Faster Scalar Multiplication on Ordinary Weierstrass Elliptic Curves over Fields of Characteristic Three

Hongfeng Wu; Chang-An Zhao

Paper 2011/468

Faster Scalar Multiplication on Ordinary Weierstrass Elliptic Curves over Fields of Characteristic Three

Hongfeng Wu and Chang-An Zhao

Abstract

This paper proposes new explicit formulae for the point doubling, tripling and addition on ordinary Weierstrass elliptic 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 formulae 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. We also provide the unified and complete group laws. Finally, we present several examples of ordinary elliptic curves in characteristic three for high security levels.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic curve scalar multiplication unified addition cryptography explicit formulae
Contact author(s): whfmath @ gmail com
History: 2011-09-04: last of 5 revisions; 2011-08-29: received; See all versions
Short URL: https://ia.cr/2011/468
License: CC BY

BibTeX

@misc{cryptoeprint:2011/468,
      author = {Hongfeng Wu and Chang-An Zhao},
      title = {Faster Scalar Multiplication on Ordinary Weierstrass Elliptic Curves over Fields of Characteristic Three},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/468},
      year = {2011},
      url = {https://eprint.iacr.org/2011/468}
}