Description
The Polynomial Modular Number System (PMNS) is an integer number system which aims to speed up arithmetic operations modulo a prime p. Such a system is defined by a tuple (p, n, g, r, E), where p, n, g and r are positive integers, E is a monic polynomial with integer coefficients, having g as a root modulo p. Most of the work done on PMNS focus on polynomials E such that E(X) = X^n – l, where l is a nonzero integer, because such a polynomial provides efficiency and low memory cost, in particular for l = 2 or -2.<br/> It however appeared that these are not always the best choices. In this presentation, we first start with the necessary background on PMNS. Then, we highlight a new set of polynomials E for very efficient operations in the PMNS and low memory requirement, along with new bounds and parameters. We show that these polynomials are more interesting than (most) polynomials E(X)=X^n – l. To finish, we see how to use PMNS to randomise arithmetic operations in order to randomise high level operations like elliptic curve scalar multiplication, to protect implementations against some advanced side channel attacks like differential power analysis (DPA).<br/> Joint work with Jean-Marc Robert and Pascal Véron<br/> lien: https://seminaire-c2.inria.fr/
Prochains exposés
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Adelic reduction of module lattices
Orateur : Henry Bambury - DGA-MI et Inria Rennes
We give a strict generalisation of the LLL algorithm over number fields, based on the reduction theory of $GL(n)$ over the adele ring of a number field. Our algorithm is free of heuristics, with rigorous bounds on output quality and complexity. -- based on joint work with Seungki Kim, Changmin Lee and Phong Nguyen ---
Cryptography
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European Cyber Week: atelier cryptographie post-quantique
Dans la continuité des éditions 2021, 2022 et 2024, la DGA — en partenariat avec CREACH LABS et avec le soutien de l'ANSSI, de l'IRISA, de l'IRMAR et du Pôle d'Excellence Cyber — organise la 4e édition de l'atelier consacré à la cryptographie post-quantique dans le cadre de l'European Cyber Week 2026. Attention, il faut s'inscrire (gratuitement) au préalable — s'inscrire à la conférence Les[…] -
Post-quantum day of the cryptography seminar
A scientific day devoted to post-quantum cryptography, held in the wake of the European Cyber Week, with talks more technical than those presented at the ECW.