International Association
for Cryptologic Research

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 and whose key schedule is linear or almost linear. It can be used not only to help cryptanalysts find the best differential attack on a given cipher but also to assist designers in their security analysis. We applied our tool to four targets: RECTANGLE, PRESENT-80, SPEEDY-7-192 and GIFT-64. We extend the previous best attack on RECTANGLE-128 by one round and the previous best differential attack against PRESENT-80 by 2 rounds. We improve a previous key recovery step in an attack against SPEEDY and present more efficient key recovery strategies for RECTANGLE-80 and GIFT. Our tool outputs the results in only a second for most targets

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 O(2^{3c/4}) to 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 O(2^{3n/7}).

Differential attacks are among the most important families of cryptanalysis against symmetric primitives. Since their introduction in 1990, several improvements to the basic technique as well as many dedicated attacks against symmetric primitives have been proposed. Most of the proposed improvements concern the key-recovery part. However, when designing a new primitive, the security analysis regarding differential attacks is often limited to finding the best trails over a limited number of rounds with branch and bound techniques, and a poor heuristic is then applied to deduce the total number of rounds a differential attack could reach. In this work we analyze the security of the SPEEDY family of block ciphers against differential cryptanalysis and show how to optimize many of the steps of the key-recovery procedure for this type of attacks. For this, we implemented a search for finding optimal trails for this cipher and their associated multiple probabilities under some constraints and applied non-trivial techniques to obtain optimal data and key-sieving. This permitted us to fully break SPEEDY-7-192, the 7-round variant of SPEEDY supposed to provide 192-bit security. Our work demonstrates among others the need to better understand the subtleties of differential cryptanalysis in order to get meaningful estimates on the security offered by a cipher against these attacks.

Duplex-based authenticated encryption modes with a sufficiently large key length are proven to be secure up to the birthday bound 2^(c/2), where c is the capacity. However this bound is not known to be tight and the complexity of the best known generic attack, that is based on multicollisions, is much larger: it reaches (2^c)/α where α represents a small security loss factor. There is thus an uncertainty on the true extent of security beyond the bound 2^(c/2) provided by such constructions. In this paper, we describe a new generic attack against several duplex-based AEAD modes. Our attack produces a forgery in time complexity O(2^(3c/4)) using negligible memory and no encryption queries. Furthermore, for some duplex-based modes, our attack also recovers the secret key with a negligible amount of additional computations. Most notably, our attack breaks a security claim made by the designers of the NIST lightweight competition candidate Xoodyak. This attack is a step further towards determining the exact security provided by duplex-based constructions.

Elisabeth-4 is a stream cipher tailored for usage in hybrid homomorphic encryption applications that has been introduced by Cosseron et al. at ASIACRYPT 2022. In this paper, we present several variants of a key-recovery attack on the full Elisabeth-4 that break the 128-bit security claim of that cipher. Our most optimized attack is a chosen-IV attack with a time complexity of 2^88 elementary operations, a memory complexity of 2^54 bits and a data complexity of 2^41 bits. Our attack applies the linearization technique to a nonlinear system of equations relating some keystream bits to the key bits and exploits specificities of the cipher to solve the resulting linear system efficiently. First, due to the structure of the cipher, the system to solve happens to be very sparse, which enables to rely on sparse linear algebra and most notably on the Block Wiedemann algorithm. Secondly, the algebraic properties of the two nonlinear ingredients of the filtering function cause rank defects which can be leveraged to solve the linearized system more efficiently with a decreased data and time complexity. We have implemented our attack on a toy version of Elisabeth-4 to verify its correctness. It uses the efficient implementation of the Block Wiedemann algorithm of CADO-NFS for the sparse linear algebra.

In this paper, we analyze the collision resistance of the two smallest versions of Keccak which have a width of 200 and 400 bits respectively. We show that algebraic and linearization techniques can serve collision cryptanalysis by using some interesting properties of the linear part of the round function of Keccak. We present an attack on the Keccak versions that could be used in lightweight cryptography reduced to two rounds. For Keccak[40, 160] (resp. Keccak[72, 128] and Keccak[144, 256]) our attack has a computational complexity of 273 (resp. 252.5 and 2101.5) Keccak calls.