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双线性对以其独有的数学性质,成为构建许多密码体制的重要工具,但是其计算效率的提高是一个亟待解决的问题。Miller算法是计算双线性对的有效算法,本文在Miller算法的基础上,引入了双基数系统,降低了链长和非零数字的平均密度,从而减少了点加次数,同时,将点加与倍点过程合并,减少了求逆运算的次数,分析表明改进的算法效率有明显提高。
Bilinear pairings are important tools for constructing many cryptosystems because of their unique mathematical properties. However, the improvement of computational efficiency is a problem to be solved. Miller algorithm is an effective algorithm to calculate bilinear pairings. Based on Miller’s algorithm, this paper introduces a double-cardinality system, which reduces the average density of chain length and non-zero number, thus reducing the number of points plus. At the same time, Merging with the double point process reduces the number of inversion operations. Analysis shows that the efficiency of the improved algorithm is obviously improved.