On the Powers of 2

Robert Granger; Thorsten Kleinjung; Jens Zumbrägel

Paper 2014/300

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: discrete logarithm problem finite fields quasi-polynomial time algorithm
Contact author(s): thorsten kleinjung @ epfl ch
History: 2014-04-30: received
Short URL: https://ia.cr/2014/300
License: 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},
      url = {https://eprint.iacr.org/2014/300}
}