@inproceedings{0c8e60dd14584ee9ad3b83c028faed0f,
title = "Efficient arithmetic on elliptic curves over fields of characteristic three",
abstract = "This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstra{\ss} elliptic curves with a point of order 3 and their equivalent Hessian 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. Finally, we present several examples of ordinary elliptic curves in characteristic three for high security levels.",
keywords = "cryptography, Elliptic curve, Hessian curve, scalar multiplication",
author = "Farashahi, {Reza R.} and Hongfeng Wu and Zhao, {Chang An}",
year = "2013",
doi = "10.1007/978-3-642-35999-6_10",
language = "English",
isbn = "9783642359989",
volume = "7707 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "135--148",
editor = "Knudsen, {Lars R.} and Huapeng Wu",
booktitle = "Selected Areas in Cryptography - 19th International Conference, SAC 2012, Revised Selected Papers",
note = "19th International Conference on Selected Areas in Cryptography, SAC 2012 ; Conference date: 15-08-2012 Through 16-08-2012",
}