Abstract: 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.