### On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\F_{2^{1971}}$ and $\F_{2^{3164}}$

Faruk Göloğlu, Robert Granger, Gary McGuire, and 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.

Available format(s)
Publication info
Published elsewhere. Crypto 2013 IACR version
Keywords
Discrete logarithm problemfunction field sieve.
Contact author(s)
robbiegranger @ gmail com
History
2013-06-08: last of 2 revisions
See all versions
Short URL
https://ia.cr/2013/074

CC BY

BibTeX

@misc{cryptoeprint:2013/074,
author = {Faruk Göloğlu and Robert Granger and Gary McGuire and Jens Zumbrägel},
title = {On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\F_{2^{1971}}$ and $\F_{2^{3164}}$},
howpublished = {Cryptology ePrint Archive, Paper 2013/074},
year = {2013},
note = {\url{https://eprint.iacr.org/2013/074}},
url = {https://eprint.iacr.org/2013/074}
}

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