椭圆曲线倍点算法的比较研究

摘要

文章介绍了6种较新的具有代表性的椭圆曲线标量乘法，分析了各个算法的复杂度，使用Java语言实现了算法，并对这些算法进行了测试，包括算法的运行时间、算法复杂度。重点研究了滑动窗口法下针对不同长度的参数K，复杂度与窗口长度r的对应关系，并给出了对应的最佳窗口宽度。最后，对6种算法的复杂度和测试结果进行了对比分析。%Six algorithms for scalar multiplication in elliptic curve are introduced. The computation complexities of the algorithms are analyzed. They are implemented using Java programming language. The algorithms are tested extensively, including the running time and the complexity. In different parameter K, the relations between window length r and computation complexity in the sliding window method are analyzed. The best window width is proposed. Finally, the complexity and test results of six algorithms are compared and analyzed.