Description
Finding a short non zero vector in an Euclidean lattice is a well-studied problem which has proven useful to construct many cryptographic primitives. The current best asymptotic algorithm to find a relatively short vector in an arbitrary lattice is the BKZ algorithm. This algorithm recovers a vector which is at most $2^{n^{\alpha}}$ times larger than the shortest non zero vector in time $2^{n^{1-\alpha}}$ for any $\alpha$ between 0 and 1.<br/> In order to gain in efficiency, it is sometimes interesting to use structured lattices instead of general lattices. An example of such structured lattices are ideal lattices. One may then wonder whether, on the security front, it is easier to find short vectors in a structured lattice or not. Until 2016, there was no known algorithm which would perform better on ideal lattices than the BKZ algorithm (either classically or quantumly). In 2016 and 2017, Cramer-Ducas-Peikert-Regev and Cramer-Ducas-Wesolowski proposed a quantum algorithm that finds a $2^{\sqrt n}$ approximation of the shortest non zero vector in polynomial time. However, the BKZ algorithm remained the best algorithm in the classical setting or for approximation factor smaller than $2^{\sqrt n}$ in the quantum setting.<br/> In this talk, I will present an algorithm that extends the one of Cramer et al. and improves upon the BKZ algorithm for ideal lattices, both quantumly and classically. This algorithm is heuristic and non uniform (i.e., it requires an exponential time pre-processing).<br/> lien: http://desktop.visio.renater.fr/scopia?ID=723420***3028&autojoin
Next sessions
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Adelic reduction of module lattices
Speaker : 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.