Section: New Results

Advances in point counting

Determining the number of points on an elliptic curve, or more generally on the Jacobian of an algebraic curve, is a classic problem in algorithmic number theory that is now crucial for efficiently generating secure cryptographic parameters. Together with C. Scribot, F. Morain and B. Smith developed an improved version of the state-of-the-art SEA algorithm for certain families of elliptic curves with special endomorphisms; this was presented at ANTS-XII [10]. B. Smith also led a project group on special genus-2 point counting algorithms at the "Algebraic Geometry for Coding Theory and Cryptography" workshop at IPAM, UCLA, in 2016.