Table of contents

  • This session has been presented February 09, 2018.

Description

  • Speaker

    Benjamin WESOLOWSKI - École Polytechnique Federale de Lausanne

An isogeny graph is a graph whose vertices are abelian varieties (typically elliptic curves, or Jacobians of genus 2 hyperelliptic curves) and whose edges are isogenies between them. Such a graph is "horizontal" if all the abelian varieties have the same endomorphism ring. We study the connectivity and the expander properties of these graphs. We use these results, together with a recent algorithm for computing explicit isogenies in genus 2, to prove random self-reducibility of the discrete logarithm problem for Jacobians of genus 2 hyperelliptic curves with fixed endomorphism ring. In addition, we remove the heuristics in the complexity analysis of an algorithm of Galbraith for explicitly computing isogenies between two elliptic curves in the same isogeny class, and extend it to a more general setting including genus 2.

Next sessions

  • !!! Reporté !!! Encryption homomorphe sans bruit à l'aide de groupes

    • June 26, 2026 (13:45 - 14:45)

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

    Speaker : Pierre Guillot - Ravel Technologies (dispo Université de Strasbourg, IRMA)

    Je vais rappeler les travaux de Nuida et Ostrovski sur l'utilisation des groupes pour l'élaboration de schémas cryptographiques homomorphes. Je vais présenter nos travaux qui fournissent des encodages à la fois plus efficaces et plus généraux, et qui déterminent exactement quels groupes peuvent être utilisés.   Puis je vais discuter GRAFHEN, un protocole qui utilise ces idées. Je dirai juste[…]

    • Cryptography

  • MIKE: An efficient and compact NIKE Based on a Commutative Monoidal Action 

    • July 03, 2026 (13:45 - 14:45)

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

    Speaker : Jonathan Komada Eriksen - COSIC, KU Leuven

    Robert recently described a powerful correspondence between certain (Hermitian) modules and (polarized) abelian varieties, which simultaneously generalizes both the class-group action underlying protocols such as CSIDH, and the Deuring correspondence, underlying protocols such as SQIsign. Using this correspondence, he also proposed how to construct a post-quantum NIKE, called MIKE, which, at a[…]

    • Cryptography

  • TBA

    • September 25, 2026 (13:45 - 14:45)

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

    Speaker : Anmoal Porwal - Technical University of Munich

    • Cryptography

    • Asymmetric primitive

Show previous sessions
Page top