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分析Montgomery模乘算法的设计思想和模平方中乘法的计算过程,通过引入两种新的平方计算方法以及对Montgomery算法的优化,提出适合于通用32位处理器实现的Montgomery模平方算法。将该方法应用于模幂计算,给出基于滑动窗口技术的Montgomery模幂算法。实验结果表明,该算法能将模幂的计算速度提高9%~12%。
This paper analyzes the design idea of Montgomery modular multiplication algorithm and the calculation process of square multiplication. By introducing two new square calculation methods and the optimization of Montgomery algorithm, a Montgomery modular squaring algorithm suitable for general purpose 32-bit processor is proposed. The method is applied to the modular exponentiation, and the Montgomery modular exponentiation algorithm based on sliding window technique is given. Experimental results show that the proposed algorithm can increase the computational speed of modular exponentiation by 9% ~ 12%.