Paper 2014/300 Original: eprint.iacr.org/2014/300 ↗
On the Powers of 2
Abstract
In 2013 the function field sieve algorithm for computing discrete logarithms in finite fields of small characteristic underwent a series of dramatic improvements, culminating in the first heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. In this article we present an alternative descent method which is built entirely from the on-the-fly degree two elimination method of Göloğlu, Granger, McGuire and Zumbrägel. This also results in a heuristic quasi-polynomial time algorithm, for which the descent does not require any relation gathering or linear algebra eliminations and interestingly, does not require any smoothness assumptions about non-uniformly distributed polynomials. These properties make the new descent method readily applicable at currently viable bitlengths and better suited to theoretical analysis.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2014-04-30: last updated
- 2014-04-30: published
- Short URL
- https://ia.cr/2014/300
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2014/300,
author = {Robert Granger and Thorsten Kleinjung and Jens Zumbrägel},
title = {On the Powers of 2},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/300},
year = {2014},
url = {https://eprint.iacr.org/2014/300}
}