Benjamin Smith

Équipe GRACE, INRIA Saclay–Île-de-France
Laboratoire d'informatique (LIX), École polytechnique

Email: smith@lix... // PGP: public key // Phone: email first // Photo: cheese // "Summer internship?": No.

I am a research scientist (chargé de recherche) at INRIA, a French public research institute for computing and applied maths, and also an adjunct assistant professor (chargé d'enseignement) in the computer science department at the École polytechnique.

My research is in algorithmic arithmetic geometry and number theory, with a view towards applications in asymmetric cryptography. I am particularly interested in

Algorithms for primitive operations in curve-based cryptosystems
Explicit constructions and algorithms for isogenies in higher genus
Effective constructions of real and complex multiplications on arithmetic Jacobians
Applications of algebraic correspondences in computational number theory and cryptology

I studied algorithmic number theory in Sydney with David Kohel. I worked as a postdoc at Royal Holloway with Steven Galbraith. 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

Publications and preprints

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Mestre translations

I have found Jean-François Mestre's work very useful, and also a lot of fun to read.

I am making these translations available (with Mestre's kind permission) for colleagues who have difficulty reading the French originals.

Families of hyperelliptic curves with real multiplication: a translation into English of Jean-François Mestre's Familles de courbes à multiplications réelles (in Arithmetic algebraic geometry (Texel, 1989), Progr. Math. 89 (Birkhäuser Boston, 1991))
Pairs of isogenous Jacobians of hyperelliptic curves of arbitrary genus: a translation into English of Jean-François Mestre's Couples de Jacobiennes isogènes de courbes hyperelliptiques de genre arbitraire (arXiv.org:0902.3470)

"Summer internships"

I do not supervise 2- or 3-month "summer internships". This is due to a combination of French workplace laws, the particularities of the polytechnique site, and my calendar. Also, there are other things that I prefer to do in summer.

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, though normally I will not accept more than one of these per year. You should be enrolled in (at least) a Masters-level program in computer science or mathematics, with a strong mathematical and computing background.