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 Lqn(1/3,(4/9)1/3) 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 21971 and 23164 elements, setting a record for binary fields. © 2013 International Association for Cryptologic Research.
CITATION STYLE
Göloǧlu, F., Granger, R., McGuire, G., & Zumbrägel, J. (2013). On the function field sieve and the impact of higher splitting probabilities: Application to discrete logarithms in double-struck F 21971 and double-struck F23164. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8043 LNCS, pp. 109–128). https://doi.org/10.1007/978-3-642-40084-1_7
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