Abstract
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.
Supported in part by National Basic Research Program of China(973) under Grant No.2013CB338002, in part by National Research Foundation of China under Grant No. 60970153 and 61070171, and in part by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant XDA06010702.
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Yu, W., Wang, K., Li, B., Tian, S. (2013). Joint Triple-Base Number System for Multi-Scalar Multiplication. In: Deng, R.H., Feng, T. (eds) Information Security Practice and Experience. ISPEC 2013. Lecture Notes in Computer Science, vol 7863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38033-4_12
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DOI: https://doi.org/10.1007/978-3-642-38033-4_12
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