Daniel Augot

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Recently, some collisions have been exposed for a variety of cryptographic hash functions [20, 21] including some of the most widely used today. Many other hash functions using similar constructions can however still be considered secure. Nevertheless, this has drawn attention on the need for new hash function designs. In this article is presented a family(More)
MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having(More)
This paper presents an algorithmic improvement to Sudan’s list-decoding algorithm for Reed-Solomon codes and its generalization to algebraic-geometric codes from Shokrollahi and Wasserman. Instead of completely factoring the interpolation polynomial over the function field of the curve, we compute sufficiently many coefficients of a Hensel development to(More)
We consider only primitive binary cyclic codes of length n = 2 m ? 1. A BCH-code with designed distance is denoted B(n;). A BCH-code is always a narrow-sense BCH-code. A codeword is identiied with its locator polynomial, whose coeecients are the symmetric functions of the locators. The deenition of the code by its zeros-set involves some properties for the(More)
We propose a family of fast and provably secure cryptographic hash functions. The security of these functions relies directly on the well-known syndrome decoding problem for linear codes. Attacks on this problem are well identified and their complexity is known. This enables us to study precisely the practical security of the hash functions and propose(More)
Since the concept of locally decodable codes was introduced by Katz and Trevisan in 2000 [11], it is well-known that information theoretically secure private information retrieval schemes can be built using locally decodable codes [15]. In this paper, we construct a Byzantine robust PIR scheme using the multiplicity codes introduced by Kopparty et al. [12].(More)
Group Key Agreement (GKA) protocols enable the participants to derive a key based on each one’s contribution over a public network without any central authority. They also provide efficient ways to change the key when the participants change. While some of the proposed GKA protocols are too resource consuming for the constraint devices often present in ad(More)
This article presents a new algorithm to find MDS matrices that are well suited for use as a diffusion layer in lightweight block ciphers. Using an recursive construction, it is possible to obtain matrices with a very compact description. Classical field multiplications can also be replaced by simple F<sub>2</sub>-linear transformations (combinations of(More)
We consider primitive cyclic codes of length p − 1 over Fp. The codes of interest here are duals of BCH codes. For these codes, a lower bound on their minimum distance can be found via the adaptation of the Weil bound to cyclic codes (see [10]). However, this bound is of no significance for roughly half of these codes. We shall fill this gap by giving, in(More)