Cryptology ePrint Archive: Report 2012/122

Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three

Reza R. Farashahi and Hongfeng Wu and Chang-An Zhao

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.

Category / Keywords: public-key cryptography / Elliptic curve, Hessian curve, scalar multiplication, cryptography

Date: received 5 Mar 2012, last revised 9 May 2012

Contact author: whfmath at gmail com

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Version: 20120509:141131 (All versions of this report)

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