511 results
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A Residue Approach of the Finite Fields Arithmetics
Speaker : Jean-Claude Bajard - Université de Montpellier
Finite fields arithmetic is one of the challenges in current computer arithmetic. It occurs, in particular, in cryptography where the needs increase with the evolution of the technologies and also of the attacks. Through our research, we have proposed different systems based on residues representations. Different kinds of finite fields are concerned with. For each of them, some specificities of[…] -
Advances in cryptographic coprocessor design on FPGAs
Speaker : Nele Mentens - Katholieke Universiteit Leuven
Security in embedded systems requires the choice of a suitable implementation platform. For some systems, a general purpose microprocessor satisfies the requirements, but when high performance is the main criterium, cryptographic coprocessors in hardware are indispensable. When very high performance is required or when a high volume of coprocessors is needed, ASICs (Application Specific Integrated[…] -
Standard models for finite fields
Speaker : Bart de Smit - University of Leiden
We give a deterministic polynomial time algorithm that on input two finite fields of the same cardinality produces an isomorphism between the two. Moreover, if for three finite fields of the same cardinality one applies the algorithm to the three pairs of fields then one obtains a commutative triangle. The algorithm depends on the definition of F_q as an actual field rather than a field up to[…] -
Hardware Operators for Pairing-Based Cryptography
Speaker : Jean-Luc Beuchat - University of Tsukuba
This talk is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing. We propose here a novel hardware implementation of Miller's loop based on a pipelined Karatsuba-Ofman multiplier. Thanks to a careful choice of the mean of computing the Tate pairing and algorithms for tower field arithmetic, we manage to keep the pipeline busy. We also describe the strategies[…] -
Calcul du Groupe de Galois
Speaker : Guénael Renault - LIP6
Lors de son édification, la théorie de Galois a été établie de manière constructive. Même si la méthode de base pour le calcul du groupe de Galois était déjà connue des mathématiciens de la fin du 19ème siècle (par exemple exposée dans l'ouvrage de Jordan), il faut attendre les techniques de la théorie algorithmique des nombres pour avoir des algorithmes efficaces permettant un tel calcul.<[…] -
Le problème de la reconnaissance d'un point de vue théorie de l'information
Speaker : Mathieu Cluzeau - INRIA-Rocquencourt
Dans le cadre de l'étude de canaux dans un contexte non-coopératif, nous nous intéressons à la reconstruction des codes correcteurs d'erreurs. Dans ce contexte, un attaquant dispose d'une séquence interceptée provenant d'une communication codée et souhaite retrouver quel code correcteur d'erreur a été utilisé lors de la transmission. D'un point de vue de la théorie de[…]