Charles Bouillaguet

Second preimage attacks on dithered hash functions

We develop a new generic long-message second preimage attack, based on combining the techniques in the second preimage attacks of Dean [8] and Kelsey and Schneier [16] with the herding attack of Kelsey and Kohno [15]. We show that these generic attacks apply to hash functions using the Merkle-Damgard construction with only slightly more work than the previously known attack, but allow enormously more control of the contents of the second preimage found. Additionally, we show that our new attack applies to several hash function constructions which are not vulnerable to the previously known attack, including the dithered hash proposal of Rivest [25], Shoups UOWHF[26] and the ROX hash construction [2].We analyze the properties of the dithering sequence used in [25], and develop a time-memory tradeoff which allows us to apply our second preimage attack to a wide range of dithering sequences, including sequences which are much stronger than those in Rivests proposals. Finally, we show that both the existing second preimage attacks [8,16] and our new attack can be applied even more efficiently to multiple target messages; in general, given a set of many target messages with a total of 2R message blocks, these second preimage attacks can find a second preimage for one of those target messages with no more work than would be necessary to find a second preimage for a single target message of 2R message blocks.

Automatic search of attacks on round-reduced AES and applications

In this paper, we describe versatile and powerful algorithms for searching guess-and-determine and meet-in-the-middle attacks on byte-oriented symmetric primitives. To demonstrate the strengh of these tool, we show that they allows to automatically discover new attacks on round-reduced AES with very low data complexity, and to find improved attacks on the AES-based MACs Alpha-MAC and Pelican-MAC, and also on the AES-based stream cipher LEX. Finally, the tools can be used in the context of fault attacks. These algorithms exploit the algebraically simple byte-oriented structure of the AES. When the attack found by the tool are practical, they have been implemented and validated.

Using first-order theorem provers in the Jahob data structure verification system

This paper presents our integration of efficient resolution-based theorem provers into the Jahob data structure verification system. Our experimental results show that this approach enables Jahob to automatically verify the correctness of a range of complex dynamically instantiable data structures, such as hash tables and search trees, without the need for interactive theorem proving or techniques tailored to individual data structures. Our primary technical results include: (1) a translation from higher-order logic to first-order logic that enables the application of resolution-based theorem provers and (2) a proof that eliminating type (sort) information in formulas is both sound and complete, even in the presence of a generic equality operator. Our experimental results show that the elimination of type information often dramatically decreases the time required to prove the resulting formulas. These techniques enabled us to verify complex correctness properties of Java programs such as a mutable set implemented as an imperative linked list, a finite map implemented as a functional ordered tree, a hash table with a mutable array, and a simple library system example that uses these container data structures. Our system verifies (in a matter of minutes) that data structure operations correctly update the finite map, that they preserve data structure invariants (such as ordering of elements, membership in appropriate hash table buckets, or relationships between sets and relations), and that there are no run-time errors such as null dereferences or array out of bounds accesses.

Low-Data Complexity Attacks on AES

The majority of current attacks on reduced-round variants of block ciphers seeks to maximize the number of rounds that can be broken, using less data than the entire codebook and less time than exhaustive key search. In this paper, we pursue a different approach, restricting the data available to the adversary to a few plaintext/ciphertext pairs. We argue that consideration of such attacks (which received little attention in recent years) improves our understanding of the security of block ciphers and of other cryptographic primitives based on block ciphers. In particular, these attacks can be leveraged to more complex attacks, either on the block cipher itself or on other primitives (e.g., stream ciphers, MACs, or hash functions) that use a small number of rounds of the block cipher as one of their components. As a case study, we consider the Advanced Encryption Standard (AES)-the most widely used block cipher. The AES round function is used in many cryptographic primitives, such as the hash functions Lane, SHAvite-3, and Vortex or the message authentication codes ALPHA-MAC, Pelican, and Marvin. We present attacks on up to four rounds of AES that require at most three known/chosen plaintexts. We then apply these attacks to cryptanalyze an AES-based stream cipher (which follows the leak extraction methodology), and to mount the best known plaintext attack on six-round AES.

Another look at complementation properties

In this paper we present a collection of attacks based on generalisations of the complementation property of DES. We find symmetry relations in the key schedule and in the actual rounds, and we use these symmetries to build distinguishers for any number of rounds when the relation is deterministic. This can be seen as a generalisation of the complementation property of DES or of slide/related-key attacks, using different kinds of relations. We further explore these properties, and show that if the relations have easily found fixed points, a new kind of attacks can be applied. Our main result is a self-similarity property on the SHA-3 candidate Lesamnta, which gives a very surprising result on its compression function. Despite the use of round constants which were designed to thwart any such attack, we show a distinguisher on the full compression function which needs only one query, and works for any number of rounds. We also show how to use this self-similarity property to find collisions on the full compression function of Lesamnta much faster than generic attacks. The main reason for this is the structure found in these round constants, which introduce an interesting and unexpected symmetry relation. This casts some doubt on the use of highly structured constants, as it is the case in many designs, including the AES and several SHA-3 candidates. Our secondmain contribution is a new related-key differential attack on round-reduced versions of the XTEA block-cipher. We exploit the weakness of the key-schedule to suggest an iterative related-key differential. It can be used to recover the secret key faster than exhaustive search using two related keys on 37 rounds. We then isolate a big class of weak keys for which we can attack 51 rounds out of the ciphers 64 rounds. We also apply our techniques to ESSENCE and PURE.

Practical cryptanalysis of the identification scheme based on the isomorphism of polynomial with one secret problem

This paper presents a practical cryptanalysis of the Identification Scheme proposed by Patarin at Crypto 1996. This scheme relies on the hardness of the Isomorphism of Polynomial with One Secret (IP1S), and enjoys shorter key than many other schemes based on the hardness of a combinatorial problem (as opposed to number-theoretic problems). Patarin proposed concrete parameters that have not been broken faster than exhaustive search so far. On the theoretical side, IP1S has been shown to be harder than Graph Isomorphism, which makes it an interesting target. We present two new deterministic algorithms to attack the IP1S problem, and we rigorously analyze their complexity and success probability. We show that they can solve a (big) constant fraction of all the instances of degree two in polynomial time. We verified that our algorithms are very efficient in practice. All the parameters with degree two proposed by Patarin are now broken in a few seconds. The parameters with degree three can be broken in less than a CPU-month. The identification scheme is thus quite badly broken.

A family of weak keys in HFE and the corresponding practical key-recovery

Abstract. The HFE (hidden field equations) cryptosystem is one of the most interesting public-key multivariate schemes. It has been proposed more than 10 years ago by Patarin and seems to withstand the attacks that break many other multivariate schemes, since only subexponential ones have been proposed. The public key is a system of quadratic equations in many variables. These equations are generated from the composition of the secret elements: two linear mappings and a polynomial of small degree over an extension field. In this paper we show that there exist weak keys in HFE when the coefficients of the internal polynomial are defined in the ground field. In this case, we reduce the secret key recovery problem to an instance of the Isomorphism of Polynomials (IP) Problem between the equations of the public key and themselves. Even though the hardness of recovering the secret-key of schemes such as SFLASH or relies on the hardness of the IP Problem, this is normally not the case for HFE, since the internal polynomial is kept secret. However, when a weak key is used, we show how to recover all the components of the secret key in practical time, given a solution to an instance of the IP Problem. This breaks in particular a variant of HFE proposed by Patarin to reduce the size of the public key and called the “subfield variant”. Recovering the secret key takes a few minutes.

Attacks on hash functions based on generalized Feistel: application to reduced-round Lesamnta and SHAvite-3 512

In this paper we study the strength of two hash functions which are based on Generalized Feistels. We describe a new kind of attack based on a cancellation property in the round function. This new technique allows to efficiently use the degrees of freedom available to attack a hash function. Using the cancellation property, we can avoid the non-linear parts of the round function, at the expense of some freedom degrees. Our attacks are mostly independent of the round function in use, and can be applied to similar hash functions which share the same structure but have different round functions. We start with a 22-round generic attack on the structure of Lesamnta, and adapt it to the actual round function to attack 24-round Lesamnta (the full function has 32 rounds). We follow with an attack on 9-round SHAvite-3512 which also works for the tweaked version of SHAvite-3512.

Graph-Theoretic Algorithms for the “Isomorphism of Polynomials” Problem

We give three new algorithms to solve the “isomorphism of polynomial” problem, which was underlying the hardness of recovering the secret-key in some multivariate trapdoor one-way functions. In this problem, the adversary is given two quadratic functions, with the promise that they are equal up to linear changes of coordinates. Her objective is to compute these changes of coordinates, a task which is known to be harder than Graph-Isomorphism. Our new algorithm build on previous work in a novel way. Exploiting the birthday paradox, we break instances of the problem in time q 2n/3 (rigorously) and q n/2 (heuristically), where q n is the time needed to invert the quadratic trapdoor function by exhaustive search. These results are obtained by turning the algebraic problem into a combinatorial one, namely that of recovering partial information on an isomorphism between two exponentially large graphs. These graphs, derived from the quadratic functions, are new tools in multivariate cryptanalysis.

Fast Exhaustive Search for Polynomial Systems in \({\mathbb{F}_2}\)

We analyze how fast we can solve general systems of multivariate equations of various low degrees over \({\mathbb{F}_{2}}\); this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive search technique, our improved approach is more efficient both asymptotically and practically. We implemented several optimized versions of our techniques on CPUs and GPUs. Our technique runs more than 10 times faster on modern graphic cards than on the most powerful CPU available. Today, we can solve 48+ quadratic equations in 48 binary variables on a 500-dollar NVIDIA GTX 295 graphics card in 21 minutes. With this level of performance, solving systems of equations supposed to ensure a security level of 64 bits turns out to be feasible in practice with a modest budget. This is a clear demonstration of the computational power of GPUs in solving many types of combinatorial and cryptanalytic problems.