Description
Nous présenterons dans cet exposé le test AKS et ses améliorations, qui permettent de prouver qu'un entier N est un nombre premier. Nous verrons comment il nous a été récemment possible d'obtenir une variante de ces tests plus efficace, en généralisant aux courbes elliptiques, des idées de Berrizbeitia - Cheng - Avanzi - Mihailescu - Bernstein. En particulier, il nous est possible de nous débarrasser de l'exposant f auparavant nécessaire pour que N^f-1 possède un diviseur proche de log2 N.
Next sessions
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Computational assumptions in the quantum world
Speaker : 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[…]-
Cryptography
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Speaker : 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[…]-
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Asymmetric primitive
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Mode and protocol
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Post-quantum Group-based Cryptography
Speaker : Delaram Kahrobaei - The City University of New York