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Title:
On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in \F_{2^{1971}} and \F_{2^{3164}}
Authors: Faruk Göloğlu, Robert Granger, Gary McGuire, Jens Zumbrägel
Abstract:In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as L_{q^n}(1/3,(4/9)^{1/3}) for computing arbitrary logarithms, but also in an heuristic {\em 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^{1971} and 2^{3164} elements, setting a record for binary fields.
ePrint: https://eprint.iacr.org/2013/074
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