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Кандидат наук
Подразделение : ALMASTY
Местонахождение : Campus Pierre et Marie Curie
    Sorbonne Université - LIP6
    Boîte courrier 169
    Couloir 24-25, Étage 4, Bureau 413
    4 place Jussieu
    75252 PARIS CEDEX 05
Tel: +33 1 44 27 47 28, Thomas.Espitau (at)
Научны(е)й руководител(и)ь : Antoine JOUX
Со-руководитель : FOUQUE Pierre-Alain

Algorithmic aspects of algebraic lattices

Lattices are mathematical objects generalizing the concrete idea of grid embedded in the plane. They play a fundamental role in the study of various subfields of mathematics and computer science, in particular, algebraic number theory and cryptography. This thesis deals with so-called "algebraic" lattices, that is, constructed above a maximal order of a number field, with a particular emphasis on computational methods. After developing generic techniques enabling the certified manipulation of such objects, we will turn to the development of an effective algorithms for the reduction of lattices over cyclotomic fields, in particular exploiting their natural recursive and symplectic structure. This study is then used for the resolution of a central problem in algorithmic number theory, namely the principal ideal problem, consisting of the finding of a generator a principal ideal in a number field. We eventually look at the implications of these works in public-key cryptography, where we present attacks on a fully homomorphic encryption scheme and on the BLISS digital signature.
Защита диссертаций : 14.01.2020 - 14h - Campus Jussieu, salle Jacques Pitrat (25-26/105)
Члены жюри :
M. Philippe Elbaz-Vincent , Professeur, Université Grenoble-Alpes [rapporteur]
M. Claus Fieker, Professor Dr., Technische Universitat Kaiserslautern [rapporteur]
Mme. Valérie Berthé, Directrice de Recherche, IRIF
M. Pierre-Alain Fouque, Professeur, Université de Rennes
M. Antoine Joux, Tenured Research Faculty , CISPA, Helmholtz Center
Mme. Ariane Mézard, Professeur, IMJ-PRG, Sorbonne Université
M. Phong Nguyen , Directeur de Recherche, INRIA

Публикации 2016-2020

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