Description
Let A be an abelian variety over a finite field. Liftable endomorphisms of A act on the deformation space. In the ordinary case there's a canonical way of lifting Frobenius. We will show, that the action of Frobenius has a unique fixpoint, the canonical lift. A proof will be given in terms of Barsotti-Tate groups using the Serre-Tate theorem. Drinfeld's proof of this theorem will be sketched (see [1]). It will be explained how to make the above action explicit for elliptic curves. In characterictic 2 one can describe the action by the AGM (arithmetic geometric mean) sequence. References :<br/> [1] N.Katz: Serre-Tate local moduli, in 'surfaces algebriques', Springer lecture notes 868, 1981<br/> [2] R.Carls: in prep., http://www.math.leidenuniv.nl/~carls/extract.ps
Prochains exposés
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Séminaire C2 à INRIA Paris
Emmanuel Thomé et Pierrick Gaudry Rachelle Heim Boissier Épiphane Nouetowa Dung Bui Plus d'infos sur https://seminaire-c2.inria.fr/ -
Attacking the Supersingular Isogeny Problem: From the Delfs–Galbraith algorithm to oriented graphs
Orateur : Arthur Herlédan Le Merdy - COSIC, KU Leuven
The threat of quantum computers motivates the introduction of new hard problems for cryptography.One promising candidate is the Isogeny problem: given two elliptic curves, compute a “nice’’ map between them, called an isogeny.In this talk, we study classical attacks on this problem, specialised to supersingular elliptic curves, on which the security of current isogeny-based cryptography relies. In[…]-
Cryptography
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