一种改进的模逆算法与硬件实现  

An Improved Modular Inversion Algorithm and Hardware Implementation

作　　者：胡锦[1] 李勇彬 HU Jin;LI Yongbin(School of Physics and Electronics,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学物理与微电子科学学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2022年第2期101-105,共5页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(61674055)。

摘　　要：在公钥密码体系中,无论是RSA密码还是椭圆曲线密码,模逆运算都是非常关键的运算.模逆运算的前提是两数的最大公约数为1,否则结果是没有意义的.基于现有的二进制模逆算法的基础上提出了一种可以同时求最大公约数和进行模逆运算的算法,并且对算法进行优化,用VERILOG HDL语言进行硬件实现.通过功能仿真和FPGA验证,结果表明该设计可以正确进行32~1 024 bit的大数模逆运算.该设计应用于一款汽车安全芯片的PKI模块,采用UMC 55 nm工艺进行流片,芯片面积为10 mm^(2),工作电压3.3 V,钟频率为200 MHz时,功耗约为30.2 mW.In public-key cryptosystems(PKI),whether it is RSA cryptography or elliptic curve cryptography(ECC),modular inversion operations are very critical operations.The premise of modular inversion operations is that the greatest common divisor(GCD)of the two numbers is 1,otherwise the result is meaningless.Based on the existing binary modular inversion algorithms,an algorithm that can simultaneously find the GCD and perform modular inversion operations is proposed,and the algorithm is optimized and implemented in hardware using VERILOG HDL language.Through functional simulation and FPGA verification,the results show that this design can correctly perform the modular inversion operation of large number from 32 to 1 024 bits.The design is applied to a PKI module of an automotive security chip,using UMC 55 nm process for tape-out,and the chip area is 10 mm^(2).When the working voltage is 3.3 V and the clock frequency is 200 MHz,the power consumption is about 30.2 mW.

关 键 词：RSA密码 椭圆曲线密码 公钥密码 模逆 最大公约数 

分 类 号：TN492[电子电信—微电子学与固体电子学]