Description
The curve shape suggested by Edwards does not define elliptic curves over fields of characteristic 2. We recently generalized the concept of Edwards curves and defined binary Edwards curves. These curves offer complete addition formulas and are the first binary curves with this property. Doubling and differential addition (addition of two points with known difference, like in the Montgomery ladder) are very fast on these curves. We present the design principles behind this choice of curve shape, present the birational equivalence with Weierstrass elliptic curves and explain how to obtain fast doubling and differential addition.<br/> This is joint work with Daniel J. Bernstein and Reza Rezaeian Farashahi.
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. The talks will take place at Amphi E in building 02A. To register for lunch, please do so before oct 30th using this link. -
Chiffrement homomorphe à l'aide des groupes après Nuida
Orateur : Pierre Guillot - Ravel Technologies/Université de strasbourg
Nuida et d'autres ont montré comment on peut obtenir un protocole de chiffrement pleinement homomorphe si l'on sait chiffrer les éléments d'un groupe G convenable, tout en sachant faire l'opération de G "en homomorphe". Les exemples étaient jusqu'à présent limités au chiffrement d'un bit à la fois, avec beaucoup d'opérations à effectuer pour "simuler" les portes logiques usuelles. Je vais[…]-
Cryptography
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Post-Quantum Signatures from Symmetric-Key-Friendly Techniques: From MPC-in-the-Head to VOLE-in-the-Head
Orateur : Dung Bui - Northwestern University
The MPC-in-the-Head (MPCitH) paradigm turns a secure multiparty computation protocol into a zero-knowledge proof and, via Fiat–Shamir, into a signature scheme whose security relies only on symmetric-key primitives. The framework of Katz, Kolesnikov and Wang (KKW, CCS18), which moves most of the MPC work into a committed preprocessing phase that the verifier checks by opening all-but-one of the[…] -
Nouveaux doctorants
Exposés courts des nouveaux doctorants (Elouan, Quentin, Eliot)