Abstract: The most famous representative of public-key cryptography is the RSA cryptosystem. However, it is now losing its predominance: elliptic curve cryptography is more efficient, in terms of speed and key size.

Using curves of genus 2 may provide systems that are faster than their elliptic analogues. I will describe current efforts to find a "secure" curve of genus 2, and give an overview of the extensive computations involved.

Joint work with Pierrick Gaudry