Description
The talk will be concerned with arithmetic on elliptic and hyperelliptic curves. We show how fast the arithmetic can get by clever choices of the coordinates and present special kinds of curves which allow even faster arithmetic using the Frobenius endomorphism. For elliptic curves this has been used to achieve fast arithmetic for the past years. However, so far arithmetic in the ideal class group of hyperelliptic curves was performed using Cantor's algorithm which needs several inversions per group operation.<br/> Starting with the work of Harley and improved by Miyamoto, Doi, Matsuo, Chao, and Tsuji and by Takahashi efficient explicit formulae are at hand. Meanwhile inversion-free systems have been studied allowing even hardware implementations and depending on the system, hyperelliptic curves can even be faster than elliptic curves. Curve-endomorphisms allow to obtain further speed-up. We shortly present Koblitz curves, the generalized GLV method and trace zero subvarieties.
Next sessions
-
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
-
-
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.