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EYNARD Julien

PhD graduated
Team : PEQUAN
Departure date : 06/15/2015
http://www-almasty.lip6.fr/~eynard
Supervision : Jean-Claude BAJARD
Co-supervision : DIDIER Laurent-Stéphane

RNS arithmetic approach of asymmetric cryptography

This thesis is at the crossroads between cryptography and computer arithmetic. It deals with enhancement of cryptographic primitives with regard to computation acceleration and protection against fault injections through the use of residue number systems (RNS) and their associated arithmetic.
So as to contribute to secure the modular multiplication, which is a core operation for many asymmetric cryptographic primitives, a new modular reduction algorithm supplied with fault detection capability is presented. A formal proof guarantees that faults affecting one or more residues during a modular reduction are well detected. Furthermore, this approach is generalized to an arithmetic dedicated to non-prime finite fields.
Afterwards, RNS are used in lattice-based cryptography area. The aim is to exploit acceleration properties enabled by RNS, as it is widely done for finite field arithmetic. As first result, a new version of Babai's round-off algorithm based on hybrid RNS-MRS representation is presented. Then, a new and specific acceleration technique enables to create a full RNS algorithm computing a close lattice vector.
Defence : 05/28/2015 - 14h - Site Jussieu 25-26/105
Jury members :
Duquesne Sylvain (Université Rennes I, IRMAR) [Rapporteur]
Goubin Louis (Université de Versailles Saint-Quentin-en-Yvelines, PRiSM) [Rapporteur]
Elbaz-Vincent Philippe (Université Joseph Fourier, Institut Fourier)
Fontaine Caroline (CNRS, Lab-STICC/Télécom Bretagne)
Guillermin Nicolas (Ministère de la Défense)
Joux Antoine (Université Pierre et Marie Curie, LIP6)
Bajard Jean-Claude (Université Pierre et Marie Curie, LIP6)
Didier Laurent-Stéphane (Université de Toulon, IMATH)

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