Cryptology ePrint Archive: Report 2007/181

A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields

Kwang Ho Kim and So In Kim

Abstract: Now, It is believed that the best costs of a point doubling and addition on elliptic curves over binary fields are 4M+5S(namely, four finite field multiplications and five field squarings) and 8M+5S, respectively. In this paper we reduce the costs to less than 3M+3S and 8M+1S, respectively, by using a new projective coordinates we call PL-coordinates and rewriting the point doubling formula. Combining some programming skills, the method can speed up a elliptic curve scalar multiplication by about 15～20 percent in practice.

Category / Keywords: implementation / elliptic curve cryptosystem, binary field, point doubling, point addition

Date: received 13 May 2007

Contact author: kimkhhj1980 at yahoo com cn

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Version: 20070520:131155 (All versions of this report)

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