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684 results
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Seminar
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Cryptography
Counting points on hyperelliptic curves in average polynomial time
Speaker : Kiran Kedlaya - San Diego University
We describe an algorithm of Harvey, improved and implemented by Harvey and Sutherland, which given a hyperelliptic curve of genus g over Q computes its zeta function over F_p for all p <= N in such a way that the average time per prime is polynomial in g and log(N). The method is based on p-adic cohomology, specifically the algorithms of Kedlaya and Harvey; the key new observation is that one can[…] -
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Seminar
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Cryptography
Design and Analysis of Opaque Signatures
Speaker : Laila El Aimani - Technicolor
Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. However, and in situations where the signed data is commercially or personally sensitive, the universal verification of digital signatures is undesirable, and needs to be limited or controlled. Therefore, mechanisms which share most properties with digital signatures except the universal[…] -
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Seminar
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Cryptography
Explicit isogenies of low degree
Speaker : Kiminori Tsukazaki - University of Warwick
There are several algorithms for computing isogenies between elliptic curves, and one of them is Elkies' method using the modular curve. Motivated by that, we will look at an algebraic approach to explicitly compute isogenies of degree p for certain small primes p between elliptic curves, by using the modular curve and 'generic kernel polynomials'. -
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Seminar
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Cryptography
Un algorithme de comptage de points pour les recouvrements cycliques de la droite projective
Speaker : Cécile Goncalves - LIX
Nous présentons un algorithme à la Kedlaya pour compter les points de recouvrements cycliques $y^r = f(x)$ défini sur un corps fini de caractéristique $p$ ne divisant pas $r$, et avec $r$ et le degré de $f$ non nécessairement premiers entre eux.<br/> Cet algorithme généralise l'algorithme de Gaudry et Gürel pour les courbes superelliptiques à une classe de courbe plus générale, avec[…] -
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Seminar
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Cryptography
Noyaux et pinceaux de formes quadratiques
Speaker : Gilles Macariorat - France Telecom
La cryptographie multivariée est une vaste famille de schémas qui reposent sur la difficulté de résoudre en général un système multivarié quadratique quelconque.<br/> Parmi ces schémas on trouve SFLASH, HFE, UOV, etc. L'objet de cet exposé est une présentation de travaux récents de cryptanalyse du schéma SFLASH, ou plus généralement de schémas dans lequel un monôme central (voire un petit nombre[…] -
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Seminar
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Cryptography
Counting points in families of nondegenerate curves.
Speaker : Jan Tuitman - LIX
I will talk about an algorithm for computing zeta functions of a quite general class of algebraic curves (so called nondegenerate ones) using deformations in p-adic cohomology. I will give an overview of the mathematics that is involved, talk about my MAGMA implementation, and give some examples. -