Paper 2013/087
Square Root Algorithm in F_q for q=2^s+1 (mod 2^(s+1))
Namhun Koo, Gook Hwa Cho, and Soonhak Kwon
Abstract
We present a square root algorithm in F_q which generalizes Atkins's square root algorithm for q=5(mod 8) and Kong et al.'s algorithm for q=9(mod 16) Our algorithm precomputes a primitive 2^s-th root of unity where s is the largest positive integer satisfying 2^s| q-1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, Muller and Kong et al.
Metadata
- Available format(s)
-
PDF
- Category
- Applications
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- square root algorithmfinite fieldTonelli-Shanks algorithmCipolla-Lehmer algorithm
- Contact author(s)
- shkwon7 @ gmail com
- History
- 2013-02-20: received
- Short URL
- https://ia.cr/2013/087
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/087,
author = {Namhun Koo and Gook Hwa Cho and Soonhak Kwon},
title = {Square Root Algorithm in F_q for q=2^s+1 (mod 2^(s+1))},
howpublished = {Cryptology ePrint Archive, Paper 2013/087},
year = {2013},
note = {\url{https://eprint.iacr.org/2013/087}},
url = {https://eprint.iacr.org/2013/087}
}
