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 …

… Determine the cut-off points where FFS is surpassed by the new methods (prime-degree
extensions?). The new algorithms still rely on bits taken from FFS. … further experiments for
FFS and for the new algorithms to establish the cut-off points between these algorithms for
the prime degree extensions. …