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- Daniel Augot, Matthieu Finiasz, Nicolas Sendrier
- IACR Cryptology ePrint Archive
- 2003

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)

- Daniel Augot, Pascale Charpin, Nicolas Sendrier
- IEEE Trans. Information Theory
- 1992

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)

- Daniel Augot, Pascale Charpin, Nicolas Sendrier
- EUROCODE
- 1990

In this paper, we give a natural way of deciding whether a given cyclic code contains a word of given weight. The method is based on the manipulation of the locators and of the locator polynomial of a codeword x. Because of the dimensions of the problem, we need to use a symbolic computation software, like Maple or Scratchpad II. The method can be… (More)

- Daniel Augot, Lancelot Pecquet
- IEEE Trans. Information Theory
- 2000

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)

- Alexander Zeh, Christian Gentner, Daniel Augot
- IEEE Transactions on Information Theory
- 2011

The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation and factorization of multivariate polynomials. This article provides a link between syndrome-based decoding approaches… (More)

- Daniel Augot, Matthieu Finiasz, Pierre Loidreau
- IACR Cryptology ePrint Archive
- 2003

In this paper, we present a modication of the Augot-Finiasz cryptosystem presented at EUROCRYPT 2003. Coron managed to design an attack against the original cryptosystem enabling an attacker to decrypt any intercepted ciphertext eciently. We introduce here a modication of the scheme which appears to resist to this attack. We furthermore propose parameters… (More)

- Daniel Augot, Matthieu Finiasz, Nicolas Sendrier
- Mycrypt
- 2005

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)

- D Augot, P Charpin, N Sendrier, R Esum
- 2007

Nous montrons que la classe des polyn^ omes de F 2 mZ], qui sont les polyn^ omes localisateurs des mots de plus petit poids du code BCH primitif binaire de longueur 2 m ?1 et distance minimale 2 m?2 ?1, est en bijection avec l'ensemble des F 2-sous-espaces de dimension m ? 2 de F 2 m. Abstract We prove that the class of polynomials of F 2 mZ], which are the… (More)

- Daniel Augot, Raghav Bhaskar, Valérie Issarny, Daniele Sacchetti
- 2008 4th International Conference on Wireless…
- 2005

An ad hoc network is a collection of autonomous nodes that communicate with each other by forming a multi-top wireless network. Different from conventional wireless networks, the resource of the nodes in ad hoc networks is limited. As such, the costs of the nodes resource should be minimized when constructing a group key agreement protocol in the ad hoc… (More)

- Daniel Augot, Françoise Levy-dit-Vehel
- IEEE Trans. Information Theory
- 1996

We consider primitive cyclic codes of length p m − 1 over F p. 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,… (More)