摘要： 通过对目前常用的几类模乘方法的综合研究，充分吸取估商型模乘算法的估商思想，借助Montgomery型模乘算法中模2n易计算特性，采用窗口分段处理方式，给出了一种新的利用模N进行预计算的方法，进而提出了一种新的加法型模乘AB mod N快速实现算法。模N为1 024-bit、窗宽为6时，新算法平均仅需693次1 024-bit加法便可完成一次AB mod N模乘运算，与当前加法型模乘算法相比，较大幅度地降低了计算复杂度。

关键词: 公钥密码, 模幂运算, 模乘运算, 窗口宽度

Abstract: Researched on several recently widely used modular multiplication algorithms, adopted the ideal of window division, estimating quotient, and modular 2n easy to be calculated, which is used in Montgomery modular multiplication algorithm, a new fast calculating AB mod N algorithm based on addition is presented, which introduces pre-calculating by modular N. When the length of modular N is 1 024-bit and the length of window is 6, on the average, the new algorithm requires only 693 times 1 024-bit addition to calculate AB mod N. Comparing with current additional modular multiplication algorithm, the computing complexity is reduced largely.

Key words: Public-key cryptography, Modular exponentiation, Modular multiplication, Window length