Secure elements are small microcontrollers whose main purpose is to generate/store secrets and then execute cryptographic operations. They undergo the highest level of security evaluations that exists (Common Criteria) and are often considered inviolable, even in the worst-case attack scenarios. Hence, complex secure systems build their security upon them. FIDO hardware tokens are strong authentication factors to sign in to applications (any web service supporting FIDO); they often embed a secure element and the FIDO protocol uses Elliptic Curve Digital Signature Algorithm (ECDSA for short) as its core cryptographic primitive. YubiKey 5 Series are certainly the most widespread FIDO hardware tokens, their secure element is an Infineon SLE78. This document shows how – finding a JavaCard open platform (the Feitian A22) based on a similar Infineon SLE78 – we understood the Infineon ECDSA implementation, found a side-channel vulnerability and designed a practical side-channel attack. The attack is then demonstrated on a YubiKey 5Ci. Finally, we show that the vulnerability extends to the more recent Infineon Optiga Trust M and Infineon Optiga TPM security microcontrollers. Our work unearths a side-channel vulnerability in the cryptographic library of Infineon Technologies, one of the biggest secure element manufacturers. This vulnerability – that went unnoticed for 14 years and about 80 highest-level Common Criteria certification evaluations – is due to a non constant-time modular inversion. The attack requires physical access to the secure element (few local electromagnetic side-channel acquisitions, i.e. few minutes, are enough) in order to extract the ECDSA secret key. In the case of the FIDO protocol, this allows to create a clone of the FIDO device. All YubiKey 5 Series (with firmware version below 5.7) are impacted by the attack and in fact all Infineon security microcontrollers (including TPMs) that run the Infineon cryptographic library (as far as we know, any existing version) are vulnerable to the attack. These security microcontrollers are present in a vast variety of secure systems – often relying on ECDSA – like electronic passports and crypto-currency hardware wallets but also smart cars or homes. However, we did not check (yet) that the EUCLEAK attack applies to any of these products.

Quantum attacks using superposition queries are known to break many classically secure modes of operation. While these attacks do not necessarily threaten the security of the modes themselves, since they rely on a strong adversary model, they help us to draw limits on the provable security of these modes. Typically these attacks use the structure of the mode (stream cipher, MAC or authenticated encryption scheme) to embed a period-finding problem, which can be solved with a dedicated quantum algorithm. The hidden period can be recovered with a few superposition queries (e.g., $O(n)$ for Simon's algorithm), leading to state or key-recovery attacks. However, this strategy breaks down if the period changes at each query, e.g., if it depends on a nonce. In this paper, we focus on this case and give dedicated state-recovery attacks on the authenticated encryption schemes Rocca, Rocca-S, Tiaoxin-346 and AEGIS-128L. These attacks rely on a procedure to find a Boolean hidden shift with a single superposition query, which overcomes the change of nonce at each query. As they crucially depend on such queries, we stress that they do not break any security claim of the authors, and do not threaten the schemes if the adversary only makes classical queries.

In recent years, ML based differential distinguishers have been explored and compared with the classical methods. Complexity of a key recovery attack on block ciphers is calculated using the probability of a differential distinguisher provided by classical methods. Since theoretical computations suffice to calculate the data complexity in these cases, so there seems no restrictions on the practical availability of computational resources to attack a block cipher using classical methods. However, ML based differential cryptanalysis is based on the machine learning model that uses encrypted data to learn its features using available compute power. This poses a restriction on the accuracy of ML distinguisher for increased number of rounds and ciphers with large block size. Moreover, we can still construct the distinguisher but the accuracy becomes very low in such cases. In this paper, we present a new approach to construct the differential distinguisher with high accuracy using the existing ML based distinguisher of low accuracy. This approach outperforms all existing approaches with similar objective. We demonstrate our method to construct the high accuracy ML based distinguishers for GIFT-128 and ASCON permutation. For GIFT-128, accuracy of 7-round distinguisher is increased to 98.8% with $2^{9}$ data complexity. For ASCON, accuracy of 4-round distinguisher is increased to 99.4% with $2^{18}$ data complexity. We present the first ML based distinguisher for 8 rounds of GIFT-128 using the differential-ML distinguisher presented in Latincrypt-2021. This distinguisher is constructed with 99.8% accuracy and $2^{18}$ data complexity.

The potential advent of large-scale quantum computers in the near future poses a threat to contemporary cryptography. One ubiquitous usage of cryptography is currently present in the vibrant field of cellular networks. The cryptography of cellular networks is centered around seven secret-key algorithms $f_1, \ldots, f_5, f_1^{*}, f_5^{*}$, aggregated into an authentication and key agreement algorithm set. Still, to the best of our knowledge, these secret key algorithms have not yet been subject to quantum cryptanalysis. Instead, many quantum security considerations for telecommunication networks argue that the threat posed by quantum computers is restricted to public-key cryptography. However, various recent works have presented quantum attacks on secret key cryptography that exploit quantum period finding to achieve more than a quadratic speedup compared to the best known classical attacks. Motivated by this quantum threat to symmetric cryptography, this paper presents a quantum cryptanalysis for the Milenage algorithm set, the prevalent instantiation of the seven secret-key $f_1, \ldots, f_5, f_1^{*}, f_5^{*}$ algorithms that underpin cellular security. Building upon recent quantum cryptanalytic results, we show attacks that go beyond a quadratic speedup. Concretely, we provide quantum attack scenarios for all Milenage algorithms, including a polynomial time quantum existential forgery attack in the $Q_2$ model. Our comprehensive attack overview can serve as a basis for further research into the resilience of Milenage against quantum adversaries.

In early August 2024, three NSA researchers -- Patricia Greene, Mark Motley, and Bryan Weeks -- published the technical specifications for a new low-latency block cipher, ARADI, along with its corresponding authenticated encryption mode, LLAMA, which is specifically designed for memory encryption applications. Their manuscript offered minimal security analysis of the design, only briefly discussing the differential, linear and algebraic properties of cipher's underlying components. In this work, we present a set of distinguishers for the round reduced ARADI block cipher, discovered using the automated cryptanalysis tool CLAASP. More precisely, using CLAASP, we evaluate the resistance of ARADI against avalanche, statistical and continuous diffusion tests, differential and linear distinguishers, impossible differentials, algebraic attacks, and neural distinguishers. Accordingly, we give distinguishers that reach up to 9 out of 16 rounds of ARADI. We hope these preliminary findings will encourage further in-depth cryptanalysis of the cipher to enhance confidence in its security.

There exists a mismatch between the theory and practice of cryptography in the presence of leakage. On the theoretical front, the bounded leakage model, where the adversary learns bounded-length but noiseless information about secret components, and the random probing model, where the adversary learns some internal values of a leaking implementation with some probability, are convenient abstractions to analyze the security of numerous designs. On the practical front, side-channel attacks produce long transcripts which are inherently noisy but provide information about all internal computations, and this noisiness is usually evaluated with closely related metrics like the mutual information or statistical distance. Ideally, we would like to claim that resilience to bounded leakage or random probing implies resilience to noisy leakage evaluated according to these metrics. However, prior work (Duc, Dziembowski and Faust, Eurocrypt 2014; Brian et al., Eurocrypt 2021) has shown that proving such reductions with useful parameters is challenging. In this work, we study noisy leakage models stemming from hockey-stick divergences, which generalize statistical distance and are also the basis of differential privacy. First, we show that resilience to bounded leakage and random probing implies resilience to our new noisy leakage model with improved parameters compared to models based on the statistical distance or mutual information. Second, we establish composition theorems for our model, showing that these connections extend to a setting where multiple leakages are obtained from a leaking implementation. We complement our theoretical results with a discussion of practical relevance, highlighting that (i) the reduction to bounded leakage applies to realistic leakage functions with noise levels that are decreased by several orders of magnitude compared to Brian et al., and (ii) the reduction to random probing usefully generalizes the seminal work of Duc, Dziembowski, and Faust, although it remains limited when the field size in which masking operates grows (i.e., hockey-stick divergences can better hide the field size dependency of the noise requirements, but do not annihilate it).

Modular addition is often the most complex component of typical Addition-Rotation-XOR (ARX) ciphers, and the division property is the most effective tool for detecting integral distinguishers. Thus, having a precise division property model for modular addition is crucial in the search for integral distinguishers in ARX ciphers. Current division property models for modular addition either (a) express the operation as a Boolean circuit and apply standard propagation rules for basic operations (COPY, XOR, AND), or (b) treat it as a sequence of smaller functions with carry bits, modeling each function individually. Both approaches were originally proposed for the two-subset bit-based division property (2BDP), which is theoretically imprecise and may overlook some balanced bits. Recently, more precise versions of the division property, such as parity sets, three-subset bit-based division property without unknown subsets (3BDPwoU) or monomial prediction (MP), and algebraic transition matrices have been proposed. However, little attention has been given to modular addition within these precise models. The propagation rule for the precise division property of a vectorial Boolean function $\boldsymbol{f}$ requires that $\boldsymbol{u}$ can propagate to $\boldsymbol{v}$ if and only if the monomial $\pi_{\boldsymbol{u}}({\boldsymbol{x}})$ appears in $\pi_{\boldsymbol{v}}( \boldsymbol{f} )$. Braeken and Semaev (FSE 2005) studied the algebraic structure of modular addition and showed that for $\boldsymbol{x} \boxplus \boldsymbol{y} = \boldsymbol{z}$, the monomial $\pi_{\boldsymbol{u}}(\boldsymbol{x})\pi_{\boldsymbol{v}}(\boldsymbol{v})$ appears in $\pi_{\boldsymbol{w}}(\boldsymbol{w})$ if and only if $\boldsymbol{u} + \boldsymbol{v} = \boldsymbol{w}$. Their theorem directly leads to a precise division property model for modular addition. Surprisingly, this model has not been applied in division property searches, to the best of our knowledge. In this paper, we apply Braeken and Semaev's theorem to search for integral distinguishers in ARX ciphers, leading to several new results. First, we improve the state-of-the-art integral distinguishers for all variants of the Speck family, significantly enhancing search efficiency for Speck-32/48/64/96 and detecting new integral distinguishers for Speck-48/64/96/128. Second, we determine the exact degrees of output bits for $7$-round Speck-$32$ and all/16/2 output bits for $2/3/4$-round Alzette for the first time. Third, we revisit the choice of rotation parameters in Speck instances, providing a criterion that enhances resistance against integral distinguishers. Additionally, we offer a simpler proof for Braeken and Semaev's theorem using monomial prediction, demonstrating the potential of division property methods in the study of Boolean functions. We hope that the proposed methods will be valuable in the future design of ARX ciphers.

It is well known that the best small private exponent attack against RSA is that when the private exponent $d < N^{0.292}$, one can factor the RSA modulus $N = pq$. However, the bound $N^{0.292}$ is very difficult to achieve directly since we need to deal with some lattice with very high dimension, which seems infeasible by now. Recently, Li et al. proposed a practical attack that can solve cases when $d$ approaches $N^{0.292}$ within a month for $1024$ bit $N$. In this paper, we propose an improved practical small private exponent attack by enumerating the most significant bits of $p + q$. Together with some skills in implementations, we can also achieve the bound $N^{0.292}$, but with significantly less time compared to previous work.

Smart farming uses different vehicles to manage all the operations on the farm. These vehicles should be put to good use for secure data transmission. The Vangala et al.'s key agreement scheme [IEEE TIFS, 18 (2023), 904-9193] is designed for agricultural IoT networks. In this note, we show that the scheme fails to keep anonymity, instead pseudonymity. The scheme simply thinks that anonymity is equivalent to preventing the real identity from being recovered. But the true anonymity means that the adversary cannot attribute different sessions to target users. To the best of our knowledge, it is the first time to clarify the differences between anonymity and pseudonymity.

Always Encrypted (AE) is a Microsoft SQL Server feature that allows clients to encrypt sensitive data inside client applications and ensures that the sensitive data is hidden from untrusted servers and database administrators. AE offers two column-encryption options: deterministic encryption (DET) and randomized encryption (RND). In this paper, we explore the security implications of using AE with both DET and RND encryption modes by running Leakage Abuse Attacks (LAAs) against the system. We demonstrate how an adversary could extract the necessary data to run a frequency analysis LAA against DET-encrypted columns and an LAA for Order-Revealing Encryption against RND-encrypted columns. We run our attacks using real-world datasets encrypted in a full-scale AE instancer and demonstrate that a snooping server can recover over 95\% of the rows in 8 out of 15 DET-encrypted columns, and 10 out of 15 RND-encrypted columns.

Side-channel analysis on complex SoC devices with high-frequency microprocessors and multitasking operating systems presents significant challenges in practice due to the high costs of trace acquisition and analysis, generally involving tens of thousands to millions of traces. This work uses a cryptographic execution process on a Broadcom 2837 SoC as a case study to explore ways to reduce costs in electromagnetic side-channel analysis. In the data acquisition phase, we propose an efficient electromagnetic probe positioning strategy that does not require additional tool assistance, significantly accelerating the collection of effective electromagnetic traces. In the side-channel analysis phase, we investigate the combined use of preprocessing techniques, where the optimal preprocessing approach successfully reduces the number of required electromagnetic traces by 12 times, significantly improving the success rate of attacks. Additionally, we implement profiling attacks on such devices, including traditional template attacks, MLP-based, and CNN-based side-channel analysis, demonstrating that even minimal modeling costs can yield excellent analysis performance. Our study confirms the feasibility of low-cost side-channel analysis on complex SoCs and indicates that the sensitive applications running on these devices still require protection.

Redis (Remote Dictionary Server) is a general purpose, in-memory database that supports a rich array of functionality, including various Probabilistic Data Structures (PDS), such as Bloom filters, Cuckoo filters, as well as cardinality and frequency estimators. These PDS typically perform well in the average case. However, given that Redis is intended to be used across a diverse array of applications, it is crucial to evaluate how these PDS perform under worst-case scenarios, i.e., when faced with adversarial inputs. We offer a comprehensive analysis to address this question. We begin by carefully documenting the different PDS implementations in Redis, explaining how they deviate from those PDS as described in the literature. Then we show that these deviations enable a total of 10 novel attacks that are more severe than the corresponding attacks for generic versions of the PDS. We highlight the critical role of Redis' decision to use non-cryptographic hash functions in the severity of these attacks. We conclude by discussing countermeasures to the attacks, or explaining why, in some cases, countermeasures are not possible.

Known attacks on the tropical implementation of Stickel protocol involve solving a minimal covering problem, and this leads to an exponential growth in the time required to recover the secret key as the used polynomial degree increases. Consequently, it can be argued that Alice and Bob can still securely execute the protocol by utilizing very high polynomial degrees, a feasible approach due to the efficiency of tropical operations. The same is true for the implementation of Stickel protocol over some other semirings with idempotent addition (such as the max-min or fuzzy semiring). In this paper, we propose alternative methods to attacking Stickel protocol that avoid this minimal covering problem and the associated exponential time complexity. These methods involve framing the attacks as a mixed integer linear programming (MILP) problem or applying certain global optimization techniques.

SHA2 is widely used in various traditional public key ryptosystems, post-quantum cryptography, personal identification, and network communication protocols. Therefore, ensuring its robust security is of critical importance. Several differential fault attacks based on random word fault have targeted SHA1 and SHACAL-2. However, extending such random word-based fault attacks to SHA2 proves to be much more difficult due to the increased complexity of the Boolean functions in SHA2. In this paper, assuming random word fault, we identify distinctive differential properties within the Boolean functions of SHA2. Based on these findings, we propose a novel differential fault attack methodology that can be effectively used to recover the final message block and its corresponding initial vector in SHA2, forge HMAC-SHA2 messages, extract the key of SHACAL-2, and extend our analysis to similar algorithms such as SM3. The efficacy of these attacks is validated through rigorous simulations and theoretical deductions, illustrating that they represent a considerable threat to the security of SHA2. In simulations, our approach only requires guessing $T$ bits of a register, where $T$ is at most $5$. Moreover, the probability of successfully recovering a register (excluding the guessed bits) approaches 100\% when introducing 15 faults (in 1000 instances), and the approximate probability is at least 95\% when $T=1$. Consequently, approximately 928 random faults are necessary to successfully execute the attack on the compression function. Furthermore, we discuss potential countermeasures, including verification and infection detection, and propose methods to determine the time and location of fault injection in practical experiments.

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

FuLeeca is a signature scheme submitted to the recent NIST call for additional signatures. It is an efficient hash-and-sign scheme based on quasi-cyclic codes in the Lee metric and resembles the lattice-based signature Falcon. FuLeeca proposes a so-called concentration step within the signing procedure to avoid leakage of secret-key information from the signatures. However, FuLeeca is still vulnerable to learning attacks, which were first observed for lattice-based schemes. We present three full key-recovery attacks by exploiting the proximity of the code-based FuLeeca scheme to lattice-based primitives. More precisely, we use a few signatures to extract an $n/2$-dimensional circulant sublattice from the given length-$n$ code, that still contains the exceptionally short secret-key vector. This significantly reduces the classical attack cost and, in addition, leads to a full key recovery in quantum-polynomial time. Furthermore, we exploit a bias in the concentration procedure to classically recover the full key for any security level with at most 175,000 signatures in less than an hour.

Lyubashevsky’s signature can be viewed as a lattice-based adapation of the Schnorr signature, with the core difference being the use of aborts during signature generation process. Since the proposal of Lyubashevsky’s signature, a number of other variants of Schnorr-type signatures with aborts have been proposed, both in lattice-based and code-based setting. In this paper, we examine the security of Schnorr-type signature schemes with aborts. We give a detailed analysis of when the expected value of the signature is correlated to the secret key, and when it is not. Our analysis shows that even when abort condition is employed, it is crucial to set the parameters carefully in order to defend against statistical attack. In particular, we recommend to set δ ≥ β (where δ, β are public parameters) as in this case we prove that the signature does not reveal any information about the secret key. On the other hand, if this condition is not satisfied, then some information about the secret key are leaked, making the scheme susceptible to statistical attacks. For completeness, we also analyze the security of Schnorr-type signatures without aborts. In particular, we present a detailed key recovery attack via statistical method on the EagleSign signature, which is one of the submission to the NIST call for Additional PQC Signature. Moreover, we give a formula for determining the number of required signatures to successfully launch the statistical attack.

One distinguishable feature of file-inject attacks on searchable encryption schemes is the 100% query recovery rate, i.e., confirming the corresponding keyword for each query. The main efficiency consideration of file-injection attacks is the number of injected files. In the work of Zhang et al. (USENIX 2016), $|\log_2|K||$ injected files are required, each of which contains $|K|/2$ keywords for the keyword set $K$. Based on the construction of the uniform $(s,n)$-set, Wang et al. need fewer injected files when considering the threshold countermeasure. In this work, we propose a new attack that further reduces the number of injected files where Wang et al. need up to 38% more injections to achieve the same results. The attack is based on an increment $(s,n)$-set, which is also defined in this paper.

Syndrome decoding problem (SDP) is the security assumption of the code-based cryptography. Three out of the four NIST-PQC round 4 candidates are code-based cryptography. Information set decoding (ISD) is known for the fastest existing algorithm to solve SDP instances with relatively high code rate. Security of code-based cryptography is often constructed on the asymptotic complexity of the ISD algorithm. However, the concrete complexity of the ISD algorithm has hardly ever been known. Recently, Esser, May and Zweydinger (Eurocrypt '22) provide the first implementation of the representation-based ISD, such as May--Meurer--Thomae (MMT) or Becker--Joux--May--Meurer (BJMM) algorithm and solve the McEliece-1284 instance in the decoding challenge, revealing the practical efficiency of these ISDs. In this work, we propose a practically fast depth-2 BJMM algorithm and provide the first publicly available GPU implementation. We solve the McEliece-1409 instance for the first time and present concrete analysis for the record. Cryptanalysis for NIST-PQC round 4 code-based candidates against the improved BJMM algorithm is also conducted. In addition, we revise the asymptotic space complexity of the time-memory trade-off MMT algorithm presented by Esser and Zweydinger (Eurocrypt '23) from $2^{0.375n}$ to $2^{0.376n}$.

Considering side-channel analysis (SCA) security for cryptographic devices, the mitigation of electromagnetic leakage and electromagnetic interference (EMI) between modules poses significant challenges. This paper presents a comprehensive review and deep analysis of the utilization of EMI shielding materials, devised for reliability purposes and standards such as EMI/EMC, as a countermeasure to enhance EM-SCA security. We survey the current landscape of EMI-shields materials, including conductive polymers, metal-foams, carbon-based materials, and meta-materials, evaluating their effectiveness in attenuating emissions and preventing information-leakage, a task done with security-centric metrics for such materials for the first time. Through a systematic examination of existing literature, experimental studies and a construction of fully-simulatable EM environment in ANSYS-solver, we identify key factors influencing the performance of EMI-shield materials, such as shielding-effectiveness (SE), bandwidth, thickness, and material properties, on security characteristics. We devise a connection between SE and cryptographic-SNR, and we demonstrate from real hardware measurements how and in what conditions can such materials provide very high security levels. By synthesizing insights from multidisciplinary research domains, this paper aims to provide valuable two-way benefit and guidance for researchers, engineers, and practitioners in the design and deployment of robust side-channel security measures leveraging EMI-shields, already in utilization devised by reliability standards.

Approximate fully homomorphic encryption (FHE) schemes, such as the CKKS scheme (Cheon, Kim, Kim, Song, ASIACRYPT '17), are among the leading schemes in terms of efficiency and are particularly suitable for Machine Learning (ML) tasks. Although efficient, approximate FHE schemes have some inherent risks: Li and Micciancio (EUROCRYPT '21) demonstrated that while these schemes achieved the standard notion of CPA-security, they failed against a variant, $\mathsf{IND}\mbox{-}\mathsf{CPA}^D$, in which the adversary is given limited access to the decryption oracle. Subsequently, Li, Micciancio, Schultz, and Sorrell (CRYPTO '22) proved that with noise-flooding countermeasures which add Gaussian noise of sufficiently high variance before outputting the decrypted value, the CKKS scheme is secure. However, the variance required for provable security is very high, inducing a large loss in message precision. In this work, we consider a broad class of attacks on CKKS with noise-flooding countermeasures, which we call ``semi-honest'' attacks, in which an adversary may submit only correctly distributed ciphertexts to the decryption oracle. The ciphertexts submitted for decryption can be fresh ciphertexts, or can be ciphertexts resulting from the homomorphic evaluation of some circuit on fresh and independent ciphertexts. Our motivation is to model an internal threat scenario where an adversary can passively access the internal randomness of the system. We analyze the concrete security of CKKS with various levels of noise-flooding in the face of such attacks. The aim of this work is to outline and precisely quantify the various trade-offs between the number of allowed decryptions before refreshing the keys, noise-flooding levels, and the concrete security of the scheme after a number of decryptions have been observed by the adversary. Due to the large dimension and modulus in typical FHE parameter sets, previous techniques even for \emph{estimating} the concrete runtime of such attacks -- such as those in (Dachman-Soled, Ducas, Gong, Rossi, CRYPTO '20) -- become computationally infeasible, since they involve high dimensional and high precision matrix multiplication and inversion. We therefore develop new techniques that allow us to perform fast security estimation, even for FHE-size parameter sets.

We show that the key agreement scheme [IEEE Trans. Serv. Comput. 16(4): 3000-3013, 2023] fails to keep user anonymity, not as claimed. The scheme simply acknowledges that user anonymity is equivalent to preventing user's identity from being recovered. But the true anonymity means that the adversary cannot attribute different sessions to target users. It relates to entity-distinguishable, not just identity-revealable. To the best of our knowledge, it is the first time to clarify the explicit signification of user anonymity.

In their 2021 seminal paper, Li and Micciancio presented a passive attack against the CKKS approximate FHE scheme and introduced the notion of CPAD security. The current status quo is that this line of attacks does not apply to ``exact'' FHE. In this paper, we challenge this status quo by exhibiting a CPAD key recovery attack on the linearly homomorphic Regev cryptosystem which easily generalizes to other xHE schemes such as BFV, BGV and TFHE showing that these cryptosystems are not CPAD secure in their basic form. We also show that existing threshold variants of BFV, BGV and CKKS are particularily exposed to CPAD attackers and would be CPAD-insecure without smudging noise addition after partial decryption. Finally we successfully implement our attack against several mainstream FHE libraries and discuss a number of natural countermeasures as well as their consequences in terms of FHE practice, security and efficiency. The attack itself is quite practical as it typically takes less than an hour on an average laptop PC, requiring a few thousand ciphertexts as well as up to around a million evaluations/decryptions, to perform a full key recovery.

A recent security model for fully homomorphic encryption (FHE), called IND-CPA^D security and introduced by Li and Micciancio [Eurocrypt'21], strengthens IND-CPA security by giving the attacker access to a decryption oracle for ciphertexts for which it should know the underlying plaintexts. This includes ciphertexts that it (honestly) encrypted and those obtained from the latter by evaluating circuits that it chose. Li and Micciancio singled out the CKKS FHE scheme for approximate data [Asiacrypt'17] by giving an IND-CPA^D attack on it and claiming that IND-CPA security and IND-CPA^D security coincide for exact FHE schemes. We correct the widespread belief according to which IND-CPA^D attacks are specific to approximate homomorphic computations. Indeed, the equivalency formally proved by Li and Micciancio assumes that the schemes have a negligible probability of incorrect decryption. However, almost all competitive implementations of exact FHE schemes give away strong correctness by analyzing correctness heuristically and allowing noticeable probabilities of incorrect decryption. We exploit this imperfect correctness to mount efficient non-adaptive indistinguishability and key-recovery attacks against all major exact FHE schemes. We illustrate their strength by implementing them for BFV using OpenFHE and simulating an attack for the default parameter set of the CGGI implementation of TFHE-rs (the attack experiment is too expensive to be run on commodity desktops, because of the cost of CGGI bootstrapping). Our attacks extend to CKKS for discrete data, and threshold versions of the exact FHE schemes, when the correctness is similarly loose.

By introducing collision information, the existing side-channel Correlation-Enhanced Collision Attacks (CECAs) performed collision-chain detection, and reduced a given candidate space to a significantly smaller collision-chain space, leading to more efficient key recovery. However, they are still limited by low collision detection speed and low success rate of key recovery. To address these issues, we first give a Collision Detection framework with Genetic Algorithm (CDGA), which exploits Genetic Algorithm to detect the collision chains and has a strong capability of global searching. Secondly, we theoretically analyze the performance of CECA, and bound the searching depth of its output candidate vectors with a confidence level using a rigorous hypothesis test, which is suitable both for Gaussian and non-Gaussian leakages. This facilitates the initialization of the population. Thirdly, we design an innovative goal-directed mutation method to randomly select new gene values for replacement, thus improving efficiency and adaptability of the CDGA. Finally, to optimize the evolutionary of CDGA, we introduce roulette selection strategy to employ a probability assignment based on individual fitness values to guarantee the preferential selection of superior genes. A single-point crossover strategy is also used to introduce novel gene segments into the chromosomes, thus enhancing the genetic diversity of the population. Experiments verify the superiority of our CDGA.

Many proposals of lattice-based cryptosystems estimate security levels by following a recipe introduced in the New Hope proposal. This recipe, given a lattice dimension n, modulus q, and standard deviation s, outputs a "primal block size" β and a security level growing linearly with β. This β is minimal such that some κ satisfies ((n+κ)s^2+1)^{1/2} < (d/β)^{1/2} δ^{2β−d−1} q^{κ/d}, where d = n + κ + 1 and δ = (β(πβ)^{1/β}/(2π exp 1))^{1/2(β−1)}. This paper identifies how β grows with n, with enough precision to show the impact of adjusting q and s by constant factors. Specifically, this paper shows that if lg q grows as Q_0 lg n + Q_1 + o(1) and lg s grows as S_0 lg n + S_1 + o(1), where 0 <= S_0 <= 1/2 < Q_0 − S_0, then β/n grows as z_0 + (z_1+o(1))/lg n, where z_0 = 2Q_0/(Q_0−S_0+1/2)^2 and z_1 has a formula given in the paper. The paper provides a traditional-format proof and a proof verified by the HOL Light proof assistant.

This work proposes a new white-box attack technique called filtering, which can be combined with any other trace-based attack method. The idea is to filter the traces based on the value of an intermediate variable in the implementation, aiming to fix a share of a sensitive value and degrade the security of an involved masking scheme. Coupled with LDA (filtered LDA, FLDA), it leads to an attack defeating the state-of-the-art SEL masking scheme (CHES 2021) of arbitrary degree and number of linear shares with quartic complexity in the window size. In comparison, the current best attacks have exponential complexities in the degree (higher degree decoding analysis, HDDA), in the number of linear shares (higher-order differential computation analysis, HODCA), or the window size (white-box learning parity with noise, WBLPN). The attack exploits the key idea of the SEL scheme - an efficient parallel combination of the nonlinear and linear masking schemes. We conclude that a proper composition of masking schemes is essential for security. In addition, we propose several optimizations for linear algebraic attacks: redundant node removal (RNR), optimized parity check matrix usage, and chosen-plaintext filtering (CPF), significantly improving the performance of security evaluation of white-box implementations.

Nair and Song (USENIX 2023) introduce the concept of a Multi-Factor Key Derivation Function (MFKDF), along with constructions and a security analysis. MFKDF integrates dynamic authentication factors, such as HOTP and hardware tokens, into password-based key derivation. The aim is to improve the security of password-derived keys, which can then be used for encryption or as an alternative to multi-factor authentication. The authors claim an exponential security improvement compared to traditional password-based key derivation functions (PBKDF). We show that the MFKDF constructions proposed by Nair and Song fall short of the stated security goals. Underspecified cryptographic primitives and the lack of integrity of the MFKDF state lead to several attacks, ranging from full key recovery when an HOTP factor is compromised, to bypassing factors entirely or severely reducing their entropy. We reflect on the different threat models of key-derivation and authentication, and conclude that MFKDF is always weaker than plain PBKDF and multi-factor authentication in each setting.

We show that the Chunka-Banerjee-Goswami authentication and key agreement scheme [Wirel. Pers. Commun., 117, 1361-1385, 2021] fails to keep user anonymity, not as claimed. It only keeps pseudonymity. Anonymous actions are designed to be unlinkable to any entity, but pseudonymous actions can be traced back to a certain entity. We also find the scheme is insecure against offline dictionary attack.

We uncover a critical side-channel vulnerability in the Hamming Quasi-Cyclic (HQC) round 4 optimized implementation arising due to the use of the modulo operator. In some cases, compilers optimize uses of the modulo operator with compile-time known divisors into constant-time Barrett reductions. However, this optimization is not guaranteed: for example, when a modulo operation is used in a loop the compiler may emit division (div) instructions which have variable execution time depending on the numerator. When the numerator depends on secret data, this may yield a timing side-channel. We name vulnerabilities of this kind Divide and Surrender (DaS) vulnerabilities. For processors supporting Simultaneous Multithreading (SMT) we propose a new approach called DIV-SMT which enables precisely measuring small division timing variations using scheduler and/or execution unit contention. We show that using only 100 such side-channel traces we can build a Plaintext-Checking (PC) oracle with above 90% accuracy. Our approach may also prove applicable to other instances of the DaS vulnerability, such as KyberSlash. We stress that exploitation with DIV-SMT requires co-location of the attacker on the same physical core as the victim. We then apply our methodology to HQC and present a novel way to recover HQC secret keys faster, achieving an 8-fold decrease in the number of idealized oracle queries when compared to previous approaches. Our new PC oracle attack uses our newly developed Zero Tester method to quickly determine whether an entire block of bits contains only zero-bits. The Zero Tester method enables the DIV-SMT powered attack on HQC-128 to complete in under 2 minutes on our targeted AMD Zen2 machine.

Cumplido, María et al. have recently shown that the Wang-Hu digital signature is not secure and has presented a potential attack on the root extraction problem. The effectiveness of generic attacks on solving this problem for braids is still uncertain and it is unknown if it is possible to create braids that require exponential time to solve these problems. In 2023, Lin and al. has proposed a post-quantum signature scheme similar to the Wang-Hu scheme that is proven to be able to withstand attacks from quantum computers. However, evidence is presented here for the existence of an algorithm based on mean-set attacks that can recover the private key in both schemes without solving the root extraction problem. In the post-quantum signature version, we prove that the attacker can forge a signature passing the verification without recovering the private key

SNOVA is a variant of a UOV-type signature scheme over a noncommutative ring. In this article, we demonstrate that certain parameters provided by authors in SNOVA fail to meet the NIST security level, and the complexities are lower than those claimed by SNOVA.

Post-quantum cryptography represents a category of cryptosystems resistant to quantum algorithms. Recently, NIST launched a process to standardize one or more of such algorithms in the key encapsulation mechanism and signature categories. Such schemes are under the scrutiny of their mathematical security, but they are not side-channel secure at the algorithm level. That is why their side-channel vulnerabilities must be assessed by the research community. In this paper, we present a non-profiled correlation electromagnetic analysis against an FPGA implementation of the chosen NIST key-encapsulation mechanism standard, CRYSTALS-Kyber. The attack correlates an electromagnetic radiation model of the polynomial multiplication execution with the captured traces. With 166,620 traces, this attack correctly recovers 100% of the subkeys. Furthermore, a countermeasure is presented for securing the target implementation against the presented attack.

We show that the authentication protocol [IEEE Internet Things J., 2023, 10(1), 867-876] is not correctly specified, because the server cannot complete its computations. To revise, the embedded device needs to compute an extra point multiplication over the underlying elliptic curve. We also find the protocol cannot provide anonymity, not as claimed. It can only provide pseudonymity.

Side-channel-analysis (SCA) resistance with cost optimization in AES hardware implementations remains a significant challenge. While traditional masking-based schemes offer provable security, they often incur substantial resource overheads (latency, area, randomness, performance, power consumption). Alternatively, the RAMBAM scheme introduced a redundancy-based approach to control the signal-to-noise ratio, and achieves exponential leakage reduction as redundancy increases. This method results in only a slight increase in area and in power consumption, and a significant decrease in the amount of randomness needed, without any increase in latency. However, it lacks a formal security proof. In this study, we introduce a scheme, denoted STORM, that synergizes RAMBAM's methodology with the utilization of look-up-tables (LUTs) in memory (ROM/RAM) in a redundant domain. STORM, like RAMBAM, is as fast as a typical unprotected implementation and has the same latency, but has a significantly higher maximal clock frequency than RAMBAM, and consumes less than half the power. RAMBAM and STORM are code-based schemes in the sense that their set of representations is a code in the vector space $GF(2)^{8+d}$. RAMBAM requires a richer structure of a ring on $GF(2)^{8+d}$ and a ring homomorphism whereas STORM utilizes a simple vector space. In code-based-masking (CBM), as in all masking schemes, non-interference based notions (t-S/NI) are fundamental for establishing provable security. RAMBAM and STORM diverge from this approach. While CBM employs codes in vector spaces over $GF(2^8)$ for AES protection, RAMBAM and STORM use codes over $GF(2)$ without the need for t-S/NI-gadgets, leaving them both smaller and more efficient. Independence in security proofs typically means that in each individual computation (in a clock-cycle), at least one share does not participate. This approach does not work for RAMBAM where several field multiplications are executed sequentially in a cycle. However, in STORM no multiplications are performed due to its memory based tables, leaving only (independent) bitwise-XORs. Therefore, the reasoning necessary for proving security is different and STORM, unlike RAMBAM, enjoys provable security. We consider two distinct scenarios, \emph{both with provable security}: (1) STORM1 --- ``leakage-free’’ memory reads, demonstrating (1,1,0)-robustness for LUTs with redundancy 2 in the 1-probe model and for LUTs with redundancy 6 in the 2-probe model, and (2) STORM2 --- leaky memory reads, where additional protection mechanisms and a notion of memory-read robustness are introduced. STORM can be implemented not only in HW, but in SW as well. However, this paper and the proofs in it relate to STORM's HW implementations.

As the use of the internet and digital devices has grown rapidly, keeping digital communications secure has become very important. Authenticated Key Agreement (AKA) protocols play a vital role in securing digital communications. These protocols enable the communicating parties to mutually authenticate and securely establish a shared secret key. The emergence of quantum computers makes many existing AKA protocols vulnerable to their immense computational power. Consequently, designing new protocols that are resistant to quantum attacks has become essential. Extensive research in this area had led to the design of several post-quantum AKA schemes. In this paper, we analyze two post-quantum AKA schemes proposed by Dharminder et al. [2022] and Pursharthi and Mishra. [2024] and demonstrate that these schemes are not secure against active adversaries. An adversary can impersonate an authorized user to the server. We then propose reliable solutions to prevent these attacks.

As a prominent category of side-channel attacks (SCAs), plaintext-checking (PC) oracle-based SCAs offer the advantages of generality and operational simplicity on a targeted device. At TCHES 2023, Rajendran et al. and Tanaka et al. independently proposed the multiple-valued (MV) PC oracle, significantly reducing the required number of queries (a.k.a., traces) in the PC oracle. However, in practice, when dealing with environmental noise or inaccuracies in the waveform classifier, they still rely on majority voting or the other technique that usually results in three times the number of queries compared to the ideal case. In this paper, we propose an improved method to further reduce the number of queries of the MV-PC oracle, particularly in scenarios where the oracle is imperfect. Compared to the state-of-the-art at TCHES 2023, our proposed method reduces the number of queries for a full key recovery by more than $42.5\%$. The method involves three rounds. Our key observation is that coefficients recovered in the first round can be regarded as prior information to significantly aid in retrieving coefficients in the second round. This improvement is achieved through a newly designed grafted tree. Notably, the proposed method is generic and can be applied to both the NIST key encapsulation mechanism (KEM) standard Kyber and other significant candidates, such as Saber and Frodo. We have conducted extensive software simulations against Kyber-512, Kyber-768, Kyber-1024, FireSaber, and Frodo-1344 to validate the efficiency of the proposed method. An electromagnetic attack conducted on real-world implementations, using an STM32F407G board equipped with an ARM Cortex-M4 microcontroller and Kyber implementation from the public library \textit{pqm4}, aligns well with our simulations.

In side-channel testing, the standard timing analysis works when the vendor can provide a measurement to indicate the execution time of cryptographic algorithms. In this paper, we find that there exists timing leakage in power/electromagnetic channels, which is often ignored in traditional timing analysis. Hence a new method of timing analysis is proposed to deal with the case where execution time is not available. Different execution time leads to different execution intervals, affecting the locations of plaintext and ciphertext transmission. Our method detects timing leakage by studying changes in plaintext-ciphertext correlation when traces are aligned forward and backward. Experiments are then carried out on different cryptographic devices. Furthermore, we propose an improved timing analysis framework which gives appropriate methods for different scenarios.

Private Stream Aggregation (PSA) allows clients to send encryptions of their private values to an aggregator that is then able to learn the sum of these values but nothing else. It has since found many applications in practice, e.g. for smart metering or federated learning. In 2018, Becker et al. proposed the first lattice-based PSA scheme LaPS (NDSS 2018), with putative post-quantum security, which has subsequently been patented. In this paper, we describe two attacks on LaPS that break the claimed aggregator obliviousness security notion, where the second attack even allows to recover the secret keys of the clients, given enough encryptions. Moreover, we review the PSA literature for other occurrences of the responsible flawed proof steps. By explicitly tracking down and discussing these flaws, we clarify and hope to contribute to the literature on PSA schemes, in order to prevent further insecure schemes in practice. Finally, we point out that a Real-or-Random variant of the security notion that is often used as a substitute to make proofs easier, is not well-defined and potentially weaker than the standard PSA security notion. We propose a well defined variant and show that it is equivalent to the standard security notion of PSA under mild assumptions.

We show that the authentication key agreement scheme [IEEE Trans. Smart Grid, 2023, 14(5), 3816-3827] is flawed due to its inconsistent computations. We also show that the scheme fails to keep anonymity, not as claimed.

With the increasing interest for advanced protocols for Multi Party Computation, Fully-Homomorphic Encryption or Zero Knowledge proofs, a need for cryptographic algorithms with new constraints has emerged. These algorithms, called Arithmetization-Oriented ciphers, seek to minimize the number of field multiplications in large finite fields $\mathbb{F}_{2^n}$ or $\mathbb{F}_{p}$. Among them, Ciminion is an encryption algorithm proposed by Dobraunig et al. in Eurocrypt 2021. In this paper, we show a new univariate modelization on a variant of Ciminion proposed by the designers. This instance restricts the attacker to at most $2^{s/2}$ data, where $s$ is the security level. Because the designers chose to reduce the number of rounds in that specific attacker model, we are able to attack the cipher for large security levels. We also propose some slight modifications of Ciminion that would overcome this vulnerability.

In this short note, we introduce a specific class of rank two lattices over CM fields endowed with additional symmetries, which are involved in the decomposition of algebraic integers in Hermitian squares. As an application, we show an elementary reduction from the module-LIP problem in rank 2 over a CM or totally real number field to the finding of a square basis in such lattices.

We show that the data storage scheme [IEEE/ACM Trans. Netw., 2023, 31(4), 1550-1565] is flawed due to the false secret sharing protocol, which requires that some random $4\times 4$ matrixes over the finite field $F_p$ (a prime $p$) are invertible. But we find its mathematical proof for invertibility is incorrect. To fix this flaw, one needs to check the invertibility of all 35 matrixes so as to generate the proper 7 secret shares.

EagleSign is one of the 40 “Round 1 Additional Signatures” that is accepted for consideration in the supplementary round of the Post-Quantum Cryptography standardization process, organized by NIST. Its design is based on structured lattices, and it boasts greater simplicity and performance compared to the two lattice signatures already selected for standardization: Falcon and Dilithium. In this paper, we show that those claimed advantages come at the cost of security. More precisely, we show that the distribution of EagleSign signatures leaks information about the private key, to the point that only a few hundred signatures on arbitrary known messages suffice for a full key recovery, for all proposed parameters. A related vulnerability also affects EagleSign-V2, a subsequent version of the scheme specifically designed to thwart the initial attack. Although a larger number of signatures is required for key recovery, the idea of the attack remains largely similar. Both schemes come with proofs of security that we show are flawed.

The SHA-3 standard consists of four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, and two extendable-output functions (XOFs), called SHAKE128 and SHAKE256. In this paper, we study the collision resistance of the SHA-3 instances. By analyzing the nonlinear layer, we introduce the concept of maximum difference density subspace, and develop a new target internal difference algorithm by probabilistic linearization. We also exploit new strategies for optimizing the internal differential characteristic. Further more, we figure out the expected size of collision subsets in internal differentials, by analyzing the collision probability of the digests rather than the intermediate states input to the last nonlinear layer. These techniques enhance the analysis of internal differentials, leading to the best collision attacks on four round-reduced variants of the SHA-3 instances. In particular, the number of attacked rounds is extended to 5 from 4 for SHA3-384, and to 6 from 5 for SHAKE256.

Enhanced pqsigRM is a code-based hash-and-sign scheme proposed to the second National Institute of Standards and Technology call for post-quantum signatures. The scheme is based on the $(U,U+V)$-construction and it enjoys remarkably small signature lengths, about $1$KBytes for a security level of $128$ bits. Unfortunately we show that signatures leak information about the underlying $(U,U+V)$-structure. It allows to retrieve the private-key with~$100, 000$ signatures.

In this work, we use some recent developments in lattice-based cryptanalytic tools to revisit a fault attack on RSA-CRT signatures based on the Partial Approximate Common Divisor (PACD) problem. By reducing the PACD to a Hidden Number Problem (HNP) instance, we decrease the number of required faulted bits from 32 to 7 in the case of a 1024-bit RSA. We successfully apply the attack to RSA instances up to 8192-bit and present an enhanced analysis of the error-tolerance in the Bounded Distance Decoding (BDD) with predicate approach. Finally, evaluating the impact of standard side-channel and fault countermeasures, we show that merely verifying the signature before output is not an adequate protection against this attack. The reduction from PACD to HNP might be of independent interest.

Physical attacks, and among them fault injection attacks, are a significant threat to the security of embedded systems. Among the means of fault injection, laser has the significant advantage of being extremely spatially accurate. Numerous state-of-the-art studies have investigated the use of lasers to inject faults into a target at run-time. However, the high precision of laser fault injection comes with requirements on the knowledge of the implementation and exact execution time of the victim code. The main contribution of this work is the demonstration on experimental basis that it is also possible to perform laser fault injection on an unpowered device. Specifically, we targeted the Flash non-volatile memory of a 32-bit microcontroller. The advantage of this new attack path is that it does not require any synchronisation between the victim and the attacker. We provide an experimental characterization of this phenomenon with a description of the fault model from the physical level up to the software level. Finally, we applied these results to carry out a persistent fault analysis on a 128-bit AES with a particularly realistic attacker model which reinforces the interest of the PFA.

We show that the scalar product protocol [IEEE Trans. Parallel Distrib. Syst. 2023, 1060-1066] is insecure against semi-honest server attack, not as claimed. Besides, its complexity increases exponentially with the number $n$, which cannot be put into practice.

In order to challenge the security of cryptographic systems, Side-Channel Attacks exploit data leaks such as power consumption and electromagnetic emissions. Classic Side-Channel Attacks, which mainly focus on mono-channel data, fail to utilize the joint information of multi-channel data. However, previous studies of multi-channel attacks have often been limited in how they process and adapt to dynamic data. Furthermore, the different data types from various channels make it difficult to use them effectively. This study introduces the Fusion Channel Attack with POI Learning Encoder (FCA), which employs a set of POI Learning encoders that learn the inverse base transformation function family and project the data of each channel into a unified fusion latent space. Furthermore, our method introduces an optimal transport theory based metric for evaluating feature space fusion, which is used to assess the differences in feature spaces between channels. This model not only enhances the ability to process and interpret multi-source data, but also significantly improves the accuracy and applicability of SCAs in different environments.

In 2022, NIST selected Kyber and Dilithium as post-quantum cryptographic standard algorithms. The Number Theoretic Transformation (NTT) algorithm, which facilitates polynomial multiplication, has become a primary target for side-channel attacks. In this work, we embed the NTT transformation matrix in Dilithium and Kyber into the SIS search problem, and further, we propose a divide and conquer strategy for dimensionality reduction of the SIS problem by utilizing the properties of NTT, and discuss the effectiveness of the BKZ algorithm for solving the problem by using the LLL and with different blocksize, respectively. When using BKZ-60, the time required to recover private keys $\mathbf{s}_1$ for Dilithium2 after using the dimensionality reduction strategy is reduced from 82 hours to 1 minute, which is a 4,900$\times$ improvement, and the minimum number of coefficients required is reduced from 65 to 32, which is close to the theoretical lower limit value of 28. Furthermore, we propose a parameter-adjustable CPA scheme to expedite the recovery of a single coefficient in NTT domain. Combining this CPA scheme with the SIS-assisted approach, we executed practical attacks on both unprotected and masked implementations of Dilithium and Kyber on an ARM Cortex-M4. The results demonstrate that, using 5,000 power traces, we can recover complete $\mathbf{s}_1$ of Dilithium2 in 2.4 minutes, which achieve a 400$\times$ speedup compared to the best-known attacks. And Kyber512 takes only 0.5 minutes, a 7.5$\times$ improvement over what's already working. Moreover, we successfully break the first-order masked implementations and explore the potential applicable to higher-order implementations.

After the Kotov-Ushakov attack on the tropical implementation of Stickel protocol, various attempts have been made to create a secure variant of such implementation. Some of these attempts used a special class of commuting matrices resembling tropical circulants, and they have been proposed with claims of resilience against the Kotov-Ushakov attack, and even being potential post-quantum candidates. This paper, however, reveals that a form of the Kotov-Ushakov attack remains applicable and, moreover, there are heuristic implementations of that attack which have a polynomial time complexity and show an overwhelmingly good success rate.

Garbled circuits (GC) are a secure multiparty computation protocol that enables two parties to jointly compute a function using their private data without revealing it to each other. While garbled circuits are proven secure at the protocol level, implementations can still be vulnerable to side-channel attacks. Recently, side-channel analysis of GC implementations has garnered significant interest from researchers. We investigate popular open-source GC frameworks and discover that the AES encryption used in the garbling process follows a secret-dependent sequence. This vulnerability allows private inputs to be exposed through side-channel analysis. Based on this finding, we propose a side-channel attack on garbled circuits to recover the private inputs of both parties. Our attack does not require access to any plaintexts or ciphertexts in the protocol and is single-trace, adhering to the constraint that a garbled circuit can be executed only once. Furthermore, unlike existing attacks that can only target input non-XOR gates, our method applies to both input and internal non-XOR gates. Consequently, the secrets associated with every non-XOR gate are fully exposed as in an open book. We comprehensively evaluate our attack in various scenarios. First, we perform the attack on single-platform software implementations of standard AES and interleaved AES on a 32-bit ARM processor, achieving a $100\%$ success rate in both cases. Next, we target a hardware implementation on a Xilinx Artix-7 FPGA, where the resolution of power consumption measurements and the number of samples are significantly limited. In this scenario, our attack achieves a success rate of $79.58\%$. Finally, we perform a cross-platform attack on two processors with different microarchitectures representing the two parties. The differing execution cycles and power sensors across the platforms increase the difficulty of side-channel analysis. Despite these challenges, our point-of-interest (POI) selection method allows our attack to achieve a $100\%$ success rate in this scenario as well. We also discuss effective countermeasures that can be readily applied to GC frameworks to mitigate this vulnerability.

We give an algebraic attack to forge the signature of a scheme called MPPK/DS, which can be achieved by solving a linear system in 5 variables with coefficients on $\mathbb{Z}/2^x q \mathbb{Z}$ for some odd prime $q$ and $x ≥ 1$.

In 2018, Aono et al. (ASIACRYPT 2018) proposed to use quantum backtracking algorithms (Montanaro, TOC 2018; Ambainis and Kokainis, STOC 2017) to speedup lattice point enumeration. Quantum lattice sieving algorithms had already been proposed (Laarhoven et al., PQCRYPTO 2013), being shown to provide an asymptotic speedup over classical counterparts, but also to lose competitiveness at dimensions relevant to cryptography if practical considerations on quantum computer architecture were taken into account (Albrecht et al., ASIACRYPT 2020). Aono et al.'s work argued that quantum walk speedups can be applied to lattice enumeration, achieving at least a quadratic asymptotic speedup à la Grover search while not requiring exponential amounts of quantum accessible classical memory, as it is the case for sieving. In this work, we explore how to lower bound the cost of using Aono et al.'s techniques on lattice enumeration with extreme cylinder pruning, assuming a limit to the maximum depth that a quantum computation can achieve without decohering, with the objective of better understanding the practical applicability of quantum backtracking in lattice cryptanalysis.

This paper presents SNOW-SCA, the first power side-channel analysis (SCA) attack of a 5G mobile communication security standard candidate, SNOW-V, running on a 32-bit ARM Cortex-M4 microcontroller. First, we perform a generic known-key correlation (KKC) analysis to identify the leakage points. Next, a correlation power analysis (CPA) attack is performed, which reduces the attack complexity to two key guesses for each key byte. The correct secret key is then uniquely identified utilizing linear discriminant analysis (LDA). The profiled SCA attack with LDA achieves 100% accuracy after training with < 200 traces, which means the attack succeeds with just a single trace. Overall, using the combined CPA and LDA attack model, the correct secret key byte is recovered with < 50 traces collected using the ChipWhisperer platform. The entire 256-bit secret key of SNOW-V can be recovered incrementally using the proposed SCA attack. Finally, we suggest low-overhead countermeasures that can be used to prevent these SCA attacks.

The boomerang attack is a cryptanalytic technique which allows combining two short high-probability differentials into a distinguisher for a large number of rounds. Since its introduction by Wagner in 1999, it has been applied to many ciphers. One of the best-studied targets is a 6-round variant of AES, on which the boomerang attack is outperformed only by the dedicated Square attack. Recently, two new variants of the boomerang attack were presented: retracing boomerang (Eurocrypt'20) and truncated boomerang (Eurocrypt'23). These variants seem incompatible: the former achieves lower memory complexity by throwing away most of the data in order to force dependencies, while the latter achieves lower time complexity by using large structures, which inevitably leads to a large memory complexity. In this paper we show that elements of the two techniques can be combined to get `the best of the two worlds' – the practical memory complexity of the retracing attack and the lower time complexity of the truncated attack. We obtain an attack with data complexity of $2^{57}$ (compared to $2^{59}$ and $2^{55}$ of truncated and retracing boomerang, respectively), memory complexity of $2^{33}$ (compared to $2^{59}$ and $2^{31}$), and time complexity of $2^{61}$ (compared to $2^{61}$ and $2^{80}$). This is the second-best attack on 6-round AES, after the Square attack.

Automatic tools to search for boomerang distinguishers have seen significant advances over the past few years. However, most previous work has focused on ciphers based on a Substitution Permutation Network (SPN), while analyzing the Feistel structure is of great significance. Boukerrou et al. recently provided a theoretical framework to formulate the boomerang switch over multiple Feistel rounds, but they did not provide an automatic tool to find distinguishers. In this paper, by enhancing the recently proposed method by Hadipour et al., we provide an automatic tool to search for boomerang distinguishers and apply it to block ciphers following the Generalized Feistel Structure (GFS). Applying our tool to a wide range of GFS ciphers, we show that it significantly improves the best previous results on boomerang analysis. In particular, we improve the best previous boomerang distinguishers for 20 and 21 rounds of WARP by a factor of $2^{38.28}$ and $2^{36.56}$, respectively. Thanks to the effectiveness of our method, we can extend the boomerang distinguishers of WARP by two rounds and distinguish 23 rounds of this cipher from a random permutation. Applying our method to the internationally-standardized cipher CLEFIA, we achieve a 9-round boomerang distinguisher which improves the best previous boomerang distinguisher by one round. Based on this distinguisher, we build a key-recovery attack on 11 rounds of CLEFIA, which improves the best previous sandwich attack on this cipher by one round. We also apply our method to LBlock, LBlock-s, and TWINE and improve the best previous boomerang distinguisher of these ciphers.

QARMAv2 is a general-purpose and hardware-oriented family of lightweight tweakable block ciphers (TBCs) introduced in ToSC 2023. QARMAv2, as a redesign of QARMAv1 with a longer tweak and tighter security margins, is also designed to be suitable for cryptographic memory protection and control flow integrity. The designers of QARMAv2 provided a relatively comprehensive security analysis in the design specification, e.g., some bounds for the number of attacked rounds in differential and boomerang analysis, together with some concrete impossible differential, zero-correlation, and integral distinguishers. As one of the first third-party cryptanalysis of QARMAv2, Hadipour et al. significantly improved the integral distinguishers of QARMAv2, and provided the longest concrete distinguishers of QARMAv2 up to now. However, they provided no key recovery attack based on their distinguishers. This paper delves into the cryptanalysis of QARMAv2 to enhance our understanding of its security. Given that the integral distinguishers of QARMAv2 are the longest concrete distinguishers for this cipher so far, we focus on integral attack. To this end, we first further improve the automatic tool introduced by Hadipour et al. for finding integral distinguishers of TBCs following the TWEAKEY framework. This new tool exploits the MixColumns property of QARMAv2 to find integral distinguishers more suitable for key recovery attacks. Then, we combine several techniques for integral key recovery attacks, e.g., Meet-in-the-middle and partial-sum techniques to build a fine-grained integral key recovery attack on QARMAv2. Notably, we demonstrate how to leverage the low data complexity of the integral distinguishers of QARMAv2 to reduce the memory complexity of the meet-in-the-middle technique. As a result, we successfully present the first concrete key recovery attacks on reduced-round versions of QARMAv2. This includes attacking 13 rounds of QARMAv2-64-128 with a single tweak block ($\mathscr{T} = 1$), 14 rounds of QARMAv2-64-128 with two independent tweak blocks ($\mathscr{T} = 2$), and 16 rounds of QARMAv2-128-256 with two independent tweak blocks ($\mathscr{T} = 2$), all in an unbalanced setting. Our attacks do not compromise the claimed security of QARMAv2, but they shed more light on the cryptanalysis of this cipher.

Impossible differential (ID), zero-correlation (ZC), and integral attacks are a family of important attacks on block ciphers. For example, the impossible differential attack was the first cryptanalytic attack on 7 rounds of AES. Evaluating the security of block ciphers against these attacks is very important but also challenging: Finding these attacks usually implies a combinatorial optimization problem involving many parameters and constraints that is very hard to solve using manual approaches. Automated solvers, such as Constraint Programming (CP) solvers, can help the cryptanalyst to find suitable attacks. However, previous CP-based methods focus on finding only the ID, ZC, and integral distinguishers, often only in a limited search space. Notably, none can be extended to a unified optimization problem for finding full attacks, including efficient key-recovery steps. In this paper, we present a new CP-based method to search for ID, ZC, and integral distinguishers and extend it to a unified constraint optimization problem for finding full ID, ZC, and integral attacks. To show the effectiveness and usefulness of our method, we applied it to several block ciphers, including SKINNY, CRAFT, SKINNYe-v2, and SKINNYee. For the ISO standard block cipher SKINNY, we significantly improve all existing ID, ZC, and integral attacks. In particular, we improve the integral attacks on SKINNY-$n$-$3n$ and SKINNY-$n$-$2n$ by 3 and 2 rounds, respectively, obtaining the best cryptanalytic results on these variants in the single-key setting. We improve the ZC attack on SKINNY-$n$-$n$ (SKINNY-$n$-$2n$) by 2 (resp. 1) rounds. We also improve the ID attacks on all variants of SKINNY. Particularly, we improve the time complexity of the best previous single-tweakey (related-tweakey) ID attack on SKINNY-$128$-$256$ (resp. SKINNY-$128$-$384$) by a factor of $2^{22.57}$ (resp. $2^{15.39}$). On CRAFT, we propose a 21-round (20-round) ID (resp. ZC) attack, which improves the best previous single-tweakey attack by 2 (resp. 1) rounds. Using our new model, we also provide several practical integral distinguishers for reduced-round SKINNY, CRAFT, and Deoxys-BC. Our method is generic and applicable to other strongly aligned block ciphers.

Resilience against side-channel attacks is an important consideration for cryptographic implementations deployed in devices with physical access to the device. However, noise in side-channel measurements has a significant impact on the complexity of these attacks, especially when an implementation is protected with masking. Therefore, it is important to assess the ability of an attacker to deal with noise. While some previous works have considered approaches to remove (some) noise from measurements, these approaches generally require considerable expertise to be effectively employed or necessitate the ability of the attacker to capture a 'clean' set of traces without the noise. In this paper, we introduce a method for utilizing diffusion models to remove measurement noise from side-channel traces in a fully non-profiled setting. Denoising traces using our method considerably lowers the complexity of mounting attacks in both profiled and non-profiled settings. For instance, for a collision attack against the ASCADv2 dataset, we reduced the number of traces required to retrieve the key by 40%, and we showed similar improvements for ESHARD using a state-of-the-art MORE attack. Furthermore, we provide analyses into the scenarios where our method is useful and generate insights into how the diffusion networks denoise traces.

The Tensor Isomorphism Problem (TIP) has been shown to be equivalent to the matrix code equivalence problem, making it an interesting candidate on which to build post-quantum cryptographic primitives. These hard problems have already been used in protocol development. One of these, MEDS, is currently in Round 1 of NIST's call for additional post-quantum digital signatures. In this work, we consider the TIP for a special class of tensors. The hardness of the decisional version of this problem is the foundation of a commitment scheme proposed by D'Alconzo, Flamini, and Gangemi (Asiacrypt 2023). We present polynomial-time algorithms for the decisional and computational versions of TIP for special orbits, which implies that the commitment scheme is not secure. The key observations of these algorithms are that these special tensors contain some low-rank points, and their stabilizer groups are not trivial. With these new developments in the security of TIP in mind, we give a new commitment scheme based on the general TIP that is non-interactive, post-quantum, and statistically binding, making no new assumptions. Such a commitment scheme does not currently exist in the literature.

Integral, impossible-differential (ID), and zero-correlation (ZC) attacks are three of the most important attacks on block ciphers. However, manually finding these attacks can be a daunting task, which is why automated methods are becoming increasingly important. Most automatic tools regarding integral, ZC, and ID attacks have focused only on finding distinguishers rather than complete attacks. At EUROCRYPT 2023, Hadipour et al. proposed a generic and efficient constraint programming (CP) model based on satisfiability for finding ID, ZC, and integral distinguishers. This new model can be extended to a unified CP model for finding full key recovery attacks. However, it has limitations, including determining the contradiction location beforehand and a cell-wise model unsuitable for weakly aligned ciphers like Ascon and PRESENT. They also deferred developing a CP model for the partial-sum technique in key recovery as future work. In this paper, we enhance Hadipour et al.'s method in several ways. First, we remove the limitation of determining the contradiction location in advance. Second, we show how to extend the distinguisher model to a bit-wise model, considering the internal structure of S-boxes and keeping the model based on satisfiability. Third, we introduce a CP model for the partial-sum technique for the first time. To show the usefulness and versatility of our approach, we apply it to various designs, from strongly aligned ones like ForkSKINNY and QARMAv2 to weakly aligned ones such as Ascon and PRESENT, yielding significantly improved results. To mention a few of our results, we improve the integral distinguisher of QARMAv2-128 (resp. QARMAv2-64) by 7 (resp. 5) rounds, and the integral distinguisher of ForkSKINNY by 1 round, only thanks to our cell-wise distinguishe modelings. By using our new bit-wise modeling, our tool can find a group of $2^{155}$ 5-round ID and ZC distinguishers for Ascon in only one run, taking a few minutes on a regular laptop. The new CP model for the partial-sum technique enhances integral attacks on all SKINNY variants, notably improving the best attack on SKINNY-$n$-$n$ in the single-key setting by 1 round. We also enhance ID attacks on ForkSKINNY and provide the first analysis of this cipher in a limited reduced-round setting. Our methods are generic and applicable to other block ciphers.

Quantitative analyses of the costs of cryptographic attack algorithms play a central role in comparing cryptosystems, guiding the search for improved attacks, and deciding which cryptosystems to standardize. Unfortunately, these analyses often turn out to be wrong. Sometimes errors are not caught until years later. This paper introduces CryptAttackTester (CAT), a software framework for high-assurance quantification of attack effectiveness. CAT enforces complete definitions of attack algorithms all the way down through the model of computation, enforces complete definitions of probability predictions and cost predictions all the way down through the cost metric, and systematically tests the predictions on small-scale inputs. For example, CAT gives a fully defined meaning to the statement "the median cost of brute-force search for an AES-128 key is under 2^{141.89} bit operations", and provides clear, auditable reasons to believe that the statement is correct. This does not rule out all possible analysis errors, but with CAT it is no longer possible for bugs to hide inside ambiguous or untested security-level claims. The paper gives various examples of errors in the literature that survived typical informal testing practices and that would have been caught if CAT-enforced links had been in place. As an important case study, the bulk of the current CAT release consists of full definitions of a broad spectrum of algorithms for information-set decoding (ISD), along with cost/probability predictions for each algorithm. ISD is the top attack strategy against the McEliece cryptosystem. The predictions cover interactions between (1) high-level search strategies from Prange, Lee–Brickell, Leon, Stern, Dumer, May–Meurer–Thomae, and Becker–Joux–May–Meurer; (2) random walks from Omura, Canteaut–Chabaud, Canteaut–Sendrier, and Bernstein–Lange–Peters; and (3) speedups in core subroutines such as linear algebra and sorting. The predictions also account for various attack overheads that were omitted from previous analyses. These gaps add up to roughly 10 bits, depending on parameters. CAT's tests catch much smaller errors than this. The cost metric selected in CAT has a very simple definition, is a lower bound for the price-performance ratio of non-quantum special-purpose hardware (although the bound is loose for attacks bottlenecked by long-distance communication), and allows many optimization efforts to be shared with the design of cryptographic circuits.

Cryptographic constructions often base security on structured problem variants to enhance efficiency or to enable advanced functionalities. This led to the introduction of the Regular Syndrome Decoding (RSD) problem, which guarantees that a solution to the Syndrome Decoding (SD) problem follows a particular block-wise structure. Despite recent attacks exploiting that structure by Briaud and Øygarden (Eurocrypt ’23) and Carozza, Couteau and Joux (CCJ, Eurocrypt ’23), many questions about the impact of the regular structure on the problem hardness remain open. In this work we initiate a systematic study of the hardness of the RSD problem starting from its asymptotics. We classify different parameter regimes revealing large regimes for which RSD instances are solvable in polynomial time and on the other hand regimes that lead to particularly hard instances. Against previous perceptions, we show that a classification solely based on the uniqueness of the solution is not sufficient for isolating the worst case parameters. Further, we provide an in-depth comparison between SD and RSD in terms of reducibility and computational complexity, identifying regimes in which RSD instances are actually harder to solve. We provide the first asymptotic analyses of the algorithms presented by CCJ, establishing their worst case decoding complexities as $2^{0.141n}$ and $2^{0.135n}$, respectively. We then introduce regular-ISD algorithms by showing how to tailor the whole machinery of advanced Information Set Decoding (ISD) techniques from attacking SD to the RSD setting. The fastest regular-ISD algorithm improves the worst case decoding complexity significantly to $2^{0.112n}$. Eventually, we show that also with respect to suggested parameters regular-ISD outperforms previous approaches in most cases, reducing security levels by up to 30 bits.

Billions of dollars and countless GPU hours are currently spent on training Deep Neural Networks (DNNs) for a variety of tasks. Thus, it is essential to determine the difficulty of extracting all the parameters of such neural networks when given access to their black-box implementations. Many versions of this problem have been studied over the last 30 years, and the best current attack on ReLU-based deep neural networks was presented at Crypto’20 by Carlini, Jagielski, and Mironov. It resembles a differential chosen plaintext attack on a cryptosystem, which has a secret key embedded in its black-box implementation and requires a polynomial number of queries but an exponential amount of time (as a function of the number of neurons). In this paper, we improve this attack by developing several new techniques that enable us to extract with arbitrarily high precision all the real-valued parameters of a ReLU-based DNN using a polynomial number of queries and a polynomial amount of time. We demonstrate its practical efficiency by applying it to a full-sized neural network for classifying the CIFAR10 dataset, which has 3072 inputs, 8 hidden layers with 256 neurons each, and about 1.2 million neuronal parameters. An attack following the approach by Carlini et al. requires an exhaustive search over 2^256 possibilities. Our attack replaces this with our new techniques, which require only 30 minutes on a 256-core computer.

The analysis of the reduction effort of the lattice reduction algorithm is important in estimating the hardness of lattice-based cryptography schemes. Recently many lattice challenge records have been cracked by using the Pnj-BKZ algorithm which is the default lattice reduction algorithm used in G6K, such as the TU Darmstadt LWE and SVP Challenges. However, the previous estimations of the Pnj-BKZ algorithm are simulator algorithms rather than theoretical upper bound analyses. In this work, we present the first dynamic analysis of Pnj-BKZ algorithm. More precisely, our analysis results show that let $L$ is the lattice spanned by $(\mathbf{a}_i)_{i\leq d}$. The shortest vector $\mathbf{b}_1$ output by running $\Omega \left ( \frac{2Jd^2}{\beta(\beta-J)}\left ( \ln_{}{d} +\ln_{} \ln_{}{\max_{i}\frac{\left \| \mathbf{a}_i^{*} \right \| }{(\mathrm{det}L )^{1/d} } } \right ) \right ) $ tours reduction of pnj-BKZ$(\beta,J)$, $\mathbf{b}_1$ satisfied that $\left \| \mathbf{b}_1 \right \| \le {\gamma}_{\beta}^{\frac{d-1}{2(\beta-J)}+2 } \cdot \left ( \mathrm{det}L \right ) ^{\frac{1}{d} } $.

Number Theoretic Transform (NTT) has been widely used in accelerating computations in lattice-based cryptography. However, attackers can potentially launch power analysis targeting NTT because it is usually the most time-consuming part of the implementation. This extended time frame provides a natural window of opportunity for attackers. In this paper, we investigate the first CPU frequency leakage (Hertzbleed-like) attacks against NTT in lattice-based KEMs. Our key observation is that different inputs to NTT incur different Hamming weights in its output and intermediate layers. By measuring the CPU frequency during the execution of NTT, we propose a simple yet effective attack idea to find the input to NTT that triggers NTT processing data with significantly low Hamming weight. We further apply our attack idea to real-world applications that are built upon NTT: CPA-secure Kyber without Compression and Decompression functions, and CCA-secure NTTRU. This leads us to extract information or frequency Hints about the secret key. Integrating these Hints into the LWE-estimator framework, we estimate a minimum of $35\%$ security loss caused by the leakage. The frequency and timing measurements on the Reference and AVX2 implementations of NTT in both Kyber and NTTRU align well with our theoretical analysis, confirming the existence of frequency side-channel leakage in NTT. It is important to emphasize that our observation is not limited to a specific implementation but rather the algorithm on which NTT is based. Therefore, our results call for more attention to the analysis of power leakage against NTT in lattice-based cryptography.

We analyse the cryptographic protocols underlying Delta Chat, a decentralised messaging application which uses e-mail infrastructure for message delivery. It provides end-to-end encryption by implementing the Autocrypt standard and the SecureJoin protocols, both making use of the OpenPGP standard. Delta Chat's adoption by categories of high-risk users such as journalists and activists, but also more generally users in regions affected by Internet censorship, makes it a target for powerful adversaries. Yet, the security of its protocols has not been studied to date. We describe five new attacks on Delta Chat in its own threat model, exploiting cross-protocol interactions between its implementation of SecureJoin and Autocrypt, as well as bugs in rPGP, its OpenPGP library. The findings have been disclosed to the Delta Chat team, who implemented fixes.

This work *completely breaks* the sequentiality assumption (and broad generalizations thereof) underlying the candidate lattice-based proof of sequential work (PoSW) recently proposed by Lai and Malavolta at CRYPTO 2023. In addition, it breaks an essentially identical variant of the PoSW, which differs from the original in only an arbitrary choice that is immaterial to the design and security proof (under the falsified assumption). This suggests that whatever security the original PoSW may have is fragile, and further motivates the search for a construction based on a sound lattice-based assumption. Specifically, for sequentiality parameter $T$ and SIS parameters $n,q,m = n \log q$, the attack on the sequentiality assumption finds a solution of quasipolynomial norm $m^{\lceil \log T \rceil}$ (or norm $O(\sqrt{m})^{\lceil \log T \rceil}$ with high probability) in only *logarithmic* $\tilde{O}_{n,q}(\log T)$ depth; this strongly falsifies the assumption that finding such a solution requires depth *linear* in $T$. (The $\tilde{O}$ notation hides polylogarithmic factors in the variables appearing in its subscript.) Alternatively, the attack finds a solution of polynomial norm $m^{1/\varepsilon}$ in depth $\tilde{O}_{n,q}(T^{\varepsilon})$, for any constant $\varepsilon > 0$. Similarly, the attack on the (slightly modified) PoSW constructs a valid proof in \emph{polylogarithmic} $\tilde{O}_{n,q}(\log^2 T)$ depth, thus strongly falsifying the expectation that doing so requires linear sequential work.

In post-quantum cryptography, Learning With Errors (LWE) is one of the dominant underlying mathematical problems. The dual attack is one of the main strategies for solving the LWE problem, and it has recently gathered significant attention within the research community. The attack strategy consists of a lattice reduction part and a distinguishing part. The latter includes an enumeration subroutine over a certain number of positions of the secret key. Our contribution consists of giving a precise and efficient approach for calculating the expected complexity of such an enumeration procedure, which was missing in the literature. This allows us to decrease the estimated cost of the whole dual attack, both classically and quantumly, on well-known protocols such as Kyber, Saber, and TFHE. In addition, we explore different enumeration strategies to investigate some potential further improvements. As our method of calculating the expected cost of enumeration is pretty general, it might be of independent interest in other areas of cryptanalysis or even in different research areas.

WARP is a 128-bit block cipher published by Banik et al. at SAC 2020 as a lightweight alternative to AES. It is based on a generalized Feistel network and achieves the smallest area footprint among 128-bit block ciphers in many settings. Previous analysis results include integral key-recovery attacks on 21 out of 41 rounds. In this paper, we propose integral key-recovery attacks on up to 32 rounds by improving both the integral distinguisher and the key-recovery approach substantially. For the distinguisher, we show how to model the monomial prediction technique proposed by Hu et al. at ASIACRYPT 2020 as a SAT problem and thus create a bit-oriented model of WARP taking the key schedule into account. Together with two additional observations on the properties of WARP's construction, we extend the best previous distinguisher by 2 rounds (as a classical integral distinguisher) or 4 rounds (for a generalized integral distinguisher). For the key recovery, we create a graph-based model of the round function and demonstrate how to manipulate the graph to obtain a cipher representation amenable to FFT-based key recovery.

Cryptanalysis of modern symmetric ciphers may be done by using linear equation systems with multiple right hand sides, which describe the encryption process. The tool was introduced by Raddum and Semaev where several solving methods were developed. In this work, the probabilities are ascribed to the right hand sides and a statistical attack is then applied. The new approach is a multivariate generalisation of the correlation attack by Siegenthaler. A fast version of the attack is provided too. It may be viewed as an extension of the fast correlation attack by Meier and Staffelbach, based on exploiting so called parity-checks for linear recurrences. Parity-checks are a particular case of the relations that we introduce in the present work. The notion of a relation is irrelevant to linear recurrences. We show how to apply the method to some LFSR-based stream ciphers including those from the Grain family. The new method generally requires a lower number of the keystream bits to recover the initial states than other techniques reported in the literature.

Over the past ten years, there have been many attacks on symmetric constructions using the statistical properties of random functions. Initially, these attacks targeted iterated hash constructions and their combiners, developing a wide array of methods based on internal collisions and on the average behavior of iterated random functions. More recently, Gilbert et al. (EUROCRYPT 2023) introduced a forgery attack on so-called duplex-based Authenticated Encryption modes which was based on exceptional random functions, i.e., functions whose graph admits a large component with an exceptionally small cycle. In this paper, we expand the use of such functions in generic cryptanalysis with several new attacks. First, we improve the attack of Gilbert et al. from $\mathcal{O}(2^{3c/4})$ to $\mathcal{O}(2^{2c/3})$, where $c$ is the capacity. This new attack uses a nested pair of functions with exceptional behavior, where the second function is defined over the cycle of the first one. Next, we introduce several new generic attacks against hash combiners, notably using small cycles to improve the complexities of the best existing attacks on the XOR combiner, Zipper Hash and Hash-Twice. Last but not least, we propose the first quantum second preimage attack against Hash-Twice, reaching a quantum complexity $\mathcal{O}(2^{3n/7})$.

ECMQV is a standardized key agreement protocol based on ECC with an additional implicit signature authentication. In this paper we investigate the vulnerability of ECMQV against fault attacks and propose two efficient lattice-based fault attacks. In our attacks, by inducing a storage fault to the ECC parameter $a$ before the execution of ECMQV, we can construct two kinds of weak curves and successfully pass the public-key validation step in the protocol. Then, by solving ECDLP and using a guess-and-determine method, some information of the victim's temporary private key and the implicit-signature result can be deduced. Based on the retrieved information, we build two new lattice-attack models and recover the upper half of the static private key. Compared with the previous lattice-attack models, our models relax the attack conditions and do not require the exact partial knowledge of the nonces. The validity of the attacks is proven by experimental simulations, which show our attacks pose real threats to the unprotected ECMQV implementations since only one permanent fault is sufficient to retrieve half bits of the secret key.

The fast correlation attack (FCA) is a powerful cryptanalysis technique that targets stream ciphers based on linear feedback shift registers (LFSRs). Several FCAs were applied to small state stream ciphers (SSCs). In this paper, the idea of multiple sampling is proposed to use the available keystream bits more efficiently and decrease the data complexity of the attacks. This idea helps to overcome the limitation of SSCs on the number of output keystream bits. Moreover, we classify the parity check equations obtained from the different sampling rounds into different groups to ensure that the round keys used in these equations are the same. Our attack is applied to the Fruit-80 and reduces the data complexity from 2^56.82 to 2^49.82. This modified FCA can be applied to all SSCs with limited round key periods. Finally, we suggest a new design idea to strengthen SSCs against FCAs.

Verifiable Delay Functions (VDF) are a class of cryptographic primitives aiming to guarantee a minimum computation time, even for an adversary with massive parallel computational power. They are useful in blockchain protocols, and several practical candidates have been proposed based on exponentiation in a large finite field: Sloth++, Veedo, MinRoot. The underlying assumption of these constructions is that computing an exponentiation $x^e$ requires at least $\log_2 e$ sequential multiplications. In this work, we analyze the security of these algebraic VDF candidates. In particular, we show that the latency of exponentiation can be reduced using parallel computation, against the preliminary assumptions.

We present a framework for speeding up the search for preimages of candidate one-way functions based on highly biased differential-linear distinguishers. It is naturally applicable to preimage attacks on hash functions. Further, a variant of this framework applied to keyed functions leads to accelerated key-recovery attacks. Interestingly, our technique is able to exploit related-key differential-linear distinguishers in the single-key model without querying the target encryption oracle with unknown but related keys. This is in essence similar to how we speed up the key search based on the well known complementation property of DES, which calls for caution from the designers in building primitives meant to be secure in the single-key setting without a thorough cryptanalysis in the related-key model. We apply the method to sponge-based hash function Ascon-HASH, XOFs XOEsch/Ascon-XOF and AEAD Schwaemm, etc. Accelerated preimage or key-recovery attacks are obtained. Note that all the differential-linear distinguishers employed in this work are highly biased and thus can be experimentally verified.

This paper proposes general meet-in-the-middle (MitM) attack frameworks for preimage and collision attacks on hash functions based on (generalized) sponge construction. As the first contribution, our MitM preimage attack framework covers a wide range of sponge-based hash functions, especially those with lower claimed security level for preimage compared to their output size. Those hash functions have been very widely standardized (e.g., Ascon-Hash, PHOTON, etc.), but are rarely studied against preimage attacks. Even the recent MitM attack framework on sponge construction by Qin et al. (EUROCRYPT 2023) cannot attack those hash functions. As the second contribution, our MitM collision attack framework shows a different tool for the collision cryptanalysis on sponge construction, while previous collision attacks on sponge construction are mainly based on differential attacks. Most of the results in this paper are the first third-party cryptanalysis results. If cryptanalysis previously existed, our new results significantly improve the previous results, such as improving the previous 2-round collision attack on Ascon-Hash to the current 4 rounds, improving the previous 3.5-round quantum preimage attack on SPHINCS$^+$-Haraka to our 4-round classical preimage attack, etc.

In this paper, we study the robustness of Kyber, the Learning With Errors (LWE)-based Key Encapsulation Mechanism (KEM) chosen for standardization by NIST, against key mismatch attacks. We demonstrate that Kyber's security levels can be compromised with a few mismatch queries by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in CPA-secure Kyber. We further propose an adaptive method to enhance parallel mismatch attacks, initially proposed by Shao et al. at AsiaCCS 2024, thereby significantly reducing query complexity. This method combines the adaptive attack with post-processing via lattice reduction to retrieve the final secret key entries. Our method proves its efficacy by reducing query complexity by 14.6 % for Kyber512 and 7.5 % for Kyber768/Kyber1024. Furthermore, this approach has the potential to substantially improve multi-value Plaintext-Checking (PC) oracle-based side-channel attacks against the CCA-secure version of Kyber KEM.

This paper deals with reducing the secret key computation time of small scale variants of the AES cipher using algebraic cryptanalysis, which is accelerated by data mining methods. This work is based on the known plaintext attack and aims to speed up the calculation of the secret key by processing the polynomial equations extracted from plaintext-ciphertext pairs. Specifically, we propose to transform the overdefined system of polynomial equations over GF(2) into a new system so that the computation of the Gröbner basis using the F4 algorithm takes less time than in the case of the original system. The main idea is to group similar polynomials into clusters, and for each cluster, sum the two most similar polynomials, resulting in simpler polynomials. We compare different data mining techniques for finding similar polynomials, such as clustering or locality-sensitive hashing (LSH). Experimental results show that using the LSH technique, we get a system of equations for which we can calculate the Gröbner basis the fastest compared to the other methods that we consider in this work. Experimental results also show that the time to calculate the Gröbner basis for the transformed system of equations is significantly reduced compared to the case when the Gröbner basis was calculated from the original non-transformed system. This paper demonstrates that reducing an overdefined system of equations reduces the computation time for finding a secret key.

As quantum computing progresses, extensive research has been conducted to find quantum advantages in the field of cryptography. Combining quantum algorithms with classical cryptographic analysis methods, such as differential cryptanalysis and linear cryptanalysis, has the potential to reduce complexity. In this paper, we present a quantum differential finding circuit for differential cryptanalysis. In our quantum circuit, both plaintext and input difference are in a superposition state. Actually, while our method cannot achieve a direct speedup with quantum computing, it offers a different perspective by relying on quantum probability in a superposition state. For the quantum simulation, given the limited number of qubits, we simulate our quantum circuit by implementing the Toy-ASCON quantum circuit.

At Asiacrypt 2022, Ducas, Postlethwaite, Pulles, and van Woerden introduced the Lattice Isomorphism Problem for module lattices in a number field $K$ (module-LIP). In this article, we describe an algorithm solving module-LIP for modules of rank $2$ in $K^2$, when $K$ is a totally real number field. Our algorithm exploits the connection between this problem, relative norm equations and the decomposition of algebraic integers as sums of two squares. For a large class of modules (including $\mathcal{O}_K^2$), and a large class of totally real number fields (including the maximal real subfield of cyclotomic fields) it runs in classical polynomial time in the degree of the field and the residue at 1 of the Dedekind zeta function of the field (under reasonable number theoretic assumptions). We provide a proof-of-concept code running over the maximal real subfield of some cyclotomic fields. As a side contribution, we also provide some algorithmic and theoretical tools for the future study of the module-LIP problem.

In this paper, we present a new attack against search-LWE instances with a small secret key. The method consists of lifting the public key to $\mathbb Z$ and finding a good Diophantine approximation of the public key divided by the modulus $a$. This is done using lattice reduction algorithms. The lattice considered, and the approximation quality needed is similar to known decision-LWE attacks for small keys. However, we do not require an in-depth analysis of the reduction algorithm (any reduction algorithm giving small enough vectors is enough for us), and our method solves the search problem directly, which is harder than the decision problem.

It is well-known that a system of equations becomes easier to solve when it is overdefined. In this work, we study how to overdefine the system of equations to describe the arithmetic oriented (AO) ciphers Friday, Vision, and RAIN, as well as a special system of quadratic equations over $\mathbb F_{2^{\ell}}$ used in the post-quantum signature scheme Biscuit. Our method is inspired by Courtois-Pieprzyk's and Murphy-Robshaw's methods to model AES with overdefined systems of quadratic equations over $\mathbb F_2$ and $\mathbb F_{2^8}$, respectively. However, our method is more refined and much simplified compared with Murphy-Robshaw's method, since it can take full advantage of the low-degree $\mathbb F_2$-linearized affine polynomials used in Friday and Vision, and the overdefined system of equations over $\mathbb F_{2^{\ell}}$ can be described in a clean way with our method. For RAIN, we instead consider quadratic Boolean equations rather than equations over large finite fields $\mathbb F_{2^{\ell}}$. Specifically, we demonstrate that the special structure of RAIN allows us to set up much more linearly independent quadratic Boolean equations than those obtained only with Courtois-Pieprzyk's method. Moreover, we further demonstrate that the underlying key-recovery problem in Biscuit (NIST PQC Round 1 Additional Signatures) can also be described by solving a much overdefined system of quadratic equations over $\mathbb F_{2^{\ell}}$. On the downside, the constructed systems of quadratic equations for these ciphers cannot be viewed as semi-regular, which makes it challenging to upper bound the complexity of the Gröbner basis attack. However, such a new modelling method can significantly improve the lower bound of the complexity of the Gröbner basis attacks on these ciphers, i.e., we view the complexity of solving a random system of quadratic equations of the same scale as the lower bound. How to better estimate the upper and lower bounds of the Gröbner basis attacks on these ciphers based on our modelling method is left as an open problem.

Unbalanced Oil and Vinegar is a multivariate signature scheme that was introduced in 1999. Most multivariate candidates for signature schemes at NIST's PQC standardization process are either based on UOV or closely related to it. The UOV trapdoor is a secret subspace, the "oil subspace". We show how to recover an equivalent secret key from the knowledge of a single vector in the oil subspace in any characteristic. The reconciliation attack was sped-up by adding some bilinear equations in the subsequent computations, and able to conclude after two vectors were found. We show here that these bilinear equations contain enough information to dismiss the quadratic equations and retrieve the secret subspace with linear algebra for practical parametrizations of UOV, in at most 15 seconds for modern instanciations of UOV. This proves that the security of the UOV scheme lies in the complexity of finding exactly one vector in the oil space. In addition, we deduce a key recovery attack from any forgery attack by applying a corollary of our main result. We show how to extend this result to schemes related to UOV, such as MAYO and VOX.

The Learning With Errors ($\mathsf{LWE}$) problem asks to find $\mathbf{s}$ from an input of the form $(\mathbf{A}, \mathbf{b} = \mathbf{A}\mathbf{s}+\mathbf{e}) \in (\mathbb{Z}/q\mathbb{Z})^{m \times n} \times (\mathbb{Z}/q\mathbb{Z})^{m}$, for a vector $\mathbf{e}$ that has small-magnitude entries. In this work, we do not focus on solving $\mathsf{LWE}$ but on the task of sampling instances. As these are extremely sparse in their range, it may seem plausible that the only way to proceed is to first create $\mathbf{s}$ and $\mathbf{e}$ and then set $\mathbf{b} = \mathbf{A}\mathbf{s}+\mathbf{e}$. In particular, such an instance sampler knows the solution. This raises the question whether it is possible to obliviously sample $(\mathbf{A}, \mathbf{A}\mathbf{s}+\mathbf{e})$, namely, without knowing the underlying $\mathbf{s}$. A variant of the assumption that oblivious $\mathsf{LWE}$ sampling is hard has been used in a series of works to analyze the security of candidate constructions of Succinct Non interactive Arguments of Knowledge (SNARKs). As the assumption is related to $\mathsf{LWE}$, these SNARKs have been conjectured to be secure in the presence of quantum adversaries. Our main result is a quantum polynomial-time algorithm that samples well-distributed $\mathsf{LWE}$ instances while provably not knowing the solution, under the assumption that $\mathsf{LWE}$ is hard. Moreover, the approach works for a vast range of $\mathsf{LWE}$ parametrizations, including those used in the above-mentioned SNARKs. This invalidates the assumptions used in their security analyses, although it does not yield attacks against the constructions themselves.

In 2017, Petzoldt, Szepieniec, and Mohamed proposed a blind signature scheme, based on multivariate cryptography. This construction has been expanded on by several other works. This short paper shows that their construction is susceptible to an efficient polynomial-time attack. The problem is that the authors implicitly assumed that for a random multivariate quadratic map $\mathcal{R}:\mathbb{F}_q^m \rightarrow \mathbb{F}_q^m$ and a collision-resistant hash function $H: \{0,1\}^* \rightarrow \mathbb{F}_q^m$, the function $\mathsf{Com}(m;\mathbf{r}) := H(m) - \mathcal{R}(\mathbf{r})$ is a binding commitment, which is not the case. There is a "folklore" algorithm that can be used to, given any pair of messages, efficiently produce a commitment that opens to both of them. We hope that by pointing out that multivariate quadratic maps are not binding, similar problems can be avoided in the future.

The cube attack extracts the information of secret key bits by recovering the coefficient called superpoly in the output bit with respect to a subset of plaintexts/IV, which is called a cube. While the division property provides an efficient way to detect the structure of the superpoly, superpoly recovery could still be prohibitively costly if the number of rounds is sufficiently high. In particular, Core Monomial Prediction (CMP) was proposed at ASIACRYPT 2022 as a scaled-down version of Monomial Prediction (MP), which sacrifices accuracy for efficiency but ultimately gets stuck at 848 rounds of \trivium. In this paper, we provide new insights into CMP by elucidating the algebraic meaning to the core monomial trails. We prove that it is sufficient to recover the superpoly by extracting all the core monomial trails, an approach based solely on CMP, thus demonstrating that CMP can achieve perfect accuracy as MP does. We further reveal that CMP is still MP in essence, but with variable substitutions on the target function. Inspired by the divide-and-conquer strategy that has been widely used in previous literature, we design a meet-in-the-middle (MITM) framework, in which the CMP-based approach can be embedded to achieve a speedup. To illustrate the power of these new techniques, we apply the MITM framework to \trivium, \grain and \kreyvium. As a result, not only can the previous computational cost of superpoly recovery be reduced (e.g., 5x faster for superpoly recovery on 192-round \grain), but we also succeed in recovering superpolies for up to 851 rounds of \trivium and up to 899 rounds of \kreyvium. This surpasses the previous best results by respectively 3 and 4 rounds. Using the memory-efficient M\"obius transform proposed at EUROCRYPT 2021, we can perform key recovery attacks on target ciphers, even though the superpoly may contain over $2^{40}$ monomials. This leads to the best cube attacks on the target ciphers.

We analyze Layered ROLLO-I, a code-based cryptosystem published in IEEE Communications Letters and submitted to the Korean post-quantum cryptography competition. Four versions of Layered ROLLO-I have been proposed in the competition. We show that the first two versions do not provide the claimed security against rank decoding attacks and give reductions to small instances of the original ROLLO-I scheme, which was a candidate in the NIST competition and eliminated there due to rank decoding attacks. As a second contribution, we provide two efficient message recovery attacks, affecting every security level of the first three versions of Layered ROLLO-I and security levels 128 and 192 of the fourth version.

Solving a system of $m$ multivariate quadratic equations in $n$ variables over finite fields (the MQ problem) is one of the important problems in the theory of computer science. The XL algorithm (XL for short) is a major approach for solving the MQ problem with linearization over a coefficient field. Furthermore, the hybrid approach with XL (h-XL) is a variant of XL guessing some variables beforehand. In this paper, we present a variant of h-XL, which we call the polynomial XL (PXL). In PXL, the whole $n$ variables are divided into $k$ variables to be fixed and the remaining $n-k$ variables as ``main variables'', and we generate a Macaulay matrix with respect to the $n-k$ main variables over a polynomial ring of the $k$ (sub-)variables. By eliminating some columns of the Macaulay matrix over the polynomial ring before guessing $k$ variables, the amount of operations required for each guessed value can be reduced compared with h-XL. Our complexity analysis of PXL (under some practical assumptions and heuristics) gives a new theoretical bound, and it indicates that PXL could be more efficient than other algorithms in theory on the random system with $n=m$, which is the case of general multivariate signatures. For example, on systems over the finite field with ${2^8}$ elements with $n=m=80$, the numbers of operations deduced from the theoretical bounds of the hybrid approaches with XL and Wiedemann XL, Crossbred, and PXL with optimal $k$ are estimated as $2^{252}$, $2^{234}$, $2^{237}$, and $2^{220}$, respectively.

RSA is an incredibly successful and useful asymmetric encryption algorithm. One of the types of implementation flaws in RSA is low entropy of the key generation, specifically the prime number creation stage. This can occur due to flawed usage of random prime number generator libraries, or on computers where there is a lack of a source of external entropy. These implementation flaws result in some RSA keys sharing prime factors, which means that the full factorization of the public modulus can be recovered incredibly efficiently by performing a computation GCD between the two public key moduli that share the prime factor. However, since one does not know which of the composite moduli share a prime factor a-priori, to determine if any such shared prime factors exist, an all-to-all GCD attack (also known as a batch GCD attack, or a bulk GCD attack) can be performed on the available public keys so as to recover any shared prime factors. This study describes a novel all-to-all batch GCD algorithm, which will be referred to as the binary tree batch GCD algorithm, that is more efficient than the current best batch GCD algorithm (the remainder tree batch GCD algorithm). A comparison against the best existing batch GCD method (which is a product tree followed by a remainder tree computation) is given using a dataset of random RSA moduli that are constructed such that some of the moduli share prime factors. This proposed binary tree batch GCD algorithm has better runtime than the existing remainder tree batch GCD algorithm, although asymptotically it has nearly identical scaling and its complexity is dependent on how many shared prime factors exist in the set of RSA keys. In practice, the implementation of the proposed binary tree batch GCD algorithm has a roughly 6x speedup compared to the standard remainder tree batch GCD approach.

In white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner's masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko (ASIACRYPT 2018) and Seker-Eisenbarth-Liskiewicz (CHES 2021) prevent LDA and force to use its higher-degree generalizations with much higher complexity. In this work, we study the relationship between the security of these and related schemes to the Learning Parity with Noise (LPN) problem and propose a new automated attack by applying an LPN-solving algorithm to white-box implementations. The attack effectively exploits strong linear approximations of the masking scheme and thus can be seen as a combination of the DCA and LDA techniques. Different from previous attacks, the complexity of this algorithm depends on the approximation error, henceforth allowing new practical attacks on masking schemes that previously resisted automated analysis. We demonstrate it theoretically and experimentally, exposing multiple cases where the LPN-based method significantly outperforms LDA and DCA methods, including their higher-order variants. This work applies the LPN problem beyond its usual post-quantum cryptography boundary, strengthening its interest in the cryptographic community, while expanding the range of automated attacks by presenting a new direction for breaking masking schemes in the white-box model.

Introduced as a new protocol implemented in “Chrome Canary” for the Google Inc. Chrome browser, “New Hope” is engineered as a post-quantum key exchange for the TLS 1.2 protocol. The structure of the exchange is revised lattice-based cryptography. New Hope incorporates the key-encapsulation mechanism of Peikert which itself is a modified Ring-LWE scheme. The search space used to introduce the closest-vector problem is generated by an intersection of a tesseract and hexadecachoron, or the ℓ∞- ball and ℓ1-ball respectively. This intersection results in the 24-cell 𝒱 of lattice 𝒟̃4. With respect to the density of the Voronoi cell 𝒱, the proposed mitigation against backdoor attacks proposed by the authors of New Hope may not withstand such attempts if enabled by a quantum computer capable of implementing Grover’s search algorithm.

We show the Seyhan-Akleylek key exchange protocol [J. Supercomput., 2023, 79:17859-17896] cannot resist offline dictionary attack and impersonation attack, not as claimed.

In this audit we started from the security analysis provided in the design documentation of XHash8/12. We extended the analysis in several directions and confirmed the security claims that were made by the designers.

We show the authentication mechanism [Ad Hoc Networks, 2023, 103003] fails to keep user anonymity, not as claimed.

The security of lattice-based crytography (LWE, NTRU, and FHE) depends on the hardness of the shortest-vector problem (SVP). Sieving algorithms give the lowest asymptotic runtime to solve SVP, but depend on exponential memory. Memory access costs much more in reality than in the RAM model, so we consider a computational model where processors, memory, and meters of wire are in constant proportions to each other. While this adds substantial costs to route data during lattice sieving, we modify existing algorithms to amortize these costs and find that, asymptotically, a classical computer can achieve the previous RAM model cost of $2^{0.2925d+o(d)}$ to sieve a $d$-dimensional lattice for a computer existing in 3 or more spatial dimensions, and can reach $2^{0.3113d+o(d)}$ in 2 spatial dimensions, where "spatial dimensions" are the dimensions of the physical geometry in which the computer exists. Under some assumptions about the constant terms of memory access, we estimate increases in bit security between $7$ to $23$ bits for different Kyber parameter sets and $8$ to $22$ bits for Dilithium.

It has been shown that the selfish mining attack enables a miner to achieve an unfair relative revenue, posing a threat to the progress of longest-chain blockchains. Although selfish mining is a well-studied attack in the context of Proof-of-Work blockchains, its impact on the longest-chain Proof-of-Stake (LC-PoS) protocols needs yet to be addressed. This paper involves both theoretical and implementation-based approaches to analyze the selfish proposing attack in the LC-PoS protocols. We discuss how factors such as the nothing-at-stake phenomenon and the proposer predictability in PoS protocols can make the selfish proposing attack in LC-PoS protocols more destructive compared to selfish mining in PoW. In the first part of the paper, we use combinatorial tools to theoretically assess the selfish proposer’s block ratio in simplistic LC-PoS environments and under simplified network connection. However, these theoretical tools or classical MDP-based approaches cannot be applied to analyze the selfish proposing attack in real-world and more complicated LC-PoS environments. To overcome this issue, in the second part of the paper, we employ deep reinforcement learning techniques to find the near-optimal strategy of selfish proposing in more sophisticated protocols. The tool implemented in the paper can help us analyze the selfish proposing attack across diverse blockchain protocols with different reward mechanisms, predictability levels, and network conditions.

Restricted syndrome decoding problems (R-SDP and R-SDP($G$)) provide an interesting basis for post-quantum cryptography. Indeed, they feature in CROSS, a submission in the ongoing process for standardizing post-quantum signatures. This work improves our understanding of the security of both problems. Firstly, we propose and implement a novel collision attack on R-SDP($G$) that provides the best attack under realistic restrictions on memory. Secondly, we derive precise complexity estimates for algebraic attacks on R-SDP that are shown to be accurate by our experiments. We note that neither of these improvements threatens the updated parameters of CROSS.