On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger; Thorsten Kleinjung; Jens Zumbrägel

Paper 2015/685

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, and Jens Zumbrägel

Abstract

For $q$ a prime power, the discrete logarithm problem (DLP) in $F_{q}^{\times}$ consists in finding, for any $g \in F_{q}^{\times}$ and $h \in ⟨ g ⟩$ , an integer $x$ such that $g^{x} = h$ . For each prime $p$ we exhibit infinitely many extension fields $F_{p^{n}}$ for which the DLP in $F_{p^{n}}^{\times}$ can be solved in expected quasi-polynomial time.

Note: In submission.

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: 2015-07-13: received
Short URL: https://ia.cr/2015/685
License: CC BY

BibTeX

@misc{cryptoeprint:2015/685,
      author = {Robert Granger and Thorsten Kleinjung and Jens Zumbrägel},
      title = {On the discrete logarithm problem in finite fields of fixed characteristic},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/685},
      year = {2015},
      url = {https://eprint.iacr.org/2015/685}
}