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Seminar
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Cryptography
Structure galoisienne de l'anneau d'entiers d'une extension d'Artin-Schreier
Speaker : Lara Thomas - EPFL
Soit L/K une extension de corps locaux de degré [L:K]=car K=p>0. Soit O_L l'anneau des entiers de L. Lorsque L/K est totalement ramifiée, on étudie la structure de O_L comme module sur l'ordre A associé à l'extension L/K. A l'aide d'arguments essentiellement combinatoires nous donnerons un critère purement algébrique pour que O_L soit libre sur A : ce résultat renforce des travaux récents de Aiba[…] -
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Seminar
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Cryptography
Extraction d'entropie et courbes elliptiques
Speaker : Nicolas Gurel - LIX
Lors d'un protocole de mise en accord de clé (comme Diffie-Hellman) basé sur un groupe générique G, les protagonistes aboutissent à un élément commun K_{AB} de G qui est indistinguable d'un autre élément de G mais pas d'une suite de bits aléatoire de même taille. Nous présenterons deux nouvelles méthodes pour extraire des bits de K_{AB} lorsque G est une courbe elliptique définie sur une extension[…] -
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Seminar
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Cryptography
Protecting security protocols against guessing attacks: towards
Speaker : Mathieu Baudet - ENS Cachan
Designing secure protocols based on passwords is a difficult task. Indeed, passwords, and more generally low-entropy secrets, are potentially vulnerable to guessing attacks, that is, exhaustive, "brute force" searches. Preventing guessing attacks typically requires a protocol to conceal any partial information on the password (e.g. its checksum) which could help the attacker confirm his guess[…] -
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Seminar
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Cryptography
On the Subexponentiality of the Elliptic Curve Discrete Logarithm Problem over Extension Fields
Speaker : Clauss Diem - Universität Essen
The purpose of the talk is to present the following heuristic result.<br/> Let a, b in R with 0 < a < b. Then discrete logarithms in E(F_q^n), where q is a prime power, a log_2(q) \leq n \leq b \log_2(q)$ and E/F_q^n is any elliptic curve over F_q^n, can be solved in probabilistic subexponential time L[3/4].<br/> The algorithm is a variant of a recent index calculus algorithm by Gaudry. The main[…] -
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Seminar
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Cryptography
Constructions in public-key cryptography over matrix groups
Speaker : Ilia Ponomarenko - Université de Saint Petersbourg
A new two-parties key agreement protocol based on identities in groups is proposed. For abelian groups this protocol is, in fact, the Diffie-Hellman one. We also discuss a general scheme producing matrix groups for which our protocol can have a secure realization. -
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Seminar
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Cryptography
Constructing elliptic curves by p-adic methods
Speaker : Peter Stevenhagen - University of Leiden
We will discuss a p-adic method to construct an elliptic curve over a finite field such that the group of rational points over the base field has some prescribed order N. The method uses ideas of Couveignes-Henocq, and is being developed and improved by my PhD student Reinier Broker. -