Fast Multi-Scalar Multiplication Using the Multi-Based Number System

As a generalization of double base chains, multi-base number system is very suitable for efficient computation of scalar multiplications of elliptic curves because of shorter representation length and less Hamming weight. In this paper, combined with the given formulas for computing the 5-fold of an elliptic curve point P, an efficient scalar multiplication algorithm of elliptic curve is proposed using 2, 3 and 5 as bases of the multi-based number system. The algorithms cost less compared with Shamir´s trick and interleaving with NAFs method.