Computation of Discrete Logarithms in F{sub}(2{sup}607)

摘要

We describe in this article how we have been able to extend the record for computations of discrete logarithms in characteristic 2 from the previous record over F{sub}(2{sup}503) to a newer mark of F{sub}(2{sup}607), using Coppersmith's algorithm. This has been made possible by several practical improvements to the algorithm. Although the computations have been carried out on fairly standard hardware, our opinion is that we are nearing the current limits of the manageable sizes for this algorithm, and that going substantially further will require deeper improvements to the method.