Encrypted Search Algorithms (ESAs) are a technique to encrypt data while the user can still search over it. ESAs can protect privacy and ensure security of sensitive data stored on a remote storage. Originally, ESAs were used in the context of documents that consist of keywords. The user encrypts the documents, sends them to a remote server and is still able to search for keywords, without exposing information about the plaintext. The idea of ESAs has also been applied to relational...

Using a purity theorem for exponential sums due to Rojas-Léon, we upper bound the absolute correlations of linear approximations of the Flystel construction used in Anemoi. This resolves open problem 7.1 in [Bouvier, 2023].

We present a key recovery attack on SQIsign2D-East that reduces its security level from $\lambda$ to $\lambda/2$. We exploit the fact that each signature leaks a Legendre symbol modulo the secret degree of the private key isogeny. About $\lambda/2$ signatures are enough for these Legendre symbols to fully determine the secret degree, which can then be recovered by exhaustive search over a set of size $O(2^{\lambda/2})$. Once the degree is known, the private key isogeny itself can be found,...

Cryptography is a crucial method for ensuring the security of communication and data transfers across networks. While it excels on devices with abundant resources, such as PCs, servers, and smartphones, it may encounter challenges when applied to resource-constrained Internet of Things (IoT) devices like Radio Frequency Identification (RFID) tags and sensors. To address this issue, a demand arises for a lightweight variant of cryptography known as lightweight cryptography (LWC). In...

At Asiacrypt 2022, a holistic key guessing strategy was proposed to yield the most efficient key recovery for the rectangle attack. Recently, at Crypto 2023, a new cryptanalysis technique--the differential meet-in-the-middle (MITM) attack--was introduced. Inspired by these two previous works, we present three generic key recovery attacks in this paper. First, we extend the holistic key guessing strategy from the rectangle to the differential attack, proposing the generic classical...

In this paper, we present the first third-party cryptanalysis of SCARF, a tweakable low-latency block cipher designed to thwart contention-based cache attacks through cache randomization. We focus on multiple-tweak differential attacks, exploiting biases across multiple tweaks. We establish a theoretical framework explaining biases for any number of rounds and verify this framework experimentally. Then, we use these properties to develop a key recovery attack on 7-round SCARF with a time...

The machine learning problem of extracting neural network parameters has been proposed for nearly three decades. Functionally equivalent extraction is a crucial goal for research on this problem. When the adversary has access to the raw output of neural networks, various attacks, including those presented at CRYPTO 2020 and EUROCRYPT 2024, have successfully achieved this goal. However, this goal is not achieved when neural networks operate under a hard-label setting where the raw output...

Recently, there has been a lot of interest in improving the understanding of the practical hardness of the 3-Tensor Isomorphism (3-TI) problem, which, given two 3-tensors, asks for an isometry between the two. The current state-of-the-art for solving this problem is the algebraic algorithm of Ran et al. '23 and the graph-theoretic algorithm of Narayanan et al. '24 that have both slightly reduced the security of the signature schemes MEDS and ALTEQ, based on variants of the 3-TI problem...

The see-in-the-middle (SITM) attack combines differential cryptanalysis and the ability to observe differential patterns in the side-channel leakage traces to reveal the secret key of SPN-based ciphers. While SITM presents a fresh perspective to side-channel analysis and allows attacks on deeper cipher rounds, there are practical difficulties that come with this method. First, one must realize a visual inspection of millions of power traces. Second, there is a strong requirement to reduce...

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....

In this paper, we present an improved attack on the stream cipher Salsa20. Our improvements are based on two technical contributions. First, we make use of a distribution of a linear combination of several random variables that are derived from different differentials and explain how to exploit this in order to improve the attack complexity. Secondly, we study and exploit how to choose the actual value for so-called probabilistic neutral bits optimally. Because of the limited influence of...

The impossible differential (ID) attack is one of the most important cryptanalytic techniques for block ciphers. There are two phases to finding an ID attack: searching for the distinguisher and building a key recovery upon it. Previous works only focused on automated distinguisher discovery, leaving key recovery as a manual post-processing task, which may lead to a suboptimal final complexity. At EUROCRYPT~2023, Hadipour et al. introduced a unified constraint programming (CP) approach based...

Sieving using near-neighbor search techniques is a well-known method in lattice-based cryptanalysis, yielding the current best runtime for the shortest vector problem in both the classical [BDGL16] and quantum [BCSS23] setting. Recently, sieving has also become an important tool in code-based cryptanalysis. Specifically, using a sieving subroutine, [GJN23, DEEK24] presented a variant of the information-set decoding (ISD) framework, which is commonly used for attacking cryptographically...

In 2023, Mfungo et al. presented an image encryption scheme that relies on a series of diffusion techniques and uses a chaotic map to generate three secret keys. Note that two out of three keys are dynamically generated based on the size of the original image, while the remaining key is static. The authors claim that their proposal offers $149$ bits of security. Unfortunately, we found a chosen plaintext attack that requires $2$ oracle queries and has a worse case complexity of $\mathcal...

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

Coppersmith's method, combined with the Jochemsz-May strategy, is widely used to find the small roots of multivariate polynomials for cryptanalysis. At Asiacrypt'23, Meers and Nowakowski improved the Jochemsz-May strategy from a single polynomial equation to a system of polynomial equations and proposed a new method, called Automated Coppersmith. Note that it is typically a tedious and non-trivial task to determine asymptotic upper bounds for Coppersmith’s method and manual analysis has...

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...

Recently, Picnic3 has introduced several alternative LowMC instances, which prompts the cryptanalysis competition for LowMC. In this paper, we provide new solutions to the competition with full S-box layers under single-data complexity. First, we present a new guess-and-determine attack framework that achieves the best trade-off in complexity, while effectively enhancing two algorithms applicable to 2-round LowMC cryptanalysis. Next, we present a new meet-in-the-middle attack framework for...

At CRYPTO 2019, A. Gohr introduced Neural Differential Cryptanalysis by applying deep learning to modern block cipher cryptanalysis. Surprisingly, the resulting neural differential distinguishers enabled a new state-of-the-art key recovery complexity for 11 rounds of SPECK32. As of May 2024, according to Google Scholar, Gohr’s article has been cited 178 times. The wide variety of targets, techniques, settings, and evaluation methodologies that appear in these follow-up works grants a careful...

SNOVA is a multivariate signature scheme submitted to the NIST project for additional signature schemes by Cho, Ding, Kuan, Li, Tseng, Tseng, and Wang. With small key and signature sizes good performance, SNOVA is one of the more efficient schemes in the competition, which makes SNOVA an important target for cryptanalysis. In this paper, we observe that SNOVA implicitly uses a structured version of the ``whipping'' technique developed for the MAYO signature scheme. We show that the...

In this paper, we propose quantum key recovery attacks on 4-round iterated Even-Mansour (IEM) with a key schedule that applies two keys alternately. We first show that a conditional periodic function such that one of the secret keys appears as a period conditionally can be constructed using the encryption function and internal permutations. By applying the offline Simon's algorithm to this function, we construct a key recovery attack with a complexity of $O(\sqrt{N} \log N)$ for $N = 2^n$,...

\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...

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

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...

This paper introduces the Koala PRF, which maps a variable-length sequence of $64$-bit input blocks to a single $257$-bit output block. Its design focuses on achieving low latency in its implementation in ASIC. To construct Koala, we instantiate the recently introduced Kirby construction with the Koala-P permutation and add an input encoding layer. The Koala-P permutation is obtained as the $8$-fold iteration of a simple round function inspired by that of Subterranean. Based on...

In our paper, we explore the consequences of replacing the commutative group operation used in Lai-Massey structures with a quasigroup operation. We introduce four quasigroup versions of the Lai-Massey structure, and prove that for quasigroups isotopic with a group $\mathbb{G}$, the complexity of launching a differential attack against these variants of the Lai-Massey structure is equivalent to attacking an alternative structure based on $\mathbb{G}$. Then we provide the conditions needed...

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus, understanding their concrete security is critical. Most work on LWE security focuses on theoretical estimates of attack performance, which is important but may overlook attack nuances arising in real-world implementations. The sole existing concrete...

Quantum computers can model and solve several problems that have posed challenges for classical super computers, leveraging their natural quantum mechanical characteristics. A large-scale quantum computer is poised to significantly reduce security strength in cryptography. In this context, extensive research has been conducted on quantum cryptanalysis. In this paper, we present optimized quantum circuits for Korean block ciphers, HIGHT and LEA. Our quantum circuits for HIGHT and LEA...

In this short note we examine one of the impossible boomerang distinguishers of Skinny-128-384 provided by Zhang, Wang and Tang at ToSC 2024 Issue 2 and disprove it. The issue arises from the use of the Double Boomerang Connectivity Table (DBCT) as a tool to establish that a boomerang switch over 2 rounds has probability zero, whereas the DBCT only covers specific cases of difference propagation, missing a large set of events that might make the connection possible. We study in...

The rectangle attack has shown to be a very powerful form of cryptanalysis against block ciphers. Given a rectangle distinguisher, one expects to mount key recovery attacks as efficiently as possible. In the literature, there have been four algorithms for rectangle key recovery attacks. However, their performance varies from case to case. Besides, numerous are the applications where the attacks lack optimality. In this paper, we delve into the rectangle key recovery and propose a unified and...

Dimension 4 isogenies have first been introduced in cryptography for the cryptanalysis of Supersingular Isogeny Diffie-Hellman (SIDH) and have been used constructively in several schemes, including SQIsignHD, a derivative of SQIsign isogeny based signature scheme. Unlike in dimensions 2 and 3, we can no longer rely on the Jacobian model and its derivatives to compute isogenies. In dimension 4 (and higher), we can only use theta-models. Previous works by Romain Cosset, David Lubicz and Damien...

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...

At Eurocrypt'24, Mureau et al. formally defined the Lattice Isomorphism Problem for module lattices (module-LIP) in a number field $\mathbb{K}$, and proposed a heuristic randomized algorithm solving module-LIP for modules of rank 2 in $\mathbb{K}^2$ with a totally real number field $\mathbb{K}$, which runs in classical polynomial time for a large class of modules and a large class of totally real number field under some reasonable number theoretic assumptions. In this paper, by introducing a...

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...

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...

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.

The aim of an algebraic attack is to find the secret key by solving a collection of relations that describe the internal structure of a cipher for observations of plaintext/cipher-text pairs. Although algebraic attacks are addressed for cryptanalysis of block and stream ciphers, there is a limited understanding of the impact of algebraic representation of the cipher on the efficiency of solving the resulting collection of equations. In this paper, we investigate on how different S-box...

Given the recent progress in machine learning (ML), the cryptography community has started exploring the applicability of ML methods to the design of new cryptanalytic approaches. While current empirical results show promise, the extent to which such methods may outperform classical cryptanalytic approaches is still somewhat unclear. In this work, we initiate exploration of the theory of ML-based cryptanalytic techniques, in particular providing new results towards understanding whether...

Advanced Encryption Standard in Galois/Counter Mode (AES-GCM) is the most widely used Authenticated Encryption with Associated Data (AEAD) algorithm in the world. In this paper, we analyze the use of GCM with all the Initialization Vector (IV) constructions and lengths approved by NIST SP 800-38D when encrypting multiple plaintexts with the same key. We derive attack complexities in both ciphertext-only and known-plaintext models, with or without nonce hiding, for collision attacks...

As quantum computing progresses, the assessment of cryptographic algorithm resilience against quantum attack gains significance interests in the field of cryptanalysis. Consequently, this paper implements the depth-optimized quantum circuit of Korean hash function (i.e., LSH) and estimates its quantum attack cost in quantum circuits. By utilizing an optimized quantum adder and employing parallelization techniques, the proposed quantum circuit achieves a 78.8\% improvement in full depth and a...

The field of Fully Homomorphic Encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners from neighbouring fields such as machine learning have sought to understand FHE to provide privacy to their work. Unfortunately, selecting secure and efficient parameters in FHE is a daunting task due to the many interdependencies between the parameters involved. In this work, we...

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...

We revisit the question of relating the elliptic curve discrete logarithm problem (ECDLP) between ordinary elliptic curves over finite fields with the same number of points. This problem was considered in 1999 by Galbraith and in 2005 by Jao, Miller, and Venkatesan. We apply recent results from isogeny cryptography and cryptanalysis, especially the Kani construction, to this problem. We improve the worst case bound in Galbraith's 1999 paper from $\tilde{O}( q^{1.5} )$ to (heuristically)...

In this note, we present additional preliminary analysis dedicated to Ascon-Xof and Ascon-Hash [DEMS19].

This paper presents an optimization of the memory cost of the quantum Information Set Decoding (ISD) algorithm proposed by Bernstein (PQCrypto 2010), obtained by combining Prange's ISD with Grover's quantum search. When the code has constant rate and length $n$, this algorithm essentially performs a quantum search which, at each iteration, solves a linear system of dimension $\mathcal{O}(n)$. The typical code lengths used in post-quantum public-key cryptosystems range from $10^3$ to...

This paper presents quantum algorithms for fast correlation attacks, one of the most powerful techniques for cryptanalysis on LFSR-based stream ciphers in the classical setting. Typical fast correlation attacks recover a value related to the initial state of the underlying LFSR by solving a decoding problem on a binary linear code with the Fast Walsh-Hadamard Transform (FWHT). Applying the FWHT on a function in the classical setting is mathematically equivalent to applying the Hadamard...

The rapid development of advanced cryptographic applications like multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge (ZK) proofs have motivated the designs of the so-called arithmetic-oriented (AO) primitives. Efficient AO primitives typically build over large fields and use large S-boxes. Such design philosophy brings difficulties in the cryptanalysis of these primitives as classical cryptanalysis methods do not apply well. The generally recognized attacks...

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...

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...

Differential-linear cryptanalysis was introduced by Langford and Hellman in 1994 and has been extensively studied since then. In 2019, Bar-On et al. presented the Differential-Linear Connectivity Table (DLCT), which connects the differential part and the linear part, thus an attacked cipher is divided to 3 subciphers: the differential part, the DLCT part, and the linear part. In this paper, we firstly present an accurate mathematical formula which establishes a relation between...

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...

In this research, we introduce MIND-Crypt, a novel attack framework that uses deep learning (DL) and transfer learning (TL) to challenge the indistinguishability of block ciphers, specifically SPECK32/64 encryption algorithm in CBC mode (Cipher Block Chaining) against Known Plaintext Attacks (KPA). Our methodology includes training a DL model with ciphertexts of two messages encrypted using the same key. The selected messages have the same byte-length and differ by only one bit at the binary...

The increasing importance of graph databases and cloud storage services prompts the study of private queries on graphs. We propose PathGES, a graph encryption scheme (GES) for single-pair shortest path queries. PathGES is efficient and mitigates the state-of-the-art attack by Falzon and Paterson (2022) on the GES by Ghosh, Kamara, and Tamassia (2021), while only incurring an additional logarithmic factor in storage overhead. PathGES leverages a novel data structure that minimizes leakage and...

The Keyed Hashing and Asymmetric Nonce (KHAN) encryption algorithm is a novel cryptographic scheme that utilizes the unique properties of full reptend prime numbers. This paper details the algorithm, its theoretical foundations, and the rigorous proofs of its security properties. By leveraging the characteristics of cyclic sequences derived from full reptend primes, KHAN provides robust encryption with high resistance to cryptanalytic attacks.

In this paper, we present three types of variations of the ALTEQ cryptosystem, a recent submission to the NIST's additional call for signatures. We name these Dangerous Variations of ALTEQ (DVA), as there is always a certain danger in stepping out of usual constructions, although we attempt to maintain heuristic security. First, we present DVA-GG (Graph Generalization), that can be seen as a more abstract point-of-view on the operations done in ALTEQ and encourages more research on the...

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...

In this paper we study the S-box known as Chi or \chi initially proposed by Daemen in 1995 and very widely used ever since in Keccak, Ascon, and many other. This type of ciphers is typically analyzed [in recent research] in terms of subspace trail attacks [TeDi19] and vector space invariants. An interesting question is then, when different spaces are mapped to each other by translations with a constant. In this paper we relax this fundamental question and we consider arbitrary sets of...

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....

Provable security based on a robust mathematical framework is the gold standard for security evaluation in cryptography. Several provable secure cryptosystems have been studied for public key cryptography. However, provably secure symmetric-key cryptography has received little attention. Although there are known provably secure symmetric-key cryptosystems based on the hardness of factorization and discrete logarithm problems, they are not only slower than conventional block ciphers but can...

In this work we introduce PERK a compact digital signature scheme based on the hardness of a new variant of the Permuted Kernel Problem (PKP). PERK achieves the smallest signature sizes for any PKP-based scheme for NIST category I security with 6 kB, while obtaining competitive signing and verification timings. PERK also compares well with the general state-of-the-art. To substantiate those claims we provide an optimized constant-time AVX2 implementation, a detailed performance analysis and...

A systematic method to analyze divisibility properties is proposed. In integral cryptanalysis, divisibility properties interpolate between bits that sum to zero (divisibility by two) and saturated bits (divisibility by $2^{n - 1}$ for $2^n$ inputs). From a theoretical point of view, we construct a new cryptanalytic technique that is a non-Archimedean multiplicative analogue of linear cryptanalysis. It lifts integral cryptanalysis to characteristic zero in the sense that, if all quantities...

The discourse herein pertains to a directional encryption cryptosystem predicated upon logarithmic signatures interconnected via a system of linear equations (we call it LINE). A logarithmic signature serves as a foundational cryptographic primitive within the algorithm, characterized by distinct cryptographic attributes including nonlinearity, noncommutativity, unidirectionality, and factorizability by key. The confidentiality of the cryptosystem is contingent upon the presence of an...

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...

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...

This work introduces DEFI - an efficient hash-and-sign digital signature scheme based on isotropic quadratic forms over a commutative ring of characteristic 0. The form is public, but the construction is a trapdoor that depends on the scheme's private key. For polynomial rings over integers and rings of integers of algebraic number fields, the cryptanalysis is reducible to solving a quadratic Diophantine equation over the ring or, equivalently, to solving a system of quadratic Diophantine...

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...

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...

Lattice-based cryptography typically uses lattices with special properties to improve efficiency. We show how blockwise reduction can exploit lattices with special geometric properties, effectively reducing the required blocksize to solve the shortest vector problem to half of the lattice's rank, and in the case of the hypercubic lattice $\mathbb{Z}^n$, further relaxing the approximation factor of blocks to $\sqrt{2}$. We study both provable algorithms and the heuristic well-known primal...

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...

FUTURE is a recently proposed lightweight block cipher that achieved a remarkable hardware performance due to careful design decisions. FUTURE is an Advanced Encryption Standard (AES)-like Substitution-Permutation Network (SPN) with 10 rounds, whose round function consists of four components, i.e., SubCell, MixColumn, ShiftRow and AddRoundKey. Unlike AES, it is a 64-bit-size block cipher with a 128-bit secret key, and the state can be arranged into 16 cells. Therefore, the operations of...

Timed cryptography studies primitives that retain their security only for a predetermined amount of time, such as proofs of sequential work and time-lock puzzles. This feature has proven to be useful in a large number of practical applications, e.g. randomness generation, sealed-bid auctions, and fair multi-party computation. However, the current state of affairs in timed cryptography is unsatisfactory: Virtually all efficient constructions rely on a single sequentiality assumption, namely...

We reflect on our experiences analysing cryptography deployed “in the wild” and give recommendations to fellow researchers about this process.

In their paper, Wei et al. proposed a lightweight protocol for conditional privacy-preserving authentication in VANET. The protocol aims to achieve ultra-low transmission delay and efficient system secret key (SSK) updating. Their protocol uses a signature scheme with message recovery to authenticate messages. This scheme provides security against adaptively chosen message attacks. However, our analysis reveals a critical vulnerability in the scheme. It is susceptible to replay attacks,...

We show how fixed-unitary quantum encryption schemes can be attacked in a black-box setting. We use an efficient technique to invert a unitary transformation on a quantum computer to retrieve an encrypted secret quantum state $\ket{\psi}$. This attack has a success rate of 100% and can be executed in constant time. We name a vulnerable scheme and suggest how to improve it to invalidate this attack. The proposed attack highlights the importance of carefully designing quantum encryption...

The guess and determine attack is a common method in cryptanalysis. Its idea is to firstly find some variables which can deduced all remaining variables in a cipher and then traverse all values of these variables to find a solution. People usually utilize the exhausted search to find these variables. However, it is not applicable any more when the number of variables is a bit large. In this work we propose a guess and determine analysis based on set split to find as few variables as possible...

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...

Pseudo-random generators are deterministic algorithms that take in input a random secret seed and output a flow of random-looking numbers. The Knapsack generator, presented by Rueppel and Massey in 1985 is one of the many attempt at designing a pseudo-random generator that is cryptographically secure. It is based on the subset-sum problem, a variant of the Knapsack optimization problem, which is considered computationally hard. In 2011 Simon Knellwolf et Willi Meier found a way to go...

The Advanced Encryption Standard (AES) is one of the most commonly used and analyzed encryption algorithms. In this work, we present new combinations of some prominent attacks on AES, achieving new records in data requirements among attacks, utilizing only $2^4$ and $2^{16}$ chosen plaintexts (CP) for 6-round and 7-round AES-192/256 respectively. One of our attacks is a combination of a meet-in-the-middle (MiTM) attack with a square attack mounted on 6-round AES-192/256 while ...

In this paper, we describe new quantum generic attacks on 6 rounds balanced Feistel networks with internal functions or internal permutations. In order to obtain our new quantum attacks, we revisit a result of Childs and Eisenberg that extends Ambainis' collision finding algorithm to the subset finding problem. In more details, we continue their work by carefully analyzing the time complexity of their algorithm. We also use four points structures attacks instead of two points structures...

In this study, we investigate the newly developed low energy lightweight block cipher (LELBC), specifically designed for resource-constrained Internet of Things (IoT) devices in smart agriculture. The designers conducted a preliminary differential cryptanalysis of LELBC through mixed-integer linear programming (MILP). This paper further delves into LELBC’s differential characteristics in both single and related-key frameworks using MILP, identifying a nine-round differential characteristic...

In the rapidly evolving fields of encryption and blockchain technologies, the efficiency and security of cryptographic schemes significantly impact performance. This paper introduces a comprehensive framework for continuous benchmarking in one of the most popular cryptography Rust libraries, fastcrypto. What makes our analysis unique is the realization that automated benchmarking is not just a performance monitor and optimization tool, but it can be used for cryptanalysis and innovation...

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...

The DECT Standard Cipher (DSC) is a proprietary stream cipher used for encryption in the Digital Enhanced Cordless Telecommunications (DECT), which is a standard for short range cordless communication and widely deployed worldwide both in residential and enterprise environments. New weaknesses of the DSC stream cipher which are not discovered in previous works are explored and analyzed in this paper. Based on these weaknesses, new practical key recovery attacks and distinguishing attack on...

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....

We devise algorithms for finding equivalences of trilinear forms over finite fields modulo linear group actions. Our focus is on two problems under this umbrella, Matrix Code Equivalence (MCE) and Alternating Trilinear Form Equivalence (ATFE), since their hardness is the foundation of the NIST round-$1$ signature candidates MEDS and ALTEQ respectively. We present new algorithms for MCE and ATFE, which are further developments of the algorithms for polynomial isomorphism and alternating...

The Partial Vandermonde (PV) Knapsack problem is an algebraic variant of the low-density inhomogeneous SIS problem. The problem has been used as a building block for various lattice-based constructions, including signatures (ACNS'14, ACISP'18), encryptions (DCC'15,DCC'20), and signature aggregation (Eprint'20). At Crypto'22, Boudgoust, Gachon, and Pellet-Mary proposed a key distinguishing attack on the PV Knapsack exploiting algebraic properties of the problem. Unfortunately, their attack...

The Alternating Trilinear Form Equivalence (ATFE) problem was recently used by Tang et al. as a hardness assumption in the design of a Fiat-Shamir digital signature scheme ALTEQ. The scheme was submitted to the additional round for digital signatures of the NIST standardization process for post-quantum cryptography. ATFE is a hard equivalence problem known to be in the class of equivalence problems that includes, for instance, the Tensor Isomorphism (TI), Quadratic Maps Linear...

In this paper, we extend the applicability of differential meet- in-the-middle attacks, proposed at Crypto 2023, to truncated differen- tials, and in addition, we introduce three new ideas to improve this type of attack: we show how to add longer structures than the original pa- per, we show how to improve the key recovery steps by introducing some probability in them, and we combine this type of attacks with the state- test technique, that was introduced in the context of impossible...

In this paper, we present a new type of algebraic attack that applies to many recent arithmetization-oriented families of permutations, such as those used in Griffin, Anemoi, ArionHash, and XHash8, whose security relies on the hardness of the constrained-input constrained-output (CICO) problem. We introduce the FreeLunch approach: the monomial ordering is chosen so that the natural polynomial system encoding the CICO problem already is a Gröbner basis. In addition, we present a new dedicated...

At EUROCRYPT’23, Castryck and Decru, Maino et al., and Robert present efficient attacks against supersingular isogeny Diffie-Hellman key exchange protocol (SIDH). Drawing inspiration from these attacks, Andrea Basso, Luciano Maino, and Giacomo Pope introduce FESTA, an isogeny-based trapdoor function, along with a corresponding IND-CCA secure public key encryption (PKE) protocol at ASIACRYPT’23. FESTA incorporates either a diagonal or circulant matrix into the secret key to mask torsion...

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...

DME is a multivariate scheme submitted to the call for additional signatures recently launched by NIST. Its performance is one of the best among all the candidates. The public key is constructed from the alternation of very structured linear and non-linear components that constitute the private key, the latter being defined over an extension field. We exploit these structures by proposing an algebraic attack which is practical on all DME parameters.

At CRYPTO 2019, Gohr demonstrated that differential-neural distinguishers (DNDs) for Speck32/64 can learn more features than classical cryptanalysis's differential distribution tables (DDT). Furthermore, a non-classical key recovery procedure is devised by combining the Upper Confidence Bound (UCB) strategy and the BayesianKeySearch algorithm. Consequently, the time complexity of 11-round key recovery attacks on Speck32/64 is significantly reduced compared with the state-of-the-art results...

The AES block cipher is today the most important and analyzed symmetric algorithm. While all versions of the AES are known to be secure in the single-key setting, this is not the case in the related-key scenario. In this article we try to answer the question whether the AES would resist better differential-like related-key attacks if the key schedule was different. For this, we search for alternative permutation-based key schedules by extending the work of Khoo et al. at ToSC 2017 and Derbez...

Polynomial commitment is a crucial cryptographic primitive in constructing zkSNARKs. Most practical constructions to date are either vulnerable against quantum adversaries or lack homomorphic properties, which are essential for recursive proof composition and proof batching. Recently, lattice-based constructions have drawn attention for their potential to achieve all the desirable properties, though they often suffer from concrete inefficiency or rely on newly introduced assumptions...

This paper focuses on the cryptanalysis of the ASCON family using automatic tools. We analyze two different problems with the goal to obtain new modelings, both simpler and less computationally heavy than previous works (all our models require only a small amount of code and run on regular desktop computers). The first problem is the search for Meet-in-the-middle attacks on reduced-round ASCON-Hash. Starting from the MILP modeling of Qin et al. (EUROCRYPT 2023 & ePrint 2023), we rephrase...

Differential cryptanalysis is an old and powerful attack against block ciphers. While different techniques have been introduced throughout the years to improve the complexity of this attack, the key recovery phase remains a tedious and error-prone procedure. In this work, we propose a new algorithm and its associated tool that permits, given a distinguisher, to output an efficient key guessing strategy. Our tool can be applied to SPN ciphers whose linear layer consists of a bit-permutation...

Since its introduction by Wagner (CRYPTO `02), the $k$-list algorithm has found significant utility in cryptanalysis. One important application thereof is in computing forgeries on several interactive signature schemes that implicitly rely on the hardness of the ROS problem formulated by Schnorr (ICICS `01). The current best attack strategy for these schemes relies the conjectured runtime of the $k$-list algorithm over $\mathbb{Z}_p$. The tightest known analysis of Wagner's algorithm over...

In this paper, we present an efficient attack against ${\tt PROV}$, a recent variant of the popular Unbalanced Oil and Vinegar (${\tt UOV}$) multivariate signature scheme, that has been submitted to the ongoing ${\tt NIST}$ standardization process for additional post-quantum signature schemes. A notable feature of ${\tt PROV}$ is its proof of security, namely, existential unforgeability under a chosen-message attack (${\tt EUF-CMA}$), assuming the hardness of solving the system formed by the...

At Eurocrypt 2023, a differential attack on the block cipher Speedy-7-192 was presented. This note shows that the main differential characteristic that this attack is based on has probability zero.