Description
Dans cet exposé nous nous intéressons à l'interpolation polynomiale multivariée et à ses applications. Nous présenterons tout d'abord des applications connues comme le décodage en liste des codes de Reed-Solomon (pour lequel Madhu Sudan a recu le prix Nevanlinna), mais aussi des applications nouvelles comme le décodage en liste des effacements des codes de Reed-Muller ou encore l'application au calcul de l'immunité algebrique. Ce dernier concept a de trés forte aplications en cryptographie pour contrer les attaques algébriques qui récemment ont permis d'obtenir des attaques trés efficaces sur les registres linéaires filtrés, utilisés pour le chiffrement à flot ou sur certains systèmes à clé symétrique. Ensuite nous présenterons un nouvel algorithme qui permet d'effectuer l'interpolation polynomiale multivariée à plusieurs variables en temps quadratique, améliorant la complexité cubique connue jusqu'ici pour résoudre certains des problèmes précédents. Nous nous interesserons aussi au cas des attaques algebriques rapides.
Prochains exposés
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Efficient zero-knowledge proofs and arguments in the CL framework
Orateur : Agathe Beaugrand - Institut de Mathématiques de Bordeaux
The CL encryption scheme, proposed in 2015 by Castagnos and Laguillaumie, is a linearly homomorphic encryption scheme, based on class groups of imaginary quadratic fields. The specificity of these groups is that their order is hard to compute, which means it can be considered unknown. This particularity, while being key in the security of the scheme, brings technical challenges in working with CL,[…] -
Constant-time lattice reduction for SQIsign
Orateur : Sina Schaeffler - IBM Research
SQIsign is an isogeny-based signature scheme which has recently advanced to round 2 of NIST's call for additional post-quantum signatures. A central operation in SQIsign is lattice reduction of special full-rank lattices in dimension 4. As these input lattices are secret, this computation must be protected against side-channel attacks. However, known lattice reduction algorithms like the famous[…] -
Circuit optimisation problems in the context of homomorphic encryption
Orateur : Sergiu Carpov - Arcium
Fully homomorphic encryption (FHE) is an encryption scheme that enables the direct execution of arbitrary computations on encrypted data. The first generation of FHE schemes began with Gentry's groundbreaking work in 2019. It relies on a technique called bootstrapping, which reduces noise in FHE ciphertexts. This construction theoretically enables the execution of any arithmetic circuit, but[…] -
Cycles of pairing-friendly abelian varieties
Orateur : Maria Corte-Real Santos - ENS Lyon
A promising avenue for realising scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. More specifically, such a cycle consists of two elliptic curves E/Fp and E’/Fq that both have a low embedding degree and also satisfy q = #E(Fp) and p = #E’(Fq). These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first[…]-
Cryptography
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