Description
Dans cet exposé, nous ferons une présentation de certains aspects des calculs de couplages sur les jacobiennes de courbes algébriques utiles en cryptographie.<br/> Après un rappel sur les définitions mathématiques, nous présenterons l'algorithme de Miller qui permet de calculer efficacement les couplages de Weil et Tate. Puis, nous décrirons quelques améliorations algorithmiques apportées par F. Hess et al. et nous expliquerons comment accélérer encore leur algorithme dans le cas de courbes super-singulières.
Next sessions
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Algorithms for post-quantum commutative group actions
Speaker : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
Endomorphisms via Splittings
Speaker : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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