December 12, 2018: Habilitation defense! I am defending my habilitation thesis (HDR) today. Slides, manuscript and live stream here: https://defeo.lu/hdr.

I research and develop algorithms for finite fields and algebraic curves, usually with applications to cryptology in mind. I tend to put the stress on efficient algorithms, both in the theoretical analysis and the software implementation.

I am interested in computer algebra systems and expressive programming languages for doing mathematics. I like to use Sage in my investigations and I have distributed some software using it. I also am a member of the OpenDreamKit community, seeking to enhance the ecosystem of computational mathematics tools.

Students

PhD

• Édouard Rousseau: Arithmétique efficace pour la cryptographie et la cryptanalyse.
• Robin Larrieu: Fast Finite Field Arithmetic.
• Cyril Hugounenq: Réalisation d’algorithmes efficaces pour l’arithmétique des corps finis et des variétés abéliennes, avec applications à la cryptologie.

Masters’ theses

• Mattia Veroni: Comptage de points de courbes elliptiques en moyenne caractéristique.
• Jean Kieffer: Protocoles d’échange de clefs à base d’isogénies.
• Sébastien Besnier: Participation au développement d’un framework pour les courbes elliptiques en Sage.
• Ludovic Brieulle: Calcul d’isomorphismes de corps finis.

Preprints

SeaSign: Compact isogeny signatures from class group actions with Steven Galbraith preprint, 2018 https://eprint.iacr.org/2018/824

Applications of the affine geometry of GF(qⁿ) to root finding with Christophe Petit and Michaël Quisquater In preparation. Best poster award ISSAC 2015 https://github.com/defeo/root_finding/

Journal articles

Computing isomorphisms and embeddings of finite fields with Ludovic Brieulle, Javad Doliskani, Jean-Pierre Flori and Éric Schost to appear in Mathematics of Computation, 2018 10.1090/mcom/3363
https://github.com/defeo/ffisom
https://arxiv.org/abs/1705.01221

Explicit isogenies in quadratic time in any characteristic with Cyril Hugounenq, Jérôme Plût and Éric Schost LMS Journal of Computation and Mathematics, 2016, 19 (A), pp. 267-282 10.1112/S146115701600036X
https://arxiv.org/abs/1603.00711

Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies with David Jao and Jérôme Plût Journal of Mathematical Cryptology, 2014, 8 (3), pp. 209-247 10.1515/jmc-2012-0015
http://eprint.iacr.org/2011/506

Fast Arithmetics in Artin-Schreier Towers over Finite Fields with Éric Schost Journal of Symbolic Computation, 2012, 47 (7), pp. 771-792 10.1016/j.jsc.2011.12.008
https://arxiv.org/abs/1002.2594

Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic Journal of Number Theory, 2011, 131 (5), pp. 873-893 10.1016/j.jnt.2010.07.003
https://www.arxiv.org/abs/1002.2597

transalpyne: a language for automatic transposition with Éric Schost ACM SIGSAM Bulletin, 2010, 44 (1/2), pp. 59-71 10.1145/1838599.1838624
hal-00505809

In conference proceedings

Towards practical key exchange from ordinary isogeny graphs with Jean Kieffer and Benjamin Smith AsiaCrypt 2018 https://eprint.iacr.org/2018/485

Knowledge-Based Interoperability for Mathematical Software Systems with Michael Kohlhase, Dennis Müller, Markus Pfeiffer, Florian Rabe, Nicolas M. Thiéry, Victor Vasilyev and Tom Wiesing Mathematical Aspects of Computer and Information Sciences, Springer, 2017, pp. 195-210 10.1007/978-3-319-72453-9_14  

Fast arithmetic for the algebraic closure of finite fields with Éric Schost and Javad Doliskani ISSAC ‘14, July 2014, Kobe, Japan. ACM, 2014, pp. 122-129 http://defeo.lu/ff_compositum
10.1145/2608628.2608672

Fast algorithms for ℓ-adic towers over finite fields with Éric Schost and Javad Doliskani ISSAC ‘13, June 2013, Boston (MA), USA. ACM, 2013, pp. 165-172 http://defeo.lu/towers
10.1145/2465506.2465956

Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies with David Jao Post-Quantum Cryptography, Nov 2011, Taipei, Taiwan. Springer, 7071, pp. 19-34 10.1007/978-3-642-25405-5_2

Fast Arithmetics in Artin-Schreier Towers over Finite Fields with Éric Schost ISSAC ‘09, July 2009, Seoul, Korea. ACM, 2009, pp. 127-134 10.1145/1576702.1576722

Other

Supersingular Isogeny Key Encapsulation with R. Azarderakhsh, M. Campagna, C. Costello, B. Hess, A. Jalali, D. Jao, B. Koziel, B. LaMacchia, P. Longa, M. Naehrig, J. Renes, V. Soukharev, D. Urbanik Encryption/Key Encapsulation scheme, candidate to the NIST Post-Quantum Cryptography competion, 2017 http://sike.org  

Mathematics of Isogeny Based Cryptography Lecture notes, École Mathématique Africaine, Thiès, Sénégal, 2017, 44 pp https://github.com/defeo/ema2017/
https://arxiv.org/abs/1711.04062

Thesis

Fast Algorithms for Towers of Finite Fields and Isogenies PhD Thesis. Advisors: François Morain, Éric Schost École Polytechnique, December 13, 2010. In English https://github.com/defeo/PhD-Thesis
HAL/tel-00547034

Courses

I teach the following courses in UVSQ. Follow the links for more information and course material.

Mathématiques pour l’informatique

IN310, L2 Informatique.

Applications web et sécurité

AWS, M1 Informatique.

AWS, ISTY, IATIC4.

Analyse d’algorithmes, programmation

MYMAI201, M1 Mathématiques.

Algorithmique et programmation C

MSIM914, M2 Algèbre appliquée.

Algèbre Commutative et effective (TDs)

MSMA910, M2 Algèbre appliquée.

Old courses

Applications de l’informatique

IN202, L1 Informatique.

Algorithmique pour la cryptographie

IN420, L2 Informatique.

Mathématiques

ESB1MATH, IATIC3 (1st year engineering school).

Other resources

IT Katas

A website offering coding challenges for training in Information Theory, Coding and Cryptology.

I collect here my main software projects. You can find more in my GitHub repositories.

Research projects

The following software are based upon academic research.

FAAST

A library for Fast Arithmetic in Artin-Schreier Towers.

Transalpyne

A Python implementation of the Transposable Algebraic Language.

Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies

A sage script implementing the cryptosystem described in Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies.

Other projects

eLeMents

A DIY Learning Management System based on GitHub Pages.

Pylagiarist

A Python script for detecting plagiarism.

See also my collection of vulgarization material at defeo.lu/docet.

Isogeny graphs

Isogeny graphs in cryptography. YACC, Centre Igesa, Porquerolles, France, September 2012.

Duality, transposition principle and automatic transposition of code

On the transposition of computer programs. PLMMS, CNAM, Paris, France, July 2010.

Computing explicit isogenies

Isogeny computation in small characteristics. ECC, University of Calgary, Calgary, Canada, August 2009.

Fast Arithmetic for Artin-Schreier towers

Fast arithmetic in Artin-Schreier towers over finite fields. RAIM, ENS, Lyon, France, October 2009.

Fast arithmetic in Artin-Schreier towers over finite fields. ISSAC, KIAS, Seoul, Korea, July 2009.

Other subjects

Fast algorithms: from type theory to number theory. Séminaire Algorithmes, INRIA Rocquencourt, France, October 2010.

Elliptic Curve Cryptography. Seminario d’Informatica, Università di Pisa, Italy, June 2007.