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Séminaire
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Cryptographie
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Orateur : 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[…] -
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Séminaire
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Cryptographie
CSIDH: an efficient post-quantum commutative group action
Orateur : Chloé Martindale - Technical University of Eindhoven
CSIDH, or `commutative supersingular isogeny Diffie-Hellman' is a new isogeny-based protocol of Castryck, Lange, Martindale, Panny, and Renes.<br/> The Diffie-Hellman style scheme resulting from the group action allows for public key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post[…] -
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Séminaire
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Cryptographie
Isogeny-based cryptography from superspecial genus-2 curves
Orateur : Wouter Castryck - KU Leuven
I will report on some first attempts to do isogeny-based cryptography in genus 2. More precisely, we will use isogeny graphs of superspecial principally polarized abelian surfaces over GF(p^2) for constructing variants of Charles, Goren and Lauter's hash function and of Jao and De Feo's SIDH key exchange protocol, both of which use supersingular elliptic curves over GF(p^2). This will be largely[…] -
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Séminaire
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Cryptographie
Permutations complètes en caractéristique 2.
Orateur : Valentin Suder - Université de Versailles Saint-Quentin
Dans ce travail, nous nous intéressons aux permutations complètes, c’est-à-dire aux fonctions bijectives $x\mapsto f(x)$ telles que $x\mapsto f(x)+x$ soient aussi bijectives. Plus particulièrement, nous nous intéressons aux permutations complètes sur les corps finis $\mathbb{F}_{2^n}$. En caractéristique 2, la définition des permutations complètes coincide avec celle des orthomorphismes. Nous[…] -
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Séminaire
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Cryptographie
CRYSTALS: Dilithium and Kyber
Orateur : Damien Stehlé - ENS de Lyon
Kyber -- a Key Exchange Mechanism -- and Dilithium -- a digital signature -- are the two components of the Cryptographic Suite for Algebraic Lattices (CRYSTALS). I will present the intractable problems underlying their security, overview their design and comment their practical performance. The talk is based on the following articles:<br/> https://eprint.iacr.org/2017/633.pdf<br/> https:/[…] -
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Séminaire
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Cryptographie
Open problems in isogeny-based cryptography
Orateur : Luca De Feo - Université de Versailles Saint-Quentin
Isogeny-based cryptography (IBC) is a very young field, only 10 years old. Protocols in this family include key-exchange, encryption, "provably secure" hash functions and trapdoor systems. Hardness assumptions in IBC come from the difficulty of finding paths in isogeny graphs, that is graphs of elliptic curves linked by isogenies of some prescribed degree.<br/> Recently some IBC protocols have[…] -