Ternary Method in Elliptic Curve Scalar Multiplication

Abstract

Based on ternary method, we proposed a new scalar multiplication with high performance and security. Fast computation formulae of 3P ±Q is developed for ternary method, balanced ternary coding is used to improve the efficiency of scalar multiplication, signed ternary with lowest hamming weight is used to further improve the efficiency. For the elliptic curves in GF(3m), compared with Binary Scalar Multiplication, the efficiency of the new scalar multiplication is improved with the increase of the ratio of inversion and multiplication without pre-computations and other registers.