Benjamin Smith

We jam econo. // 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; I work in the GRACE project-team at LIX, the computing laboratory of École polytechnique. I am also an adjunct professor (professeur chargé de cours) in the computer science department at École polytechnique.

I do research in algorithmic arithmetic geometry and number theory, and their applications in asymmetric cryptography. I am particularly interested in

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.

I am currently running the CACHACA Action Exploratoire at Campus Cyber and am leading Inria's participation in the HYPERFORM consortium. I am also on the editorial board for Communications in Cryptography, a new diamond-access journal published by the IACR.

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

The list above is automatically extracted from the INRIA HAL database.

Alternate (though mostly identical) versions of some preprints are also hosted on the IACR ePrint server.

Cryptographic Implementations

Wave: Code-based post-quantum signatures

Wave is a post-quantum signature scheme based on hard problems in coding theory. Gustavo Banegas, Kévin Carrier, André Chailloux, Alain Couvreur, Thomas Debris-Alazard, Philippe Gaborit, Pierre Karpman, Johanna Loyer, Ruben Niederhagen, Nicolas Sendrier, and Jean-Pierre Tillich and I have submitted Wave to the fourth-round Signature On-Ramp of the NIST Post-Quantum Cryptography Standardization Project. The project website is at and the source code for the reference implementation is available at

CTIDH: Faster constant-time CSIDH

Gustavo Banegas, Daniel J. Bernstein, Fabio Campos, Tung Chou, Tanja Lange, Michael Meyer, Jana Sotáková, and I have a developed a new algorithm and keyspace for fast constant-time CSIDH, an algorithm for postquantum non-interactive key exchange. The code and details are on a dedicated website:

Isogenies in square-root time

Daniel J. Bernstein, Luca De Feo, Antonin Leroux, and I have a developed new algorithms for computing prime-degree isogenies in square-root time (as opposed to linear time, which is how we've been doing things since the seventies). The details are on a dedicated website:

Compact crypto implementations for microcontrollers

Joost Renes, Peter Schwabe, Lejla Batina, and I developed μKummer: an efficient, open implementation of Diffie–Hellman key exchange and Schnorr signatures for 8- and 32-bit microcontrollers (AVR ATmega and Cortex M0), based on genus 2 curves. The project is described in our CHES 2016 paper, and the source code is publicly available from Joost's site.

μKummer is more or less superseded by qDSA, a Kummer-only signature scheme (similar to EdDSA) developed for microcontrollers that Joost and I designed to use much less stack space. The details are in the preprint of our ASIACRYPT 2017 paper, and the reference implementation is available from Joost's site.

Compact Diffie–Hellman implementation

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.

Isogeny data

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)".

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.

"Summer internships"

I get a lot of spam about 2- or 3-month "summer internships". If you put "summer internship" in the subject line of an email, then I will assume it is spam and delete your email without reading it. And if it looks like spam, then I'll just delete it anyway.

Preparing worthwhile internships takes time, especially in France, and especially at École polytechnique. Once a subject is agreed on, local security rules generally add two to three months' worth of paperwork, with no guarantee of approval—especially if you are not a French citizen (I don't make the rules).

So: if you're really interested in working here, then you need to have a strong background in mathematics (especially algebra) and computer science, and you also need get in touch way in advance.