Sign in finite fields

Abraham Westerbaan; Bas Westerbaan

Paper 2020/1041

Sign in finite fields

Abraham Westerbaan and Bas Westerbaan

Abstract

Often in cryptography one needs to make a consistent choice of square root in a finite field. We show that such a choice is equivalent to providing a reasonable sign function. Then we show that for $\mathbb{F}_{p^k}$ (with odd prime $p \neq 1$ and $k\neq 0$) such a sign function exists if and only if $k$ is odd.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: finite fields square root sign function
Contact author(s): bas @ westerbaan name
History: 2020-08-28: received
Short URL: https://ia.cr/2020/1041
License: CC BY

BibTeX

@misc{cryptoeprint:2020/1041,
      author = {Abraham Westerbaan and Bas Westerbaan},
      title = {Sign in finite fields},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1041},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/1041}},
      url = {https://eprint.iacr.org/2020/1041}
}