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

We have developed a new method for faster elliptic curve scalar multiplication represented in double-base chain format by cutting down redundancy using reordering sequences of field arithmetic operations. This method utilizes already-computed values obtained at some prior calculations to avoid unnecessary computations at some following calculations of a very time-consuming yet frequently executed scalar multiplication. We found that computing point doubling before point tripling reduces two computations of field squaring for curves defined over prime field, and consecutively point tripling or computing point tripling followed by point doubling reduces one computation of field squaring for curves defined over binary field. Experimental results showed achievements of 1.95% and 0.31% speed-up for curves defined over prime field and binary field respectively.