基于比特重组快速模约简的高面积效率椭圆曲线标量乘法器设计  

Design of High Area Efficiency Elliptic Curve Scalar Multiplier Based on Fast Modulo Reduction of Bit Reorganization

作　　者：刘志伟 张琦 黄海 杨晓秋 陈冠百 赵石磊 于斌 LIU Zhiwei;ZHANG Qi;HUANG Hai;YANG Xiaoqiu;CHEN Guanbai;ZHAO Shilei;YU Bin(College of Computer Science and Technology,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学计算机科学与技术学院,哈尔滨150080

出　　处：《电子与信息学报》2024年第1期344-352,共9页Journal of Electronics & Information Technology

基　　金：国家重点研发计划重点专项(2018YFB2202101);中央引导地方科技发展专项(ZY20B11);黑龙江省普通高校基本科研业务费专项资金(2019KYYWF0214)。

摘　　要：针对现有椭圆曲线密码标量乘法器难以兼顾灵活性和面积效率的问题,该文设计了一种基于比特重组快速模约简的高面积效率标量乘法器。首先,根据椭圆曲线标量乘的运算特点,设计了一种可实现乘法和模逆两种运算的硬件复用运算单元以提高硬件资源使用率,并采用Karatsuba-Ofman算法提高计算性能。其次,设计了基于比特重组的快速模约简算法,并实现了支持secp256k1, secp256r1和SCA-256(SM2标准推荐曲线)快速模约简计算的硬件架构。最后,对点加和倍点的模运算操作调度进行了优化,提高乘法与快速模约简的利用率,降低了标量乘计算所需的周期数量。所设计的标量乘法器在55 nm CMOS工艺下需要275 k个等效门,标量乘运算速度为48 309次/s,面积时间积达到5.7。To solve the problem that existing elliptic curve cryptography scalar multipliers are difficult to balance flexibility and area efficiency,a scalar multiplier with high area efficiency based on bit reorganization fast modular reduction is designed.Firstly,according to the operation characteristics of elliptic curve scalar multiplication,a hardware multiplexing operation unit that can realize two operations of multiplication and modular inversion is designed to improve the utilization rate of hardware resources,and the Karatsuba-Ofman algorithm is used to improve the calculation performance.Secondly,a fast modular reduction algorithm based on bit reorganization is designed,and a hardware architecture supporting secp256k1,secp256r1 and SCA-256(SM2 standard recommended curve)fast modular reduction calculation is implemented.Finally,the scheduling of modular operations for point addition and point doubling is optimized to improve the utilization of multiplication and fast modular reduction,and reduce the number of cycles required for scalar multiplication calculations.The designed scalar multiplier requires 275 k equivalent gates in 55 nm CMOS technology,the scalar multiplication operation speed is 48309 times/s,and the area-time product reaches 5.7.

关 键 词：椭圆曲线密码 硬件实现 Secp256k1 标量乘 快速模约简 

分 类 号：TN918[电子电信—通信与信息系统]