Laboratoire de Mathématiques de Versailles
Université de Versailles-St-Quentin-en-Yvelines
Université Paris-Saclay — CNRS
45 avenue des États-Unis, 78035 VERSAILLES
From September 2020, I am a Math Teacher in French Preparatory Classes in Normandy.
In the meantime, I remain involved in research as a Research Associate in the Crypto team at the Laboratoire de Mathématiques de Versailles (LMV).
My research topic is at the boundary between mathematics and computer science.
Particularly, I am interested in algebraic structures that are suitable for cryptographic purposes.
Class groups of number fields are among the structures I work on.
Computing efficiently their cardinality as well as the structure of such groups are hard problems in practice.
These groups naturally provide applications in cryptology, because they are finite groups.
Actually, an important proportion of current public-key cryptosystems relies on the use of discrete exponentiation in a finite group,
because the inverse operation is considered difficult: this is the so-called discrete logarithm problem.
I am also interested in other connected topics, linked for most of them to public-key cryptography: elliptic or higher genus curves or factorization for instance.
2018 - 2020: High School Math Teacher and Research Associate at LMV
2017 - 2018: Postdoc at LMV - UVSQ
2014 - 2017: PhD student at LIP6 - UPMC
2013 - 2014 : Master's degree in Mathematics for information theory & cryptography at Université de Rennes 1
2012 - 2013 : Agrégation of Mathematics (Rank 92) at Université de Rennes 1
2012 - 2014 : Normalien at Ecole Normale Supérieure de Cachan - Bretagne (ENS Rennes now)
2010 - 2012 : Bachelor's degree and 1st year of Master's degree at Magistère de Mathématiques de Rennes 1
2008 - 2010 : French preparatory classes MPSI & MP at lycée Montesquieu, Le Mans
July 2008 : Scientific Baccalauréat at lycée Marguerite Yourcenar, Le Mans
Principally polarized squares of elliptic curves with field of moduli equal to Q
Alexandre Gélin, Everett W. Howe, and Christophe Ritzenthaler Published in The Open Book Series, volume 2 (2019), pp.257-274.
Presented at ANTS XIII, Madison, 2018
The code that allows us to exhibit the curves using Magma : Squares.tar.gz.
Reducing the complexity for class group computations using small defining polynomials
Alexandre Gélin Under publication.
On the complexity of class group computations for large degree number fields
Alexandre Gélin Under publication.
Class group computations in number fields and applications to cryptology
Alexandre Gélin PhD thesis, defended in September 2017 at UPMC.
Parametrizations for families of ECM-friendly curves
Alexandre Gélin, Thorsten Kleinjung, and Arjen K. Lenstra Published in Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, pp.165-171.
Presented at ISSAC, Kaiserslautern, 2017
Loop-abort faults on supersingular isogeny cryptosystems
Alexandre Gélin and Benjamin Wesolowski Published in Post-Quantum Cryptography - 8th International Workshop, PQCrypto 2017, Proceedings, pp.93-106.
Presented at PQCrypto, Utrecht, 2017
Computing generator in cyclotomic integer rings
Jean-François Biasse, Thomas Espitau, Pierre-Alain Fouque, Alexandre Gélin, and Paul Kirchner Published in Advances in Cryptology - EUROCRYPT 2017, Proceedings Part I, pp.60-88.
Presented at EUROCRYPT, Paris, 2017
A prototype of the attack using Pari-GP: GenRec.tar.gz.
Reducing number field defining polynomials: an application to class group computations
Alexandre Gélin and Antoine Joux Published in LMS Journal of Computation and Mathematics, volume 19, issue A, pp.315-331.
Presented at ANTS XII, Kaiserslautern, 2016
A prototype of the algorithm using Magma: PolRed.m and its documentation.
ANTS XIV Summer School in Auckland - June 25th, 2020 Class groups are essential in our live
ANTS XIII in Madison - July 16th, 2018 Principally polarized squares of elliptic curves with field of moduli equal to Q
Cryptography and Algorithmic Number Theory in Caen - June 21st, 2018 Parametrizations for Families of ECM-Friendly Curves
LMV Days in Versailles - May 15th, 2018 Sur l'utilisation des groupes de classes en cryptologie
Cryptography Seminar in Rennes - December 8th, 2017 Calcul du groupe de classes et applications à la cryptologie
Crypto Seminar in Versailles - October 27th, 2017 Calcul du groupe de classes et applications à la cryptologie
PhD Defense in Paris - September 22nd, 2017 Class Group Computations in Number Fields and Applications to Cryptology
ISSAC in Kaiserslautern - July 28th, 2017 Parametrizations for Families of ECM-Friendly Curves
Journées Arithmétiques in Caen - July 3rd, 2017 Class Group Computations in Number Fields and Applications to Cryptology
PQCrypto in Utrecht - June 26th, 2017 Loop-Abort Faults on Supersingular Isogeny Cryptosystems
Cryptology and Security Seminar in Caen - June 14th, 2017 Paramétrisations de familles de courbes adaptées à ECM
EuroCrypt in Paris - May 1st, 2017 Computing Generator in Cyclotomic Integer Rings
Journées Codage et Cryptographie in La Bresse - April 25th, 2017 Calcul du groupe de classes et applications à la cryptologie
Seminar Butte aux Cailles in Paris - November 9th, 2016 Un algorithme de réduction du polynôme de définition d'un corps de nombres et applications au calcul du groupe de classes
ANTS XII in Kaiserslautern - September 2nd, 2016 Reducing Number Field Defining Polynomials: An Application to Class Group Computations
LACAL Team Seminar in Lausanne - April 18th, 2016 Class Group Computations in Number Fields
Mid-Term Defense in Paris - February 17th, 2016 Class Group Computations in Number Fields
Worshop VACHES (Abelian varieties, hyperelliptic and Shimura curves) in Paris - May 28th, 2015 Jacobiennes isomorphes à un produit de courbes elliptiques
Workshop VACHES (Abelian varieties, hyperelliptic and Shimura curves) in Paris - May 28th, 2015 Espaces de modules des courbes de genre 2
Spring 2018: Lecturer in Analyse d'algorithmes et programmation (M1 MINT) at UVSQ
Spring 2018: Supervisor of student projects (M1 INFO & M1 MINT) at UVSQ
Fall 2017: Teaching assistant in Cryptologie (M1 INFO) at UVSQ
2017 - 2018 : Oral examinator for preparatory classes at ENC Bessières, Paris
Spring 2017: Teaching assistant in Introduction à la cryptologie (3i024) at UPMC
Spring 2016: Teaching assistant in Introduction à la cryptologie (3i024) at UPMC
Spring 2016: Teaching assistant in Environnement de développement - Linux (2i012) at UPMC
Fall 2015: Teaching assistant in Structures discrètes (2i005) at UPMC
Spring 2015: Teaching assistant in Introduction au langage C (1i002) at UPMC
Fall 2014: Teaching assistant in Structures discrètes (2i005) at UPMC
2013 - 2014 : Oral examinator for preparatory classes at lycée Joliot Curie, Rennes
2013 - 2014 : Teaching assistant in geometry for second year students at INSA Rennes (engineer school)