改进的蒙哥马利算法及其模乘法器实现

Improved Montgomery Algorithm and Implementation of Modular Multiplier

模乘运算的速度决定了公钥加密系统和众多通信系统的系统性能。通过分析Walter等学者对蒙哥马利算法的研究成果,得到运算精简基2-MMM算法,实现基于运算精简算法的线性脉动阵列模乘法器。在验证改进算法正确性后,对模乘法器进行功能仿真和综合。用TSMC 0.18μm标准单元库综合,可以工作在200 MHz时钟下,等效单元为42 k门,完成1 024 bit模乘法运算需15 370 ns。

Modular multiplication operation is a key factor of determining performance system of publickey cryptography systems and most of communication systems.In this paper,an improved Montgomery Modular Multiplication（MMM） algorithm called operation reduced radix 2-MMM algorithm is developed by combining the available typical Montgomery modular algorithms.And a linear systolic array circuit scheme is used for implementing the modular multiplier.Validation of the modular multiplier functionality is conducted on ModelSim SE 6.0d platform.Based on the TSMC 0.18 μm CMOS technology,area of the modular multiplier is about 42k equivalent gates,the system frequency can up to 200 MHz,and the 1024-bit modular multiplication is 15 370 ns.