Faster elliptic curve arithmetic for triple-base chain by reordering sequences of field operations

Abstract

In this work, we propose an algorithm to produce the Triple-base chain that optimize the time usage for computing an elliptic curve cryptosystem. Triple-base Chain is a scalar multiplication algorithm, which represents an integer k using three bases {2,3,5}. This paper provides a faster scalar multiplication method of elliptic curve based on {2,3,5} Triple-base Chain. The method proposed by this research speeds up the existing Triple-base Chain algorithm by optimizing the 5P operation of elliptic curve and reordering the operation order of base {2,3,5}. This method can improve the speed of operation from 4 to 6 % compared to the existing {2,3,5} Triple-base Chain.