Description
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was previously known for ideal lattices (those of rank 1), it is the first such result in higher rank. I will give an overview of the reduction and discuss some of the challenges. The work involves deep number theoretic techniques and results, such as the equidistribution of Hecke points, which we study using the spectral theory of automorphic forms. This talk should be accessible to both cryptographers as well as number theorists.
Prochains exposés
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Encryption homomorphe sans bruit à l'aide de groupes
Orateur : Pierre Guillot - Ravel Technologies (dispo Université de Strasbourg, IRMA)
Je vais rappeler les travaux de Nuida et Ostrovski sur l'utilisation des groupes pour l'élaboration de schémas cryptographiques homomorphes. Je vais présenter nos travaux qui fournissent des encodages à la fois plus efficaces et plus généraux, et qui déterminent exactement quels groupes peuvent être utilisés. Puis je vais discuter GRAFHEN, un protocole qui utilise ces idées. Je dirai juste[…]-
Cryptography
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