Table of contents

  • This session has been presented September 13, 2013.

Description

  • Speaker

    Jean-François Biasse - Calgary University

Depuis les travaux de Hafner-MacCurley et Buchmann, le calcul du groupe de classes et d'unités d'un corps de nombres est connu comme étant possible en temps sous-exponentiel sous GRH pour les classes de corps de degré fixé.<br/> Dans cet exposé, nous montrerons qu'il est possible d'étendre ces résultats aux corps de nombres de degré tendant vers l'infini. Nous envisagerons des applications à des domaines liés à la cryptographie. En particulier, le calcul de relations entre idéaux du groupe de classes polarisé qui intervient dans le cadre du calcul d'isogénies entre variétés abéliennes, et le calcul du générateur d'un idéal principal qui permet la cryptanalyse de certain systèmes de chiffrement homomorphe.

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