On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in F 2 1971 .
Faruk Göloğlu, Robert Granger, Gary McGuire, Jens Zumbrägel · IACR Cryptology ePrint Archive · 2013
In this paper we propose a binary field variant of the JouxLercier medium-sized Function Field Sieve, which results not only in complexities as low as Lqn(1/3, (4/9) ) for computing arbitrary logarithms, but also in an heuristic polynomial time algorithm for finding the discrete logarithms of degree one and two elements when the field has a subfield of an appropriate size. To illustrate the efficiency of the method, we have successfully solved the DLP in the finite fields with 2 and 2 elements, setting a record for binary fields.