logo EDITE Alexandre GELIN
Identité
Alexandre GELIN
État académique
Soutenance prévue le 2017-09-22
Sujet: Calcul d'indice et nombre de classes d'Arakelov, calcul effectif et applications cryptographiques
Direction de thèse:
Laboratoire:
Voisinage
Ellipse bleue: doctorant, ellipse jaune: docteur, rectangle vert: permanent, rectangle jaune: HDR. Trait vert: encadrant de thèse, trait bleu: directeur de thèse, pointillé: jury d'évaluation à mi-parcours ou jury de thèse.
Productions scientifiques
oai:hal.archives-ouvertes.fr:hal-01362144
Reducing number field defining polynomials: an application to class group computations
International audience
In this paper we describe how to compute smallest monic polynomials that define a given number field K. We make use of the one-to-one correspondence between monic defining polynomials of K and algebraic integers that generate K. Thus, a smallest polynomial corresponds to a vector in the lattice of integers of K and this vector is short in some sense. The main idea is to consider weighted coordinates for the vectors of the lattice of integers of K. This allows us to find the desired polynomial by enumerating short vectors in these weighted lattices. In the context of the subexponential algorithm of Biasse and Fieker for computing class groups, this algorithm can be used as a precomputation step that speeds up the rest of the computation. It also widens the applicability of their faster conditional method, which requires a defining polynomial of small height, to a much larger set of number field descriptions.
Algorithmic Number Theory Symposium XII https://hal.archives-ouvertes.fr/hal-01362144 Algorithmic Number Theory Symposium XII, Aug 2016, Kaiserslautern, Germany. 19 (A), pp.315--331 2016, LMS Journal of Computation and Mathematics. <10.1112/S1461157016000255>ARRAY(0x7f03faaa6548) 2016-08-29
oai:hal.archives-ouvertes.fr:hal-01518438
ARRAY(0x7f03ff85a840)
International audience
The Principal Ideal Problem (resp. Short Principal Ideal Problem), shorten as PIP (resp. SPIP), consists in finding a generator (resp. short generator) of a principal ideal in the ring of integers of a number field. Several lattice-based cryptosystems rely on the presumed hardness of these two problems. In practice, most of them do not use an arbitrary number field but a power-of-two cyclotomic field. The Smart and Vercauteren fully homomorphic encryption scheme and the multilinear map of Garg, Gentry, and Halevi epitomize this common restriction. Recently, Cramer, Ducas, Peikert, and Regev showed that solving the SPIP in such cyclotomic rings boiled down to solving the PIP. In this paper, we present a heuristic algorithm that solves the PIP in prime-power cyclotomic fields in subexponential time L(1/2), where ∆ K denotes the discriminant of the number field. This is achieved by descending to its totally real subfield. The implementation of our algorithm allows to recover in practice the secret key of the Smart and Vercauteren scheme, for the smallest proposed parameters (in dimension 256).
Lecture Notes in Computer Science 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2017) https://hal.archives-ouvertes.fr/hal-01518438 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2017), Apr 2017, Paris, France. Lecture Notes in Computer Science, 10210, pp.60--88, 2017, Advances in Cryptology – EUROCRYPT 2017 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Paris, France, April 30 – May 4, 2017, Proceedings, Part I. <10.1007/978-3-319-56620-7_3>ARRAY(0x7f03ff860090) 2017-04-30
oai:hal.archives-ouvertes.fr:hal-01568343
Parametrizations for Families of ECM-Friendly Curves
International audience
We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factoriza-tion method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.
Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2017, Kaiserslautern, Germany, July 25-28, 2017 ISSAC 2017 The 42nd International Symposium on Symbolic and Algebraic Computation https://hal.archives-ouvertes.fr/hal-01568343 ISSAC 2017 The 42nd International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2017, Kaiserslautern, Germany, July 25-28, 2017, pp.165--171, 2017, <10.1145/3087604.3087606>ARRAY(0x7f03ff860c10) 2017-07-25
oai:hal.archives-ouvertes.fr:hal-01568331
Loop-Abort Faults on Supersingular Isogeny Cryptosystems
International audience
Cryptographic schemes based on supersingular isogenies have become an active area of research in the field of post-quantum cryptography. We investigate the resistance of these cryptosystems to fault injection attacks. It appears that the iterative structure of the secret isogeny computation renders these schemes vulnerable to loop-abort attacks. Loop-abort faults allow to perform a full key recovery, bypassing all the previously introduced validation methods. Therefore implementing additional countermeasures seems unavoidable for applications where physical attacks are relevant.
Post-Quantum Cryptography - 8th International Workshop, PQCrypto 2017, Utrecht, The Netherlands, June 26-28, 2017, Proceedings 8th International Conference on Post-Quantum Cryptography (PQCrypto 2017) https://hal.archives-ouvertes.fr/hal-01568331 8th International Conference on Post-Quantum Cryptography (PQCrypto 2017), Jun 2017, Utrecht, Netherlands. Post-Quantum Cryptography - 8th International Workshop, PQCrypto 2017, Utrecht, The Netherlands, June 26-28, 2017, Proceedings, 10346, pp.93-106, 2017, Lecture Notes in Computer Science. <10.1007/978-3-319-59879-6_6>ARRAY(0x7f03fee6ea68) 2017-06-26
Soutenance
Thèse: Calcul de groupes de classes d'un corps de nombres et applications à la cryptologie
Soutenance: 2017-09-22
Rapporteurs: Claus FIEKER    Andreas ENGE