Abstract
The triple-base number system is used to speed up scalar multiplication. At present, the main methods to calculate a triple-base chain are greedy algorithms. We propose a new method, called the add/sub algorithm, to calculate scalar multiplication. The density of such chains gained by this algorithm with base {2, 3, 5} is \(\frac{1}{5.61426}\). It saves 22% additions compared with the binary/ternary method; 22.1% additions compared with the multibase non-adjacent form with base {2, 3, 5}; 13.7% additions compared with the greedy algorithm with base {2, 3, 5}; 20.9% compared with the tree approach with base {2, 3}; and saves 4.1% additions compared with the add/sub algorithm with base {2, 3, 7}, which is the same algorithm with different parameters. To our knowledge, the add/sub algorithm with base {2, 3, 5} is the fastest among the existing algorithms. Also, recoding is very easy and efficient and together with the add/sub algorithm are very suitable for software implementation. In addition, we improve the greedy algorithm by plane search which searches for the best approximation with a time complexity of \(\mathcal{O}(\log^3 k)\) compared with that of the original of \(\mathcal{O}(\log^4 k)\).
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. 61272040 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). Triple-Base Number System for Scalar Multiplication. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds) Progress in Cryptology – AFRICACRYPT 2013. AFRICACRYPT 2013. Lecture Notes in Computer Science, vol 7918. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38553-7_26
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