<正>介绍了多精度整数求幂运算中的"滑动窗口"算法,并结合Montgomery约简算法,对"滑动窗口"算法进行了应用研究,分析了根据多精度整数的位数来确定相应的窗口大小。结果表明,采用这种组合的模幂运算算法具有十分高效的执行效率,4096位多精度整数的模幂计算大约需要1.5s,并可满足RSA的应用对密钥长度的安全需求。

This paper introduced a method called "sliding-window" used in multiple-precision integer exponentiation arithmetic,and studied its application combined with Montgomery reduction,and how to calculate the "window size" related to the bits of the multiple-precision integer.The result indicates that the combined algorithm carries out an efficient calculation,the elapsed time of 4 096 bits multiple-precision integers modular exponentiation is about 1.5 s,and it will be the base of applied RSA public-key cryptography used in information security.