Description
Finite fields arithmetic is one of the challenges in current computer arithmetic. It occurs, in particular, in cryptography where the needs increase with the evolution of the technologies and also of the attacks. Through our research, we have proposed different systems based on residues representations. Different kinds of finite fields are concerned with. For each of them, some specificities of the representations are exploited to ensure the efficiency, as well as for the performances, than for the robustness to side channel attacks. In this talk, we deal with three similar approaches: the first one is dedicated to prime field using residue number systems, a seconde one concerns extension finite fields of characteristic two, the last one discusses of medium characteristic finite fields. The main interest of these systems is their inherent modularity, well suited for circuit implementations.
Prochains exposés
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Algorithms for post-quantum commutative group actions
Orateur : 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
Orateur : 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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