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 $\mathbb{F}_{q}^{\times}$ consists in finding, for any $g \in \mathbb{F}_{q}^{\times}$ and $h \in \langle g \rangle$, an integer $x$ such that $g^x = h$. For each prime $p$ we exhibit infinitely many extension fields $\mathbb{F}_{p^n}$ for which the DLP in $\mathbb{F}_{p^n}^{\times}$ 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 problemfinite fieldsquasi-polynomial time algorithm
Contact author(s)
thorsten kleinjung @ epfl ch
History
2015-07-13: received
Short URL
https://ia.cr/2015/685
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2015/685}},
      url = {https://eprint.iacr.org/2015/685}
}
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