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689 results
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Seminar
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Cryptography
Computing Igusa class polynomials
Speaker : Marco Streng - Leiden University
Igusa class polynomials are the genus-2 analogue of the classical Hilbert class polynomials. We explain these notions and discuss the differences between the classical (elliptic) case and the genus-2 case, mostly from a computational perspective. One of the main applications of Igusa class polynomials is the construction of genus-2 curves that are suitable for cryptography. -
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Seminar
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Cryptography
Couplages et volcans d'isogenies.
Speaker : Sorina Ionica - Université de Versailles Saint-Quentin-en-Yvelines
Les volcans d'isogénies sont des graphes dont les noeuds sont des courbes elliptiques et les arêtes sont des l-isogénies entre les courbes. En 1996, Kohel propose l'utilisation du parcours en profondeur de ces graphes dans un algorithme qui calcule l'anneau d'endomorphismes d'une courbe elliptique. Afin d'améliorer l'algorithme de comptage de points d'une courbe elliptique, Fouquet et Morain (2001[…] -
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Seminar
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Cryptography
Anneaux d'endomorphismes de courbes elliptiques en cryptographie.
Speaker : Gaetan Bisson - LORIA
En cryptographie asymétrique, les courbes elliptiques fournissent des alternatives très compétitives aux systèmes à base de corps finis, notamment RSA. Depuis, l'introduction récente des couplages dans les protocoles, elles ne sont plus seulement compétitives mais novatrices dans la mesure où elles offrent maintenant des fonctionnalités cryptographiques uniques. La cryptographie à base de[…] -
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Seminar
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Cryptography
(Yet Another) Analysis of the Linux Random Number Generator
Speaker : Andrea Roeck - INRIA Rocquencourt
The Linux random number generator is part of the kernel since 1994. It collects entropy from user input, interrupts and disk movements and claims to output high quality random numbers. There are two different versions: /dev/random which blocks if the internal entropy count goes to zero and /dev/urandom which is faster since it produces as many bits as the user wants to. The only official[…] -
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Seminar
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Cryptography
RSA problems with Lattice Reduction
Speaker : Alexander May - Technische Universität Darmstadt
This survey addresses the problems of factoring and inverting the RSA function. We define practically relevant relaxed instances of these problems that can be solved in polynomial time. These problem instances are modelled by polynomial equations with small roots. In order to recover the roots, we make use of a method due to Coppersmith which is in turn based on the famous LLL lattice reduction.[…] -
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Seminar
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Cryptography
Standard models for finite fields
Speaker : Bart de Smit - University of Leiden
We give a deterministic polynomial time algorithm that on input two finite fields of the same cardinality produces an isomorphism between the two. Moreover, if for three finite fields of the same cardinality one applies the algorithm to the three pairs of fields then one obtains a commutative triangle. The algorithm depends on the definition of F_q as an actual field rather than a field up to[…] -