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An Improved wNAF Scalar-Multiplication Algorithm With Low Computational Complexity by Using Prime Precomputation
IEEE Access ( IF 3.9 ) Pub Date : 2021-02-22 , DOI: 10.1109/access.2021.3061124
Huang Hai , Na Ning , Xing Lin , Liu Zhiwei , Yu Bin , Zhao Shilei

To reduce the computational complexity of scalar multiplication, an improved wNAF scalar-multiplication algorithm is proposed by using prime precomputation. It replaces odd number with prime number in the precomputation stage, and makes up the difference between prime and odd by building the tiny multi-base chains. Thanks to the proposed algorithm, the computational complexity, the cost of precomputation and the creation time of addition chains are all reduced. Compared with the wNAF, the computational complexity and the running speed are optimized by 28.37% and 77.38% respectively at the fittest case. Also, lower computational complexity and higher running speed are outstanding features of the introduced algorithm than other existing algorithms.

中文翻译:

一种使用素数预计算的低计算复杂度的改进wNAF标量乘法算法

为了降低标量乘法的计算复杂度,提出了一种使用素数预计算的改进的wNAF标量乘法算法。它在预计算阶段用素数替换了奇数,并通过构建微小的多基链来弥补素数和奇数之间的差异。由于所提出的算法,减少了计算复杂度,预计算成本和加法链的创建时间。与wNAF相比,最适情况下的计算复杂度和运行速度分别优化了28.37%和77.38%。而且,与其他现有算法相比,较低的计算复杂度和较高的运行速度是引入算法的突出特点。
更新日期:2021-03-02
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