Paper 2014/300

On the Powers of 2

Robert Granger, Thorsten Kleinjung, and Jens Zumbrägel


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)
Public-key cryptography
Publication info
Preprint. MINOR revision.
discrete logarithm problemfinite fieldsquasi-polynomial time algorithm
Contact author(s)
thorsten kleinjung @ epfl ch
2014-04-30: received
Short URL
Creative Commons Attribution


      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{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.