Preprints

Computing Discrete Logarithms with Special Linear Systems. (with C. Diem)

Constructing Plane Models of Small Degree.

Brill-Noether Theory and Mumford Coordinates.

Software

Computing Discrete Logarithms in Class Groups.

The following Magma package provides two methods to compute the discrete logarithm in the class group of curves of genus ≥4. To use this package, extract it and open Magma from the directory where the package is stored. Type AttachSpec("DLP") to attach the intrinsics DLPencils, DLNet, DLPencilsMatrix and DLNetMatrix.
DLPencils uses a method which is described in Computing Discrete Logarithms with Special Linear Systems (see above). DLNet on the other hand relies on the paper Index Calculus in Class Groups of Plane Curves of Small Degree (by C. Diem). In case the group order is prime both algorithms apply the Lanczos algorithm to solve the corresponding system of linear equations; otherwise structured Gaussian elimination is used but does not work reliably.

Talks

The Discrete Logarithm Problem for non-hyperelliptic Curves and related geometric Considerations.

This is a joint talk with C. Diem given at the workshop Number Theory in Kaiserslautern 2014: Number Theory Meets Geometry.

The Discrete Logarithm Problem on non-hyperelliptic Curves of Genus g > 3.

This talk was given at the seminar of the CARAMEL group at LORIA in Nancy as well as at the Oberseminar at the University of Saarbrücken.

The Discrete Logarithm Problem on non-hyperelliptic Curves and related Geometric Considerations.

This talk was given at CAMS at the American University of Beirut. It extends the talks above by a new result but does not discuss the general index calculus method.