International Association
for Cryptologic Research

This note describes a total break of 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. Specifically, for sequentiality parameter $T$ and SIS parameters $n,q,m = n \log q$, the attack computes a solution of norm $(m+1)^{\log_{k} T}$ (or norm $O(\sqrt{m})^{\log_{k} T}$ with high probability) in depth $\tilde{O}_{n,q}(k \log_{k} T)$, where the integer $k \leq T$ may be freely chosen. (The $\tilde{O}$ notation hides polylogarithmic factors in the variables appearing in its subscript.)

In particular, with the typical parameterization $\log q = \tilde{O}_{n,T}(1)$, for $k=2$ the attack finds a solution of quasipolynomial norm $O(\sqrt{m})^{\log T}$ in only *polylogarithmic* $\tilde{O}_{n,T}(1)$ depth; this strongly falsifies the assumption that finding such a solution requires depth *linear* in $T$. Alternatively, setting $k = T^{\varepsilon}$, the attack finds a solution of polynomial norm $O(\sqrt{m})^{1/\varepsilon}$ in depth $\tilde{O}_{n,T}(T^{\varepsilon})$, for any constant $\epsilon > 0$.

We stress that the attack breaks the *assumption* underlying the proposed PoSW, but not the *PoSW itself* as originally defined. However, the attack does break a *slight modification* of the original PoSW, which has an essentially identical security proof (under the same kind of falsified assumption). This suggests that whatever security the original PoSW may have is fragile, and further motivates the search for a PoSW based on a sound lattice-based assumption.

Let $\mathcal{X}$ and $\mathcal{Y}$ be two sets and suppose that a set of participants $P=\{P_1,P_2,\dots,P_n\}$ would like to calculate the keyed hash value of some message $m\in\mathcal{X}$ known to a single participant in $P$ called the data owner. Also, suppose that each participant $P_i$ knows a secret value $x_i\in\mathcal{X}$. In this paper, we will propose a protocol that enables the participants in this setup to calculate the value $y=H(m,x_1,x_2,\dots ,x_n)$ of a hash function $H:\mathcal{X}^{n+1}\rightarrow\mathcal{Y}$ such that: - The function $H$ is a one-way function. - Participants in $P\backslash\{P_i\}$ cannot obtain $x_i$. - Participants other than the data owner cannot obtain $m$. - The hash value $y=H(m,x_1,x_2,\dots ,x_n)$ remains the same regardless the order of the secret $x_i$ values.

Public-key cryptography is widely deployed for encrypting stored files. This paper uses microbenchmarks and purchase costs to predict the performance of various post-quantum KEMs in this application, in particular concluding that Classic McEliece is (1) the most efficient option and (2) easily affordable.

In 2019, Essaid et al. introduced a chaotic map-based encryption scheme for color images. Their approach employs three improved chaotic maps to dynamically generate the key bytes and matrix required by the cryptosystem. It should be noted that these parameters are dependent on the size of the source image. According to the authors, their method offers adequate security (i.e. $279$ bits) for transmitting color images over unsecured channels. However, we show in this paper that this is not the case. Specifically, we present two cryptanalytic attacks that undermine the security of Essaid et al.'s encryption scheme. In the case of the chosen plaintext attack, we require only two chosen plaintexts to completely break the scheme. The second attack is a a chosen ciphertext attack, which requires two chosen ciphertexts and compared to the first one has a rough complexity of $2^{24}$. The attacks are feasible due to the fact that the key bits and matrix generated by the algorithm remain unaltered for distinct plaintext images.

Counter-strategies are key components of coercion-resistant voting schemes, allowing voters to submit votes that represent their own intentions in an environment controlled by a coercer. By deploying a counter-strategy a voter can prevent the coercer from learning if the voter followed the coercer’s instructions or not. Two effective counter-strategies have been proposed in the literature, one based on fake credentials and another on revoting. While fake-credential schemes assume that voters hide cryptographic keys away from the coercer, revoting schemes assume that voters can revote after being coerced. In this work, we present a new counter-strategy technique that enables flexible vote updating, that is, a revoting approach that provides protection against coercion even if the adversary is able to coerce a voter at the very last minute of the voting phase. We demonstrate that our technique is effective by implementing it in Loki, an Internet-based coercion-resistant voting scheme that allows revoting. We prove that Loki satisfies a game-based definition of coercion-resistance that accounts for flexible vote updating. To the best of our knowledge, we provide the first technique that enables deniable coercion- resistant voting and that can evade last-minute voter coercion.

Recently the notion of blockwise error in a context of rank based cryptography has been introduced by Sont et al. at AsiaCrypt 2023 . This notion of error, very close to the notion sum-rank metric, permits, by decreasing the weight of the decoded error, to greatly improve parameters for the LRPC and RQC cryptographic schemes. A little before the multi-syndromes approach introduced for LRPC and RQC schemes had also allowed to considerably decrease parameters sizes for LRPC and RQC schemes, through in particular the introduction of Augmented Gabidulin codes.

In the present paper we show that the two previous approaches (blockwise errors and multi-syndromes) can be combined in a unique approach which leads to very efficient generalized RQC and LRPC schemes. In order to do so, we introduce a new problem, the Blockwise Rank Support Learning problem, which consists of guessing the support of the errors when several syndromes are given in input, with blockwise structured errors. The new schemes we introduce have very interesting features since for 128 bits security they permit to obtain generalized schemes for which the sum of public key and ciphertext is only 1.4 kB for the generalized RQC scheme and 1.7 kB for the generalized LRPC scheme. The new approach proposed in this paper permits to reach a 40 % gain in terms of parameters size when compared to previous results, obtaining even better results in terms of size than for the KYBER scheme whose total sum is 1.5 kB.

Besides the description of theses new schemes the paper provides new attacks for the l-RD problem introduced in the paper by Song et al. of AsiaCrypt 2023, in particular these new attacks permit to cryptanalyze all blockwise LRPC parameters they proposed (with an improvement of more than 40bits in the case of structural attacks). We also describe combinatorial attacks and algebraic attacks, for the new Blockwise Rank Support Learning problem we introduce.

In 2023, Mfungo et al. introduce an image encryption scheme that employs the Kronecker xor product, the Hill cipher and a chaotic map. Their proposal uses the chaotic map to dynamically generate two out of the three secret keys employed by their scheme. Note that both keys are dependent on the size of the original image, while the Hill key is static. Despite the authors' assertion that their proposal offers sufficient security ($149$ bits) for transmitting color images over unsecured channels, we found that this is not accurate. To support our claim, we present a chosen plaintext attack that requires $2$ oracle queries and has a worse case complexity of $\mathcal O(2^{32})$. Note that in this case Mfungo et al.'s scheme has a complexity of $\mathcal O(2^{33})$, and thus our attack is two times faster than an encryption. The reason why this attack is viable is that the two keys remain unchanged for different plaintext images of the same size, while the Hill key remains unaltered for all images.

Transport Layer Security (TLS) is the backbone security protocol of the Internet. As this fundamental protocol is at risk from future quantum attackers, many proposals have been made to protect TLS against this threat by implementing post-quantum cryptography (PQC). The widespread interest in post-quantum TLS has given rise to a large number of solutions over the last decade. These proposals differ in many aspects, including the security properties they seek to protect, the efficiency and trustworthiness of their post-quantum building blocks, and the application scenarios they consider, to name a few.

Based on an extensive literature review, we classify existing solutions according to their general approaches, analyze their individual contributions, and present the results of our extensive performance experiments. Based on these insights, we identify the most reasonable candidates for post-quantum TLS, which research problems in this area have already been solved, and which are still open. Overall, our work provides a well-founded reference point for researching post-quantum TLS and preparing TLS in practice for the quantum age.

In recent years, symmetric primitives that focus on arithmetic metrics over large finite fields, characterized as arithmetization-oriented (\texttt{AO}) ciphers, are widely used in advanced protocols such as secure multi-party computations (MPC), fully homomorphic encryption (FHE) and zero-knowledge proof systems (ZK). To ensure good performance in protocols, these \texttt{AO} ciphers are commonly designed with a small number of multiplications over finite fields and low multiplicative depths. This feature makes \texttt{AO} ciphers vulnerable to algebraic attacks, especially integral attacks. While a far-developed analysis for integral attacks on traditional block ciphers defined over $\mathbb{F}_2$ exists, there is still a lack of research on this kind of attacks over large finite fields. Previous integral attacks over large finite fields are primarily higher-order differential attacks, which construct distinguishers by simply utilizing algebraic degrees without fully exploiting other algebraic properties of finite fields.

In this paper, we propose a new concept called \textit{integral multiset}, which provides a clear characterization of the integral property of multiset over the finite field $\mathbb{F}_{p^n}$. Based on multiplicative subgroups of finite fields, we present a new class of integral multisets that exhibits completely different integral property compared to the previously studied multisets based on vector subspaces over the finite field $\mathbb{F}_2$. In addition, we also present a method for merging existing integral multisets to create a new one with better integral property. Furthermore, combining with monomial detection techniques, we propose a framework for searching for integral distinguishers based on integral multisets.

We apply our new framework to some competitive \texttt{AO} ciphers, including \textsf{MiMC} and \textsf{Chaghri}. For all these ciphers, we successfully find integral distinguishers with lower time and data complexity. Especially for \textsf{MiMC}, the complexity of some distinguishers we find is only a half or a quarter of the previous best one. Due to the specific algebraic structure, all of our results could not be obtained by higher-order differential attacks. Furthermore, our framework perfectly adapts to various monomial detection techniques like general monomial prediction proposed by Cui et al. at ASIACRYPT 2022 and coefficient grouping invented by Liu et al. at EUROCRYPT 2023. We believe that our work will provide new insight into integral attacks over large finite fields.

Modern computing systems predominantly operate on the binary number system that accepts only ‘0’ or ‘1’ as logical values leading to computational homogeneity. But this helps in creating leakage patterns that can be exploited by adversaries to carry out hardware and software-level attacks. Recent research has shown that ternary systems, operating on three logical values (‘0′, ‘1', and ‘z') can surpass binary systems in terms of performance and security. In this paper, we first propose a novel approach that assigns logical values based on the direction of current flow within a conducting element, rather than relying on the voltage scale. Furthermore, we also present the mathematical models for each ternary gate.

The cube attack is a powerful cryptanalysis technique against symmetric ciphers, especially stream ciphers. The adversary aims to recover secret key bits by solving equations that involve the key. To simplify the equations, a set of plaintexts called a cube is summed up together. Traditional cube attacks use only linear or quadratic superpolies, and the size of cube is limited to an experimental range, typically around 40. However, cube attack based on division property, proposed by Todo et al. at CRYPTO 2017, overcomes these limitations and enables theoretical cube attacks on many lightweight stream ciphers. For a given cube $I$, they evaluate the set $J$ of secret key bits involved in the superpoly and require $2^{|I|+|J|}$ encryptions to recover the superpoly. However, the secret variables evaluation method proposed by Todo et al. sometimes becomes unresponsive and fails to solve within a reasonable time. In this paper, we propose an improvement to Todo's method by breaking down difficult-to-solve problems into several smaller sub-problems. Our method retains the efficiency of Todo's method while effectively avoiding unresponsive situations. We apply our method to the WAGE cipher, an NLFSR-based authenticated encryption algorithm and one of the second round candidates in the NIST LWC competition. Specifically, we successfully mount cube attacks on 29-round WAGE, as well as on 24-round WAGE with a sponge constraint. To the best of our knowledge, this is the first cube attack against the WAGE cipher, which provides a more accurate characterization of the WAGE's resistance against algebraic attacks.

Bulletin boards (BB) are important cryptographic building blocks that, at their core, provide a broadcast channel with memory. BBs are widely used within many security protocols, including secure multi-party computation protocols, e-voting systems, and electronic auctions. Even though the security of protocols crucially depends on the underlying BB, as also highlighted by recent works, the literature on constructing secure BBs is sparse. The so-far only provably secure BBs require trusted components and sometimes also networks without message loss, which makes them unsuitable for applications with particularly high security needs where these assumptions might not always be met.

In this work, we fill this gap by leveraging the concepts of accountability and universal composability (UC). More specifically, we propose the first ideal functionality for accountable BBs that formalizes the security requirements of such BBs in UC. We then propose Fabric$^\ast_\text{BB}$ as a slight extension designed on top of Fabric$^\ast$, which is a variant of the prominent Hyperledger Fabric distributed ledger protocol, and show that Fabric$^\ast_\text{BB}$ UC-realizes our ideal BB functionality. This result makes Fabric$^\ast_\text{BB}$ the first provably accountable BB, an often desired, but so far not formally proven property for BBs, and also the first BB that has been proven to be secure based only on standard cryptographic assumptions and without requiring trusted BB components or network assumptions. Through an implementation and performance evaluation we show that Fabric$^\ast_\text{BB}$ is practical for many applications of BBs.

Decentralized Finance (DeFi) has witnessed remarkable growth and innovation, with Decentralized Exchanges (DEXes) playing a pivotal role in shaping this ecosystem. As numerous DEX designs emerge, challenges such as price inefficiency and lack of user privacy continue to prevail. This paper introduces a novel DEX design, termed COMMON, that addresses these two predominant challenges. COMMON operates as an order book, natively integrated with a shielded token pool, thus providing anonymity to its users. Through the integration of zk-SNARKs, order batching, and Multiparty Computation (MPC) COMMON allows to conceal also the values in orders. This feature, paired with users never leaving the shielded pool when utilizing COMMON, provides a high level of privacy. To enhance price efficiency, we introduce a two-stage order matching process: initially, orders are internally matched, followed by an open, permissionless Dutch Auction to present the assets to Market Makers. This design effectively enables aggregating multiple sources of liquidity as well as helps reducing the adverse effects of Maximal Extractable Value (MEV), by redirecting most of the MEV profits back to the users.

There are two popular ways to measure computational entropy in cryptography: (HILL) pseudoentropy and (Yao) incompressibility entropy. Both of these computational entropy notions are based on a natural intuition.

- A random variable $X$ has $k$ bits of pseudoentropy if there exists a random variable $Y$ that has $k$ bits 'real' entropy and $Y$ is computationally indistinguishable from $X$. - A random variable $X$ has $k$ bits of incompressibility entropy if $X$ cannot be efficiently compressed to less than $k$ bits.

It is also intuitive, that if a random variable has high pseudoentropy, then it should also have high incompressibility entropy, because a high-entropy distribution cannot be compressed.

However, the above intuitions are not precise. Does 'real entropy' refer to Shannon entropy or min-entropy? What kind of correctness do we require from the compressor algorithm? Different papers use slightly different variations of both pseudoentropy and incompressibility entropy.

In this note we study these subtle differences and see how they affect the parameters in the implication that pseudoentropy implies incompressibility.

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. Among these, Correlation Power Analysis (CPA) attacks against NTT have received much attention, which aims to recover all the coefficients of the private key in NTT domain. The necessity to recover all these coefficients not only limits efficiency but also directly impacts the feasibility of such attacks. Thus, a crucial question emerges: can the remaining coefficients be recovered using only a subset of known ones? In this work, we respond affirmatively by introducing overdetermined system-based and SIS-assisted key recovery methods for both Dilithium and Kyber, tailored for scenarios with incomplete NTT domain private keys. The SIS-assisted method, by embedding NTT transform matrix into the SIS search problem, offers a complete key recovery with the minimum known coefficients in NTT domain. For Kyber512 and Dilithium2, only 64 and 32 coefficients are enough to recover a subset of the private key with 256 coefficients, respectively. 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 Kyber and Dilithium on an ARM Cortex-M4. The results demonstrate that we can recover a subset of 256 private key coefficients for Dilithium2 using 2,000 power traces in 0.5 minutes, while Kyber512 requires 0.4 minutes and 500 power traces. These attacks achieve a 400$\times$ speedup compared to the best-known attacks against Dilithium. Moreover, we successfully break the first-order mask implementations and explore the potential applicable to higher-order implementations.

We show that here standard decoding algorithms for generic linear codes over a finite field can speeded up by a factor which is essentially the size of the finite field by reducing it to a low weight codeword problem and working in the relevant projective space. We apply this technique to SDitH and show that the parameters of both the original submission and the updated version fall short of meeting the security requirements asked by the NIST.

Remote side-channel attacks on processors exploit hardware and micro-architectural effects observable from software measurements. So far, the analysis of micro-architectural leakages over physical side-channels (power consumption, electromagnetic field) received little treatment. In this paper, we argue that those attacks are a serious threat, especially against systems such as smartphones and Internet-of-Things (IoT) devices which are physically exposed to the end-user. Namely, we show that the observation of Dynamic Random Access Memory (DRAM) accesses with an electromagnetic (EM) probe constitutes a reliable alternative to time measurements in cache side-channel attacks. We describe the EVICT+EM attack, that allows recovering a full AES key on a T-Tables implementation with similar number of encryptions than state-of-the-art EVICT+RELOAD attacks on the studied ARM platforms. This new attack paradigm removes the need for shared memory and exploits EM radiations instead of high precision timers. Then, we introduce PRIME+EM, which goal is to reverse-engineer cache usage patterns. This attack allows to recover the layout of lookup tables within the cache. Finally, we present COLLISION+EM, a collision-based attack on a System-on-chip (SoC) that does not require malicious code execution, and show its practical efficiency in recovering key material on an ARM TrustZone application. Those results show that physical observation of the micro-architecture can lead to improved attacks.

Over years of the development of secure multi-party computation (MPC), many sophisticated functionalities have been made pratical and multi-dimensional operations occur more and more frequently in MPC protocols, especially in protocols involving datasets of vector elements, such as privacy-preserving biometric identification and privacy-preserving machine learning. In this paper, we introduce a new kind of correlation, called tensor triples, which is designed to make multi-dimensional MPC protocols more efficient. We will discuss the generation process, the usage, as well as the applications of tensor triples and show that it can accelerate privacy-preserving biometric identification protocols, such as FingerCode, Eigenfaces and FaceNet, by more than 1000 times.

While blockchain technologies leverage compelling characteristics in terms of decentralization, immutability, and transparency, user privacy in public blockchains remains a fundamental challenge that requires particular attention. This is mainly due to the history of all transactions being accessible and available to anyone, thus making it possible for an attacker to infer data about users that is supposed to remain private.

In this paper, we provide a threat model of possible privacy attacks on users utilizing the Bitcoin blockchain. To this end, we followed the LINDDUN GO methodology to identify threats and suggest possible mitigation.

Given a fixed-size block, cryptographic block functions gen- erate outputs by a sequence of bitwise operations. Block functions are widely used in the design of hash functions and stream ciphers. Their correct implementations hence are crucial to computer security. We pro- pose a method that leverages logic equivalence checking to verify assem- bly implementations of cryptographic block functions. Logic equivalence checking is a well-established technique from hardware verification. Using our proposed method, we verify two dozen assembly implementations of ChaCha20, SHA-256, and SHA-3 block functions from OpenSSL and XKCP automatically. We also compare the performance of our technique with the conventional SMT-based technique in experiments.