### Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

Thorsten Kleinjung and Benjamin Wesolowski

##### Abstract

We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality $p^n$ in expected time $(pn)^{2\log_2(n) + O(1)}$.

##### Metadata
Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Minor revision.Journal of the American Mathematical Society
Keywords
discrete logarithm problemfinite field
Contact author(s)
bj wesolowski @ orange fr
History
2021-09-10: last of 2 revisions
2019-06-25: received
See all versions
Short URL
https://ia.cr/2019/751
License

CC BY

BibTeX

@misc{cryptoeprint:2019/751,
author = {Thorsten Kleinjung and Benjamin Wesolowski},
title = {Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic},
howpublished = {Cryptology ePrint Archive, Paper 2019/751},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/751}},
url = {https://eprint.iacr.org/2019/751}
}

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