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: https://defeo.lu/docet.
May 23, 2019: SeaSign: Compact isogeny signatures from class group actions, talk at Eurocrypt 2019. Slides here: https://defeo.lu/docet.
March 18, 2019: Isogeny graphs in cryptography, 3 hours lecture at Mathematics of Public Key Cryptography winter school. Slides here: https://defeo.lu/docet, lots of new material!
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.
Verifiable Delay Functions from Supersingular Isogenies and Pairings with Simon Masson and Christophe Petit and Antonio Sanso submitted 2019 https://eprint.iacr.org/2019/166
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/
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
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
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
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
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
I teach the following courses in UVSQ. Follow the links for more information and course material.
I collect here my main software projects. You can find more in my GitHub repositories.
The following software are based upon academic research.
See also my collection of vulgarization material at defeo.lu/docet.