### On the Powers of 2

Robert Granger, Thorsten Kleinjung, and Jens Zumbrägel

##### 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.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
discrete logarithm problemfinite fieldsquasi-polynomial time algorithm
Contact author(s)
thorsten kleinjung @ epfl ch
History
Short URL
https://ia.cr/2014/300

CC BY

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},
note = {\url{https://eprint.iacr.org/2014/300}},
url = {https://eprint.iacr.org/2014/300}
}

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