m$ is close to a power of 2, our lattice constructed by the high-order truncated digits can yield annihilating polynomials over $\mathbb{Z}/(m)$ rather than $\mathbb{Z}$ as in [1], achieving a 41% reduction in digits and a 4x speedup for the recovery of ZUC's driving sequence with 17 high-order truncated digits. Experimental results confirm the efficacy of our methods.

We present the first power side-channel analysis of a Hybrid Homomorphic Encryption (HHE) tailored symmetric encryption scheme. HHE combines lightweight client-side Symmetric Encryption (SE) with server-side homomorphic evaluation, enabling efficient privacy-preserving computation for the client and minimizing the communication overhead. Recent integer-based HHE designs such as PASTA, MASTA, HERA, and Rubato rely on prime-field arithmetic, but their side-channel security has not been studied. This gap is critical, as modular arithmetic and large key spaces in integer-based schemes introduce new leakage vectors distinct from those in conventional Boolean symmetric ciphers. In this work, we close this gap by presenting the first power side-channel analysis of an HHE-tailored scheme - HERA. Our results demonstrate a successful key recovery from as few as 40 power traces using Correlation Power Analysis. In addition to showing that such attacks are feasible, we develop the first masking framework for integer-based SE schemes to mitigate them. Our design integrates PINI-secure gadgets with assembly-level countermeasures to address transition leakage, and we validate its effectiveness using the Test Vector Leakage Assessment. Our experiments confirm both the practicality of the attack and the strength of the proposed countermeasures. We also demonstrate that the framework extends to other integer-based HHE schemes, by applying our technique to PASTA. Thus, we provide leakage models, identify relevant attack targets, and define evaluation benchmarks for integer-based HHE-tailored SE schemes, thereby filling a longstanding gap and laying the foundation for side-channel-resilient design in this area.

The impossible boomerang attack is a powerful cryptanalytic technique, but existing key recovery methods face several limitations that restrict its applicability. Specifically, the key pre-guessing is coarse-grained, S-box details are ignored in the differential propagation, the complexity estimation and the key guessing order determination remain rudimentary. To overcome these issues, we introduce three key improvement measures. First, we propose a flexible partial key and difference pre-guessing technique based on directed graphs, enabling selective identification of required keys and differences for generating partial pairs and quartets. Second, we propose a pre-sieving technique to early eliminate invalid quartets by exploiting cipher-specific details. Third, we introduce an automatic key-guessing strategy based on the same directed graphs to efficiently determine valid guessing orders. We integrate these techniques to develop a unified key recovery framework for impossible boomerang attacks, accompanied by a formal and precise characterization of the overall complexity. This is the first framework to support flexible key and difference pre-guessing while incorporating block cipher details during key recovery for impossible boomerang attacks. Crucially, it enables the automatic generation of detailed recovery steps, a capability missing in prior work. As applications, under the four related-key/tweakey setting, we apply the framework to \ARADI{}, a low-latency cipher proposed by the National Security Agency (NSA), and \SKV{}, a threshold-implementation-friendly cipher proposed at EUROCRYPT 2020. For \ARADI{}, we achieve the first full-round attack with $2^{130}$ data, $2^{253.78}$ time, and $2^{235.75}$ memory complexity. For \SKV{}, we present the first 34-round impossible boomerang attack with $2^{66}$ data, $2^{253.75}$ time, and $2^{239.75}$ memory complexity. These results demonstrate the framework’s significance and its substantial improvement in advancing the impossible boomerang attack.

AI-powered attacks on Learning with Errors (LWE), an important hard math problem in post-quantum cryptography, rival or outperform "classical" attacks on LWE under certain parameter settings. Despite the promise of this approach, a dearth of accessible data limits AI practitioners' ability to study and improve these attacks. Creating LWE data for AI model training is time- and compute-intensive and requires significant domain expertise. To fill this gap and accelerate AI research on LWE attacks, we propose the TAPAS datasets, a Toolkit for Analysis of Post-quantum cryptography using AI Systems. These datasets cover several LWE settings and can be used off-the-shelf by AI practitioners to prototype new approaches to cracking LWE. This work documents TAPAS dataset creation, establishes attack performance baselines, and lays out directions for future work.

Key-dependent attacks are effective only for specific weak-key classes, limiting their practical impact. We present a generic statistical framework that combines multiple key-dependent distinguishers into universal attacks covering the full key space. Using log-likelihood ratio statistics, our framework tests the secret key against multiple weak-key distinguishers, aggregates their evidence to determine whether the key is weak or strong for each distinguisher, and exploits this classification to reduce the effective key entropy for key recovery. We apply this to Orthros-PRF, a sum-of-permutations (SoP) design where any differential-based distinguisher holds only for a fraction of keys. This yields the first universal 8-round differential-linear (DL) key-recovery attack with median time complexity $2^{119.58}$, whereas prior work reached at most 7 rounds in the weak-key setting. To discover the required distinguishers, we extend the open-source S-box Analyzer tool with MILP support for deterministic propagation and develop a model integrating distinguisher search with key recovery. This enables automated discovery of multidimensional DL distinguishers covering up to 10 rounds in each Orthros branch, improving prior work by 4 rounds. Our results demonstrate that statistical aggregation of multiple weak-key distinguishers enables effective universal cryptanalysis. Our framework is generic and is applicable to other primitives with multiple identifiable weak-key classes.

The growth of advanced cryptographic applications has driven the development of arithmetization-oriented (AO) ciphers over large finite fields, which are designed to minimize multiplicative complexity. However, this design advantage of AO ciphers could also serve as an attack vector. For instance, the \textsf{AIM} one-way function in the post-quantum signature \AIMer proposed at CCS 2023 has been broken by several works soon after its publication. The designers then promptly developed secure patches and proposed an enhanced version, \textsf{AIM2}, which was updated to the latest version of \AIMer that has been selected as one of the winners of the Korean PQC Competition in early 2025. In this paper, we focus on the algebraic security of AIM2 over $\mathbb{F}_{2^n}$. First, we introduce a resultant-minimized model that reduces eliminations by using a non-$k$ based substitution strategy and linearized-polynomial decomposition, achieving an attack time complexity of $2^{188.76}$ ($2^{195.05}$) primitive calls of \textsf{AIM2-III} when $\omega=2$ ($\omega=2.373$), indicating that the designers have been over-optimistic in the evaluation of their security margin; Second, we propose a subfield reduction technique for the case that exponents approach subfield extension sizes, equation degrees collapse sharply, \textit{e.g.,} the exponent $e_2=141\mapsto 13$ in \textsf{AIM2-V} when considering the subfield $\mathbb{F}_{2^{128}}$. This can lower the algebraic attack complexity to $2^{295.97}$ primitive calls at $\omega=2$, which improves upon designers' estimated bound of Gr\"{o}bner basis attack by about $2^{100}$. Besides, based on our attack methods, we have identified some weak parameter choices, which could provide concrete design guidance for \textsf{AIM2} construction, especially for the exponent of its Mersenne S-box. Finally, to address the potential vulnerabilities, we further propose \textsf{AIM2-patch} with a simple secure patch on \textsf{AIM2}, which can prevent key elimination, neutralize linearized-polynomial decomposition, and raise algebraic attack complexity, while incurring negligible overheads in \AIMer scheme.

As a theoretical cornerstone of post-quantum cryptography, the Learning With Errors (LWE) problem serves as the security foundation for standardized algorithms such as Kyber and Dilithium. Recently, a framework for provable dual attacks on LWE has been proposed by Pouly et al. in Eurocrypt 2024, addressing the limitations in effectiveness caused by existing methods' reliance on heuristic assumptions in LWE dual attacks. Their paper also poses an open problem on how to formally integrate modulus switching into this framework to reduce attack costs. The main purpose of this paper is to give a solution of this open problem by presenting an improved provable dual attack method that incorporates modulus switching and Chinese Remainder Theorem (CRT) techniques. First, we design a modulus switching mechanism that eliminates practical errors via the Poisson summation formula. By embedding the inherent noise from modulus switching into a rational lattice framework, our approach effectively preventing the risk of attack failure caused by the merging of such errors with LWE noise. Theoretical guarantees (Theorems \ref{main_theorem} and \ref{main_theorem_entire}) rigorously quantify the parameter ranges for successful attacks. Second, we introduce a CRT-based secret recovery method that aggregates partial secrets from independent sub-attacks. By leveraging the Chinese Remainder Theorem to reconstruct full secrets from congruence relations, our method adapts to arbitrary secret distributions. Furthermore, by using a tighter variant of Banaszczyk's measure inequality, we obtain a precise parameter range for the dual attack's efficacy through rigorous mathematical proof, and achieve the same complementary gap with the contradictory regime (proposed by Ducas et al.) as in Pouly et al.'s work. Experiments show $4$-$5$ bits superior performance in attack estimation compared to the original framework.

The module-lattice-based digital signature standard, formerly known as CRYSTALS-DILITHIUM, is a lattice-based post-quantum cryptographic scheme. In August 2024, the National Institute of Standards and Technology officially standardized ML-DSA under FIPS 204. ML-DSA generates one valid signature and multiple rejected signatures during a single signing process. Most side-channel attacks targeting ML-DSA have focused solely on the valid signature, while largely neglecting the hints contained in rejected signatures. Building on prior SASCA frameworks originally proposed for ML-DSA, in this paper we present an efficient and fully practical instantiation of a private-key recovery attack on ML-DSA that jointly exploits side-channel leakages from both valid and rejected signatures within a unified factor graph. This concrete instantiation maximizes the information extracted from a single signing attempt and minimizes the number of required traces for full key recovery. We conducted a proof-of-concept experiment with both reference and ASM-optimized implementations on a Cortex-M4 core chip, where the results demonstrate that incorporating rejected signatures reduces the required number of traces by at least $50.0\%$ for full key recovery. Moreover, we show that using only rejected signatures suffices to recover the key with fewer than $30$ traces under our setup. Our findings highlight that protecting rejected signatures is crucial, as their leakage provides valuable side-channel information. We strongly recommend implementing countermeasures for rejected signatures during the signing process to mitigate potential threats.

We incorporate a meet-in-the-middle strategy into the enumeration algorithm, enabling a tunable time-memory trade-off. The algorithm can achieve a minimum asymptotic time complexity of \(n^{n/(4e) + o(n)}\), which, in return, demands memory of the same order. This represents a square-root improvement over the state-of-the-art enumeration algorithms. More generally, our approach attains a time complexity of~$n^{cn/(2e) + o(n)}$ with memory usage \(n^{(1-c)n/(2e) + o(n)}\), where $c$ is any constant satisfying \(\frac{1}{2} \leq c < 1\). Our approach decouples the head and tail blocks of the lattice basis. For a properly selected parameter, each enumeration space becomes asymptotically the square root of the original search space. Each tail vector is then extended to the head block space to find its closest vectors using an efficient neighboring search algorithm. Among all pairs of neighboring vectors that we iterate through, the shortest difference vector is then the solution to the Shortest Vector Problem (SVP). Apart from the exact version of the algorithm which is of theoretical interest, we also propose heuristic strategies to improve the practical efficiency. First, we show the adaptation of our algorithm to pruned enumeration. Then we show that with a particularly chosen backbone lattice (rescaled~\(\mathbb{Z}^n\)), we are able to accelerate the neighboring search process to an extremely efficient degree. Finally, we optimize parameters and give a practical cost estimation to show how much acceleration we could bring using this new algorithm.

We provide several attacks on the BASS signature scheme introduced by Grigoriev, Ilmer, Ovchinnikov and Shpilrain in 2023. We lay out a trivial forgery attack which generates signatures passing the scheme's probabilistic signature verification with high probability. Generating these forgeries is faster than generating signatures honestly. Moreover, we describe a key-only attack which allows us to recover an equivalent private key from a signer's public key. The time complexity of this recovery is asymptotically the same as that of signing messages.

At NeurIPS 2024, Kera et al. introduced the use of transformers for computing Groebner bases, a central object in computer algebra with numerous practical applications. In this paper, we improve this approach by applying Hierarchical Attention Transformers (HATs) to solve systems of multivariate polynomial equations via Groebner bases computation. The HAT architecture incorporates a tree-structured inductive bias that enables the modeling of hierarchical relationships present in the data and thus achieves significant computational savings compared to conventional flat attention models. We generalize to arbitrary depths and include a detailed computational cost analysis. Combined with curriculum learning, our method solves instances that are much larger than those in Kera et al. (2024 Learning to compute Groebner bases)

We propose BLASter, a proof of concept LLL implementation that demonstrates the practicality of multiple theoretical improvements. The implementation uses the segmentation strategy from Neumaier–Stehlé (ISSAC 2016), parallelism and Seysen's reduction that was proposed by Kirchner–Espitau–Fouque (CRYPTO 2021) and implemented in OptLLL, and the BLAS library for linear algebra operations. It consists of only 1000 significant lines of C++ and Python code, and is made publicly available. For q-ary lattices that fplll can handle without multiprecision (dimension <180), BLASter is considerably faster than fplll, OptLLL and Ryan–Heninger's flatter (CRYPTO 2023), without degrading output reduction quality. Thanks to Seysen's reduction it can further handle larger dimension without resorting to multiprecision, making it more than 10x faster than flatter and OptLLL, and 100x faster than fplll in dimensions 256 to 1024. It further includes segmented BKZ and segmented deep-LLL variants. The latter provides bases as good as BKZ-15 and has a runtime that is only a couple of times more than our LLL baseline. This remains a proof of concept: the effective use of higher precision—which is needed to handle \(\textit{all}\) lattices—has further obstacles and is left for future work. Still, this work contains many lessons learned, and is meant to motivate and guide the development of a robust and modern lattice reduction library, which shall be much faster than fplll.

Cube attack is one of the most powerful approaches for recovering keys of stream ciphers. Practical cube attacks generate several superpolys first and solve the system constructed by these superpolys afterward. Unlike previous practical attacks, we propose a new cube attack that transfers the difficulty of generating easy-solving superpolys to solving the system built by numerous nonlinear ones. In the offline phase, we recovered lots of nonlinear superpolys by improving the approach proposed by Delaune et al. at SAC 2022 in theory. In the online phase, taking advantage of the sparsity and asymmetry of these numerous superpolys, we present a new testing method to solve the constructed system efficiently. As applications, the latest attack could practically recover the keys for 820- and 832-round Trivium with the time complexity no more extensive than $2^{46}$ and $2^{50}$, while the previous highest number of rounds of Trivium that can be attacked practically is 830. We believe the proposed approach can be used to attack more rounds of Trivium and other stream ciphers.

The hardness of finding isogenies of degree $d$ between supersingular elliptic curves is a fundamental assumption in isogeny-based cryptography. Let $E_1$ and $E_2$ be supersingular elliptic curves defined over $\mathbb{F}_{p^2}$, and let $d$ be a smooth integer. %removed > p^{1/2} part. At CRYPTO~2024, Benčina et al.\ proposed an algorithm with time complexity $\widetilde{O}(\max\{p^{1/2}, d/p^{5/8}\})$ in the classical setting and $\widetilde{O}(\max\{p^{1/4}, d^{1/2}/p^{1/4}\})$ in the quantum setting. In this work, we first observe that their analysis omits a sub-exponential factor $\exp(O(\log^{3/4} p))$. We then improve their result to $\widetilde{O}(\max\{p^{1/2}, \exp(O(\log^{4/5} p)) \cdot d/p^{2/3}\})$ classically and $\widetilde{O}(\max\{p^{1/4}, \exp(O(\log^{4/5} p)) \cdot d^{1/2}/p^{1/3}\})$ quantumly. Our approach relies on small-root bounds for Coppersmith’s method applied to a four-variable integer equation. To this end, we adapt the explicit asymptotic formulas for small-root bounds introduced by Feng et al.\ (CRYPTO~2025) in the modular setting to the integer setting. As an additional application, we strengthen the attack of Benčina et al.\ on the SIDH signature scheme by Basso et al. (ACNS~2024). We expect that these refined techniques for Coppersmith’s method will be valuable for further post-quantum cryptanalysis.

The threat of practical quantum attacks has catapulted viable alternatives like Post-Quantum Cryptography (PQC) into prominence. The adoption and integration of standardized PQC primitives across the entire digital stack are promoted by various standardization bodies, governments, and major corporate houses. A serious challenge in quantum migration is to ensure that there is no hidden backdoor in the PQC implementations of a hybrid cryptosystem (support for both pre-quantum and post-quantum algorithms), which are often procured from a third-party vendor. In this manuscript, we investigate the possibility of a kleptographic backdoor on the NIST-recommended key-encapsulation mechanism CRYSTALS-Kyber. The modified Kyber key-generation algorithm achieves indistinguishable decryption failure probability compared to the original CRYSTALS-Kyber. The kleptographic module is also implemented in FPGA, embedded inside the CRYSTALS- Kyber accelerator with a very low area overhead (283 LUTs or 2% of total area), and thus can easily pass performance and functionality tests.

We study several asymmetric structured key agreement schemes based on noncommutative matrix operations, including the recent proposal of Lizama as well as the strongly asymmetric algorithms SAA-3 and SAA-5 of Accardi et al.\ We place them in a common algebraic framework for public key agreement and identify simple structural conditions under which an eavesdropper can reconstruct an effective key-derivation map and reduce key recovery to solving linear systems over finite fields. We then show that the three matrix-based schemes mentioned above all instantiate our algebraic framework and can therefore be broken in polynomial time from public information alone. In particular, their security reduce to the hardness of linear-algebraic problems and does not exceed that of the underlying discrete logarithm problem. Our results demonstrate that the weakness of these schemes is structural rather than parametric, and that minor algebraic modifications are insufficient to repair them.

This paper presents implementations that match and, where possible, exceed current quantum factorisation records using a VIC-20 8-bit home computer from 1981, an abacus, and a dog. We hope that this work will inspire future efforts to match any further quantum factorisation records, should they arise.

Hamming Quasi-Cyclic (HQC) has recently been selected by NIST, after the Round 4 submission, as a postquantum key encapsulation mechanism (KEM) standard and will soon be widely deployed. Therefore, it is important to ensure its implementation is constant-time, i.e., resistant to side-channel attacks. Existing timing attacks on HQC exploit non-constant-time source code and the decryption that is vulnerable to chosen-ciphertext attacks. These active attacks require constructing thousands of invalid ciphertexts, and thus, they can be easily detected. The latest HQC implementation has mitigated all these attacks by making its source code constant-time. In this work, we provide a new perspective on reviewing the implementation of HQC and exploiting timing leakages. For the first time, we show that an attacker can recover the secret key of HQC without targeting the CCA-insecure decryption and internal states of message decryption. Specifically, an attacker can exploit the timing leakages that occur when processing sparse vectors, which are ciphertext-independent, to recover the secret key by measuring the leakages only once. We find two such timing leakages in the latest stable HQC implementation, supposedly constant-time, and practically extract the leakages even when the process is protected by AMD Secure Encryption Virtualization. We also show that a power side-channel can extract similar leakages on embedded devices. Our findings apply to all code-based KEMs that are submitted to the NIST Round 4 PQC submission. We show that an attacker can also perform similar passive attacks to recover the session key of BIKE and Classic McEliece. To help write constant-time code, we propose and test a workflow that uses CT-grind when developing the code. We find that CT-grind can effectively find all timing leakages in various implementations of HQC. Therefore, we suggest that cryptographic developers constantly use constant-time analysis tools when developing code.