Hi, I am Luca. I am maître de conférences (the French equivalent of assistant professor) in the Computer Science department of Université de Versailles.
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.
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.
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
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
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
Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic
Journal of Number Theory, 2011, 131 (5), pp. 873-893
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
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
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
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.
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.