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Séminaire
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Cryptographie
Serre-Tate theory and converging AGM-sequences
Orateur : Robert Carls - University of Leiden
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 […] -
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Séminaire
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Cryptographie
Application de la déscente de Weil en cryptographie
Orateur : Pierrick Gaudry - Lix Ecole Polytechnique
Nous commencerons par rappeler les méthodes algorithmiques pour manipuler les courbes hyperelliptiques, et en particulier l'attaque du problème du logarithme discret par des méthodes de calcul d'index. Nous présenterons ensuite la méthode de la restriction de Weil, dont Frey fut le premier a soupçonner les conséquences cryptographiques. En traçant une courbe hyperelliptique sur la restriction de[…] -
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Séminaire
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Cryptographie
Monsky-Washnitzer Cohomology and Computing Zeta Functions
Orateur : Kiran Kedlaya - Berkeley
Monsky-Washnitzer cohomology is a p-adic cohomology theory for algebraic varieties over finite fields, based on algebraic de Rham cohomology. Unlike the l-adic (etale) cohomology, it is well-suited for explicit computations, particularly over fields of small characteristic. We describe how to use Monsky-Washnitzer to construct efficient algorithms for computing zeta functions of varieties over[…] -
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Séminaire
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Cryptographie
Extensions of Kedlaya's algorithm
Orateur : Frederik Vercauteren - Bristol University
Kedlaya described an algorithm for computing the zeta function of a hyperelliptic curve in characteristic p > 2 using the theory of Monsky-Washnitzer cohomology. Joint work with Jan Denef has resulted in 2 extensions of Kedlaya's original algorithm: the first extension can be used to compute the zeta function of a hyperelliptic curve in characteristic 2 and the second leads to a rather general[…] -
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Séminaire
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Cryptographie
Research on Cryptographic Algorithms: beyond triple-DES, AES and RSA
Orateur : Bart Preneel - University of Leuven
In this talk we discuss the state of the art and progress in cryptographic algorithms such as encryption algorithms and digital signature techniques. We present at a high level the challenges to the designers (and users) of cryptographic algorithms and we discuss the major components of the solution, that is, research, standardization, and open evaluation. We also discuss the status of the NESSIE[…] -
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Séminaire
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Cryptographie
Computing the order of the group of rational points on the Jacobian of a hyperelliptic curve in characteristic 2
Orateur : Alan Lauder - Oxford University
I will describe an algorithm for computing the zeta function of an arbitrary hyperelliptic curve in characteristic 2. This is a generalisation of an earlier method of myself and Wan, which tackled a restricted class of curves. The algorithm reduces the problem to that of computing the L-function of an additive character sum over an open subset of the projective line. This latter task can be[…] -