Efficient Scalar Multiplication Algorithm Using Multibase Chains

In the elliptic curve cryptosystem, Scalar multiplication is the most important and computationally costliest operation, thus it becomes one of hot topics. As a generalization of double base chains, multibase chains are very suitable for efficient computation of scalar multiplications of elliptic curves because of shorter representation length and less Hamming weight. In this paper, the formulas for computing the 5-fold of an elliptic curve point P are given. Using 2, 3 and 5 as bases of the multibase chains, an efficient scalar multiplication algorithm of elliptic curve is proposed. This algorithm can offer some protections against some side-channel attacks for the huge redundancy of the multibase representation and cost less compared with stand double-and-add and nonadjacent form for scalar multiplications.