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I am a research scientist (chargé de recherche)
a French public research institute for computing and applied maths,
an adjunct assistant professor (chargé d'enseignement)
in the computer science department at the
My research is in algorithmic arithmetic
and number theory,
with a view towards applications in asymmetric cryptography.
I am particularly interested in
- Primitive operations in curve-based cryptosystems
- Efficient algorithms for elliptic and hyperelliptic curves
- Explicit constructions and algorithms for isogenies in higher genus
- Effective constructions of real and complex multiplications on
- Applications of algebraic correspondences in computational
number theory and cryptology
I studied algorithmic number theory in
I worked as a postdoc at
I've been at LIX, and with INRIA, since November 2007.
Our brain has two halves: one is responsible for the multiplication of polynomials and languages, and the other half is responsible for orientation of figures in space and all the things important in real life. Mathematics is geometry when you have to use both halves.
—V. I. Arnol'd
When a theorem, say the law of quadratic reciprocity, has been established one is apt to forget that it started life as a conjecture based on numerical evidence. Number theory is an experimental science.
—J. W. S. Cassels
The list above is automatically extracted from the INRIA HAL database
Data files for the article Families of explicitly isogenous Jacobians of variable-separated curves can be found here.
The polynomials in these files also appear in
Families of Explicit Isogenies of Hyperelliptic Jacobians, and are based on the exceptional pairs of polynomials in Pierrette Cassou-Noguès and Jean-Marc Couveignes' "Factorisations explicites de g(y)-h(z)".
Craig Costello, Huseyin Hisil, and I developed a fast, open, compact Diffie–Hellman implementation targeting the 128-bit security level on 64-bit Intel platforms. The project is detailed in our Eurocrypt 2014 paper, and the source code is publicly available from Huseyin's site. Craig has also made the Magma code from this project available.
I am making these translations available (with Mestre's kind permission)
for colleagues who have difficulty reading the French originals.
I do not supervise 2- or 3-month "summer internships"
(longer internships at other times are a different matter—see below).
This is due to a combination of French workplace laws,
French security laws,
the particularities of the polytechnique site,
and my personal calendar.
If you contact me asking for an internship of this kind,
then normally I will not reply to your email.
If you put "summer internship" in the subject line,
then typically I will delete your email without reading it.
Internships of at least four months' duration are possible. You should be enrolled in (at least) a Masters-level program in computer science or pure mathematics, with a strong general mathematical and computing background. Be warned: if you are not a French citizen, then we need at least three months advance notice (seriously) to get the necessary paperwork done.