Analyse probabiliste de la réduction des réseaux euclidiens cryptographiques

Mariya Georgieva 1
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : The topics covered in this thesis are the interfaces of cryptography, algorithms and analysis of algorithms. They focus on a particular area, the geometry of numbers, and in particular the reduction beyond Euclidean networks. Given the difficulty of an exact analysis of the LLL algorithm, we proposed a class of simplified models for the execution of the algorithm, the more simple, and already proposed by Madrisch Valley, to more complicated, which corresponds to LLL algorithm itself. We returned on the analysis of the simplest model by adopting the point of view of the chip firing game. We also tried to model in this part of cfg, main entrances that interested us, corresponding cryptographic systems. We were taken to three families of cryptographic networks: said Ajtai networks that give rise to piles "all very full," networks bag-to-back or NTRU networks, which give rise to piles of sand "with a single job "and finally networks Coppersmith, which give rise to piles of sand" with holes ". We then studied under a simplified execution model, but definitely closer to reality. We conducted a detailed analysis of this execution model: total analysis for the case of dimension 2, which corresponds to the 3-dimensional networks in the world, where the analysis of real LLL algorithm is already misunderstood --analyse partial general dimension. Finally, we made experiments to find an experimental validation of the assumptions that lead to simplified models.
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Mariya Georgieva. Analyse probabiliste de la réduction des réseaux euclidiens cryptographiques. Cryptographie et sécurité [cs.CR]. Université de Caen, 2013. Français. ⟨tel-01081679⟩

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