Table of contents

  • This session has been presented October 03, 2014.

Description

  • Speaker

    Pierrick Gaudry - LORIA

Le crible algébrique est le meilleur algorithme connu pour factoriser les entiers et pour calculer des logarithmes discrets dans des corps finis de grande caractérsitique. Bien que la complexité théorique est la même dans les deux cas, la phase d'algèbre linéaire est bien plus difficile dans le cas du logarithme discret. En revanche, les corps finis non premiers ont plus de structure, si bien que de nombreuses améliorations sont disponibles. Dans cet exposé, nous tenterons de quantifier les difficultés relatives de la factorisation d'entiers, du logarithme discret dans un corps premier, et du logarithme discret dans des corps de la forme GF(p^2). Notre discussion s'appuiera sur des expériences pratiques pour des entrées de 600 bits. Bien que cette taille est désormais plus ou moins de la routine pour la factorisation, cela constitue de nouveaux records pour le logarithme discret dans les corps finis de grande caractéristique. Cet exposé s'appuie sur des travaux communs avec Bouvier, Imbert, Jeljeli, Thomé, Barbulescu, Guillevic, Morain.

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