Paper 2012/122 Original: eprint.iacr.org/2012/122 ↗
Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
Abstract
This paper presents new explicit formulas for the point doubling, tripling and addition for Hessian curves and their equivalent Weierstrass curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulas in projective coordinates require 3M+2C, 8M+1C+1D and 4M+4C+1D respectively, where M, C and D is the cost of a field multiplication, a cubing and a multiplication by a constant. Finally, we present several examples of ordinary elliptic curves in characteristic three for high security levels.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2012-05-09: last updated
- 2012-03-13: published
- Short URL
- https://ia.cr/2012/122
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/122,
author = {Reza R. Farashahi and Hongfeng Wu and Chang-An Zhao},
title = {Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/122},
year = {2012},
url = {https://eprint.iacr.org/2012/122}
}