Description
Given two l-isogenous elliptic curves, a well-known algorithm of Elkies uses modular polynomials to compute this isogeny explicitly. In this work, we generalize his ideas to Jacobians of genus 2 curves. Our algorithms works for both l-isogenies and (in the RM case) cyclic isogenies, and uses Siegel or Hilbert type modular equations respectively. This has applications for point counting in genus 2: SEA-style methods are now available.<br/> lien: http://desktop.visio.renater.fr/scopia?ID=726145***4969&autojoin
Prochains exposés
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Computational assumptions in the quantum world
Orateur : Alex Bredariol Grilo - LIP6 (CNRS / Sorbonne Université)
QKD is a landmark of how quantum resources allow us to implement cryptographicfunctionalities with a level of security that is not achievable only with classical resources.However, key agreement is not sufficient to implement all functionalities of interest, and it iswell-known that they cannot be implemented with perfect security, even if we have accessto quantum resources. Thus, computational[…]-
Cryptographie
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Orateur : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptographie
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Primitive asymétrique
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Mode et protocole
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Post-quantum Group-based Cryptography
Orateur : Delaram Kahrobaei - The City University of New York