Gaetan Bisson

Previously, I was a research intern at Microsoft (Redmond, United States), a doctoral candidate at LORIA (Nancy, France) and TU/e (Eindhoven, Netherlands), a research student at Tokyo Tech (Tokyo, Japan), and a student at ENS (Paris, France); see my curriculum vitae.

Research

My research interests are mathematical aspects of cryptography, in particular those related to computational number theory. Lately, my work has focused on curve-based and pairing-based cryptography.

Recent work:

• On polarised class groups of orders in quartic CM-fields, with Marco Streng, preprint;
• Computing endomorphism rings of abelian varieties of dimension two, submitted for publication;
• Endomorphism Rings in Cryptography, doctoral dissertation;
• Computing endomorphism rings of elliptic curves under the GRH, published in the Journal of Mathematical Cryptology;
• A low-memory algorithm for finding short product representations in finite groups, with Andrew V. Sutherland, published in Designs, Codes and Cryptography;
• AVIsogenies, a library for computing isogenies between abelian varieties, with Romain Cosset and Damien Robert;
• Computing the endomorphism ring of an ordinary elliptic curve over a finite field, with Andrew V. Sutherland, published in the Journal of Number Theory;
• More discriminants with the Brezing-Weng method, with Takakazu Satoh, published in Indocrypt 2008.

For more, see my list of writings, which includes articles and slides.

Teaching

Teaching materials (in French):

• (March 2010) short course on computational graph theory;
• (September 2009) introduction to Unix-like operating systems;
• (September 2009) introduction to preparing documents with LaTeX;
• (May 2009) short course on integer factoring;
• (January 2008) collection of interesting exercises for undergraduate mathematics majors;
• (May 2006) short text on Bernoulli numbers and polynomials;
• (April 2005) handouts for a course on formal languages, computability, and complexity, with François Garillot, Thierry Martinez, and Sam Zoghaib.

Hobbies

I spend my spare time:

• reading fantastic books;
• diving both hemispheres;
• sailing whenever possible;
• making computers do cute things.