基于有符号数字系统的Montgomery模逆算法及其硬件实现

摘要

Modular inversion is the most complex and time consuming finite fields arithmetic operation in elliptic curve cryptography (EOC) .Further more,the hardware implementation of modular inversion is difficult.Based on signed digit system theory, this paper presents a scalable dual-field Montgomery modular inversion algorithm which supports inversion algorithm of any precision parameters in the prime fields and binary fields. According to the algorithm,the hardware architecture is designed and analyzed in area complexity and time complexity. Simulation results show that the hardware design is superior to other hardware designs in operation speed,circuit area and flexibility.%在椭圆曲线密码中,模逆运算是有限域运算中最复杂、最耗时且硬件实现难度最大的运算.本文在Kaliski算法的基础上,提出了基于有符号数字系统的Montgomery模逆算法,它支持素数域和二进制域上任意多精度参数的求模逆运算.据此算法,设计了相应的硬件结构方案,并给出了面积复杂度和时间复杂度分析.仿真结果表明,相比于其它模逆算法硬件设计方案,本文提出的基于有符号数字系统的Montgomery模逆算法在运算速度、电路面积、灵活性等方面具有显著的优越性.