关键词: 方幂模, 秦九韶算法, 分块算法, 二进制自适应分组查表法, 加法链

Abstract: Modular exponentiation is the most frequently used and time-cost part in RSA，whose fast algorithm is one of the focuses of RSA study，and to speed up the computation of modular exponentiation is most important to the performance and wide use of RSA.This paper studies Qin Jiu-shao algorithm，blocking algorithm，addition chains algorithm，and adaptive binary partition table searching method.Another contribution of this paper is that the above algorithms are analyzed from the point of view of addition chains.In the point of view of addition chains，they are accordant，and adaptive binary partition table searching method can get higher efficiency than Qin Jiu-shao algorithm and blocking algorithm，but may be further improved.

Key words: modular exponentiation, Qin Jiu-shao algorithm, blocking algorithm, adaptive binary partition table searching method, addition chains