Cryptology ePrint Archive: Report 2007/377

Fast Point Multiplication on Elliptic Curves of Even Order

Rongquan Feng, Hongfeng Wu

Abstract: Every elliptic curve of even order over a finite field of characteristic >3 is birationally equivalent to a curve in Jacobi quartic form. This paper presents the fast explicit formulas for group operations on a Jacobi quartic curve. The algorithm for doubling uses only 1M+6S, for the mixed-addition uses only 8M+2S and the unified addition formula only 9M+2S to be the best case. For elliptic curve of even order, these algorithm are more efficient than the other algorithms in the literature.

Category / Keywords: foundations / Elliptic curve, Point Multiplication, Jacobi quartic, Unified Formula,Side-Channel Analysis

Date: received 23 Sep 2007, last revised 4 Oct 2007, withdrawn 8 Oct 2007

Contact author: wuhfmail at gmail com

Available format(s): (-- withdrawn --)

Version: 20071008:090845 (All versions of this report)

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