About me

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).

Research

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.

Résumé

• 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

Publications

• 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
  Links: pdf, arXiv, MSP, slides.
  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.
  Links: pdf, arXiv.
  
• On the complexity of class group computations for large degree number fields
  Alexandre Gélin
  Under publication.
  Links: pdf, arXiv.
  
• Class group computations in number fields and applications to cryptology
  Alexandre Gélin
  PhD thesis, defended in September 2017 at UPMC.
  Link: pdf.
• 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
  Links: pdf, ePrint, ACM, slides.
  
• 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
  Links: pdf, ePrint, Springer, slides.
  
• 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
  Links: pdf, ePrint, Springer, slides.
  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
  Links: pdf, ePrint, LMS, slides.
  A prototype of the algorithm using Magma: PolRed.m and its documentation.

Talks

• 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

Teaching

• 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)