**On the discrete logarithm problem in finite fields of fixed characteristic**

*Robert Granger and 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.

**Category / Keywords: **public-key cryptography / discrete logarithm problem, finite fields, quasi-polynomial time algorithm

**Date: **received 7 Jul 2015

**Contact author: **thorsten kleinjung at epfl ch

**Available format(s): **PDF | BibTeX Citation

**Note: **In submission.

**Version: **20150713:075227 (All versions of this report)

**Short URL: **ia.cr/2015/685

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