Discrete Logarithm in GF(2809) with FFS.

The year 2013 has seen several major complexity advances for the discrete logarithm problem in multiplicative groups of small- characteristic finite fields. These outmatch, asymptotically, the Function Field Sieve FFS approach, which was so far the most efficient algorithm known for this task. Yet, on the practical side, it is not clear whether the new algorithms are uniformly better than FFS. This article presents the state of the art with regard to the FFS algorithm, and reports data from a record-sized discrete logarithm computation in a prime-degree extension field.