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Seminar
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Cryptography
Explicit higher dimensional 3-adic canonical lifting
Speaker : Robert Carls - Sydney University
Our talk is about joint work with D. Kohel and D. Lubicz. We prove equations having as solutions the theta null points of canonical lifts of ordinary abelian varieties over finite fields of characteristic 3. We describe an algorithm for 3-adic canonical lifting of ordinary abelian surfaces based on our formulas. The algorithm has been implemented in MAGMA. Examples of canonically lifted theta null[…] -
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Seminar
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Cryptography
The arithmetic of elliptic divisibility sequences
Speaker : Graham Everest - Norwich University
A very deep problem with the Mersenne and Fibonacci sequences asks if there are infinitely many prime terms. Bang and Carmichael have studied the simpler problem which asks when the terms have primitive divisors. In my seminar I study the analogous questions for elliptic divisibility sequences. -
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Seminar
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Cryptography
Sur le rang de tordues quadratiques de courbes elliptiques sur
Speaker : Emmanuel Kowalski - Université Bordeaux I
La distribution du rang de familles de courbes elliptiques sur un corps de fonction sur un corps fini est théoriquement mieux comprise que dans le cas d'un corps de nombre. En particulier, dans le cas de familles de tordues quadratiques d'une courbe fixée, il est possible de montrer que le nombre de tordues dont le rang est plus grand que ce qu'impose l'équation fonctionnelle est trés petit. Les[…] -
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Seminar
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Cryptography
Interpolation polynomiale multivariée, codes et cryptographie (travail en collaboration avec O. Ruatta)
Speaker : Philippe Gaborit - Université de Limoges
Dans cet exposé nous nous intéressons à l'interpolation polynomiale multivariée et à ses applications. Nous présenterons tout d'abord des applications connues comme le décodage en liste des codes de Reed-Solomon (pour lequel Madhu Sudan a recu le prix Nevanlinna), mais aussi des applications nouvelles comme le décodage en liste des effacements des codes de Reed-Muller ou encore l'application au[…] -
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Seminar
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Cryptography
Cryptography in the Bounded Quantum-Storage Model
Speaker : Serge Fehr - CWI Amsterdam
Most of todays cryptography relies on the assumption that a potential attacker cannot solve some computational problem (e.g. factor a large integer). It has been shown in the early 80's that with the use of quantum-mechanical effects, certain cryptographic tasks can be done unconditionally, i.e., secure against computationally unbounded attackers: Quantum-cryptography, and with it the hope that (m[…] -
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Seminar
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Cryptography
Blackbox Secret Sharing from Primitive Sets in Algebraic Number Fields
Speaker : Rolnald Cramer - CWI, Amsterdam & Mathematical Insitute, Leiden University
A {\em black-box} secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group operations and to random group elements. In particular, there is no dependence on e.g.\ the structure of the group or its order. The expansion factor of a BBSSS is the length of a vector of shares (the number of[…] -