Abstract: This paper presents a new algorithm to realize modular exponentiation multiplication by converting multiplication and modular operation into the simple shift and addition operation, thus avoiding modular operation on large number. Experiment shows that our algorithm speeds up the modular exponentiation multiplication remarkably: it realize A×B mod N in n/2 times n-bit addition operation. It’s time cost for C=me is a half of the Montgomery algorithm.

摘要： 本文提出一种宏观累加模的快速模幂乘的算法，将乘法运算和求模运算转换成简单的移位运算和加法运算，从而避免了求模运算和减少大数相乘次数。实验表明，本算法可以用接近n/2次n-bit的加法运算即可实现A×B mod N运算，在宏观上看，计算C=me要比Montgomery等算法快2倍。