The thirteenth AGCT meeting was held at the CIRM in Luminy (on the outskirts of Marseille, France) from the 14th to the 18th of March, 2011. AGCT stands for Arithmétique, Géométrie, Cryptographie et Théorie des Codes: as the name suggests, the participants are drawn from a number of fields including number theory, algebraic geometry, cryptography, and coding theory. As a result, AGCT is a great place for exchanging ideas, in a particularly beautiful natural environment.
The talks were on a wide range of topics, from explicit arithmetic geometry to APN functions. While most of the talks did not directly concern ECC, there were a number that might be of interest to curve-based cryptographers:
- Ivan Boyer gave an interesting talk on deterministic factorization of polynomials over finite fields using Schoof’s algorithm. (Of course, non-deterministic polynomial factorization is much more straightforward…)
- Safia Haloui and Vijay Singh spoke about Weil polynomials (characteristic polynomials of Frobenius). Safia described all the possible Weil polynomials for abelian varieties of dimension 3 or 4; Vijay showed how to list all of the supersingular Weil polynomials for dimensions up to 7.
- David Kohel spoke about a nice analogue of Edwards curves in characteristic 2.
- Petr Lisonek spoke about using Kedlaya’s algorithm for point counting on hyperelliptic curves to prove that certain functions are hyperbent.
- Ben Smith (excuse the self-promotion…) spoke about a middlebrow construction of (3,3)-isogenies for genus 2 curves.
- Bianca Viray spoke about denominators of Igusa class polynomials (which are used in the genus 2 CM method) from the point of view of arithmetic intersection theory.
There were a lot of interesting talks on other topics, too many to list here: the program is available online, and some of the slides are linked from the AGCT site. I particularly enjoyed the talks by Nils Bruin, Everett Howe, Kamal Khuri-Makdisi, and Henning Stichtenoth, to name just a few.
— Ben Smith