Paper 2013/400
A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic
Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, and Emmanuel Thomé
Abstract
In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. The main result gives a quasi-polynomial heuristic complexity for the discrete logarithm problem in finite field of small characteristic. By quasi-polynomial, we mean a complexity of type $n^{O(\log n)}$ where $n$ is the bit-size of the cardinality of the finite field. Such a complexity is smaller than any $L(\varepsilon)$ for $\epsilon>0$. It remains super-polynomial in the size of the input, but offers a major asymptotic improvement compared to $L(1/4+o(1))$.
Note: significantly improved version, further details given.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown status
- Keywords
- cryptanalysisnumber theorydiscrete logarithm problemfinite fields
- Contact author(s)
- Emmanuel Thome @ gmail com
- History
- 2013-11-25: revised
- 2013-06-20: received
- See all versions
- Short URL
- https://ia.cr/2013/400
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/400,
author = {Razvan Barbulescu and Pierrick Gaudry and Antoine Joux and Emmanuel Thomé},
title = {A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/400},
year = {2013},
url = {https://eprint.iacr.org/2013/400}
}
