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

Thorsten Kleinjung; Benjamin Wesolowski

Paper 2019/751

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 $(p n)^{2 \log_{2} (n) + O (1)}$ .

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. Journal of the American Mathematical Society
Keywords: discrete logarithm problem finite 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},
      url = {https://eprint.iacr.org/2019/751}
}