On the Function Field Sieve and the Impact of Higher Splitting Probabilities
Vortrag von Prof. Dr. Jens Zumbrägel
Sprecher eingeladen von: Prof. Dr. Joachim Rosenthal
Datum: 27.05.13 Zeit: 13.00 - 14.00 Raum: Y27H28
We propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results in complexities as low as L(1/3, 0.763) for computing arbitrary logarithms, and in a heuristic polynomial-time algorithm for finding the discrete logarithms of degree one elements.To illustrate the efficiency of the method, we have solved the DLP in the 2^1971-element finite field. By combining our method with a very recent approach for small-degree descent due to Joux, we have also successfully solved the DLP in the finite field with 2^6120 elements.
This is joint work with Faruk Gologlu, Robert Granger, and Gary McGuire.