Joint Triple-Base Number System for Multi-Scalar Multiplication

At present, the joint sparse form and the joint binary-ternary method are the most efficient representation systems for calculating multi-scalar multiplications [k]P + [l]Q, where k,l are scalars and P,Q are points on the same elliptic curve. We introduce the concept of a joint triple-base chain. Our algorithm, named the joint binary-ternary-quintuple method, is able to find a shorter joint triple-base chain for the sparseness of triple-base number systems. With respect to the joint sparse form, this algorithm saves 32% of the additions, saving 13% even compared with the joint binary-ternary method. The joint binary-ternary-quintuple method is the fastest method among the existing algorithms, which speeds up the signature verification of the elliptic curve digital signature algorithm. It is very suitable for software implementation.

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