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700 results

    • Seminar

    • Cryptography

    Sur la Conjecture de Patterson-Wiedeman

    • January 24, 2003

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Philippe Langevin - Université de Toulon

    La distance d'une fonction booléenne f de m variables au code de Reed-Muller est une mesure la non-linearité de f. Il s'agit d'une notion importante en cryptographie. L'analyse de Fourier est une méthode d'approche normale de cette question. En particulier, la non-linéarité de f est égale à [ 2^m - R(f) ] /2, où R(f) est l'amplitude spectrale de f i.e. le module maximal de ses coefficients de[…]

    • Seminar

    • Cryptography

    Application de la déscente de Weil en cryptographie

    • March 29, 2002

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Pierrick Gaudry - Lix Ecole Polytechnique

    Nous commencerons par rappeler les méthodes algorithmiques pour manipuler les courbes hyperelliptiques, et en particulier l'attaque du problème du logarithme discret par des méthodes de calcul d'index. Nous présenterons ensuite la méthode de la restriction de Weil, dont Frey fut le premier a soupçonner les conséquences cryptographiques. En traçant une courbe hyperelliptique sur la restriction de[…]

    • Seminar

    • Cryptography

    Correspondances modulaires, relèvement canonique et applications

    • December 20, 2002

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Jean-Marc Couveignes - Univeristé Toulouse II

    • Seminar

    • Cryptography

    Monsky-Washnitzer Cohomology and Computing Zeta Functions

    • May 31, 2002

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Kiran Kedlaya - Berkeley

    Monsky-Washnitzer cohomology is a p-adic cohomology theory for algebraic varieties over finite fields, based on algebraic de Rham cohomology. Unlike the l-adic (etale) cohomology, it is well-suited for explicit computations, particularly over fields of small characteristic. We describe how to use Monsky-Washnitzer to construct efficient algorithms for computing zeta functions of varieties over[…]

    • Seminar

    • Cryptography

    Computing the order of the group of rational points on the Jacobian of a hyperelliptic curve in characteristic 2

    • June 07, 2002

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Alan Lauder - Oxford University

    I will describe an algorithm for computing the zeta function of an arbitrary hyperelliptic curve in characteristic 2. This is a generalisation of an earlier method of myself and Wan, which tackled a restricted class of curves. The algorithm reduces the problem to that of computing the L-function of an additive character sum over an open subset of the projective line. This latter task can be[…]

    • Seminar

    • Cryptography

    Extensions of Kedlaya's algorithm

    • October 18, 2002

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Frederik Vercauteren - Bristol University

    Kedlaya described an algorithm for computing the zeta function of a hyperelliptic curve in characteristic p > 2 using the theory of Monsky-Washnitzer cohomology. Joint work with Jan Denef has resulted in 2 extensions of Kedlaya's original algorithm: the first extension can be used to compute the zeta function of a hyperelliptic curve in characteristic 2 and the second leads to a rather general[…]
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