Description
An elliptic curve addition law is said to be complete if it correctly computes the sum of any two points in the elliptic curve group. One of the main reasons for the increased popularity of Edwards curves in the ECC community is that they can allow a complete group law that is also relatively efficient (e.g., when compared to all known addition laws on Edwards curves). Such complete addition formulas can simplify the task of an ECC implementer and, at the same time, can greatly reduce the potential vulnerabilities of a cryptosystem. Unfortunately, until now, complete addition laws that are relatively efficient have only been proposed on curves of composite order and have thus been incompatible with all of the currently standardized prime order curves.<br/> In this paper we present optimized addition formulas that are complete on every prime order short Weierstrass curve defined over a field k with char(k) not 2 or 3. Compared to their incomplete counterparts, these formulas require a larger number of field additions, but interestingly require fewer field multiplications. We discuss how these formulas can be used to achieve secure, exception-free implementations on all of the prime order curves in the NIST (and many other) standards.
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
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Post-quantum day of the cryptography seminar
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