Maître de Conférences en Informatique
Université de Versailles – Saint-Quentin
Équipe CRYPTO – Laboratoire LMV
bureau 309 B
45 Avenue des États-Unis
78035 Versailles Cedex, France
tel: +33 1 39 25 40 35
fax: +33 1 39 25 40 57
ORCiD: 0000-0002-9321-0773
github: @defeo
keybase: defeo
Picture of Luca De Feo

Hi, I am Luca. I am maître de conférences (the French equivalent of assistant professor) in the Computer Science department of Université de Versailles.

As part of my research, I work on Algorithmic Number Theory, Computer Algebra and Cryptology. Read more about it in the research section.

Being some kind of nerd, I am also interested in almost everything related to Information Technology. I am fluent in many programming languages, I enjoy learning new ones, and most of all I love mixing them in the context of web programming. Part of my passion for these subjects flows into the courses I teach, and the software I write in my (rare) spare time.

And, like most nerds, I tend to share out loud my thoughts on the things I like. You can read more about science, maths, computer science, web programming, etc. in my blog.

June 04, 2019: How to prove a secret isogeny, talk at CTCrypt 2019. Slides here:

May 23, 2019: SeaSign: Compact isogeny signatures from class group actions, talk at Eurocrypt 2019. Slides here:

March 18, 2019: Isogeny graphs in cryptography, 3 hours lecture at Mathematics of Public Key Cryptography winter school. Slides here:, lots of new material!

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

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.



  • 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.


Verifiable Delay Functions from Supersingular Isogenies and Pairings with Simon Masson and Christophe Petit and Antonio Sanso submitted 2019

Applications of the affine geometry of GF(qn) to root finding with Christophe Petit and Michaël Quisquater In preparation. Best poster award ISSAC 2015

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

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

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

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

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

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

In conference proceedings

Standard Lattices of Compatibly Embedded Finite Fields with Hugues Randriam and Édouard Rousseau ISSAC 2019 10.1145/3326229.3326251

SeaSign: Compact isogeny signatures from class group actions with Steven Galbraith Eurocrypt 2019 10.1007/978-3-030-17659-4_26

Towards practical key exchange from ordinary isogeny graphs with Jean Kieffer and Benjamin Smith AsiaCrypt 2018 10.1007/978-3-030-03332-3_14

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

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

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


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  

Mathematics of Isogeny Based Cryptography Lecture notes, École Mathématique Africaine, Thiès, Sénégal, 2017, 44 pp


Fast Algorithms for Towers of Finite Fields and Isogenies PhD Thesis. Advisors: François Morain, Éric Schost École Polytechnique, December 13, 2010. In English


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

Applications web et sécurité
AWS, M1 Informatique.
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.
Mathématiques pour l’informatique
IN310, L2 Informatique.
Algorithmique pour la cryptographie
IN420, L2 Informatique.
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.

A library for Fast Arithmetic in Artin-Schreier Towers.
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

A DIY Learning Management System based on GitHub Pages.
A Python script for detecting plagiarism.

See also my collection of vulgarization material at

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.