New Families of Hyperelliptic Curves with Efficient Gallant-Lambert-Vanstone Method

摘要

The Gallant-Lambert-Vanstone method (GLV method for short) is a scalar multiplication method for elliptic curve cryptography (ECC). In WAP WTLS, SEC 2, ANSI X9.62 and X9.63, several domain parameters for applications of the GLV method are described. Curves with those parameters have efficiently-computable en-domorphisms. Recently the GLV method for hyperelliptic curve (HEC) Jacobians has also been studied. In this paper, we discuss applications of the GLV method to curves with real multiplication (RM). It is the first time to use RM in cryptography. We describe the general algorithm for using such RM, and we show that some genus 2 curves with RM have enough effciency to be used in the GLV method as in the previous CM case.