Paper 2013/074
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.
Note: Comments welcome.
Metadata
- 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
- 2013-02-20: received
- See all versions
- Short URL
- https://ia.cr/2013/074
- License
-
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}, url = {https://eprint.iacr.org/2013/074} }