Abstract: Different from binary method of modular exponentiation, the article introduces a faster and more effective sliding window method combined with Montgomery algorithm and the CRT(Chinese Remainder Theory). The flow charts of signature and verification are also given. The experiment result shows that sliding window method is 22.3% faster than the binary method. Meanwhile, it takes only 28ms to do a 1 024bit signature.

Key words: RSA algorithm; Montgomery algorithm; Chinese remainder theory (CRT); Modular exponentiation

摘要： 不同于常规的二进制幂模算法，该文采用一种更快速有效的滑动窗口法来实现幂模运算，同时结合Montgomery 算法和中国剩余定理相结合来实现RSA 签名，并给出了签名和验证的流程图。实验结果表明，以1 024bit 签名为例，采用滑动窗口算法比采用二进制算法要快22.3％；而综合采用滑动窗口和montgomery 算法结合中国剩余定理，一次1 024bit 签名仅需28ms。

关键词: RSA 算法；Montgomery 算法；中国剩余定理；幂模