抗SPA攻击的Twisted Edwards曲线标量乘法实现  

Implementation of Scalar Multiplication on Edwards Curve against SPA Attack

作　　者：王松[1] 房利国[1] 韩炼冰[1] 刘鸿博[1] 杨敏旭 WANG Song;FANG Liguo;HAN Lianbing;LIU Hongbo;YANG Minxu(No.30 Institute of CETC,Chengdu Sichuan 610041,China)

机构地区：[1]中国电子科技集团公司第三十研究所,四川成都610041

出　　处：《通信技术》2023年第2期231-235,共5页Communications Technology

摘　　要：椭圆曲线密码(Elliptic Curve Cryptography,ECC)是一种非对称密码,在信息安全领域中扮演着越来越重要的角色。目前对椭圆曲线密码的研究大多针对Weierstrass曲线,对于Twisted Edwards曲线的研究较少。针对Twisted Edwards曲线上标量乘法的效率及安全性,将Twisted Edwards曲线转换为Montgomery曲线,并采用Montgomery标量乘法在每次循环中都固定进行点加和倍点计算,从而能够抵抗简单能量攻击(Simple Power Analysis,SPA)。最后在复旦微电子公司型号为JFM7K325T的现场可编程门阵列(Field Programmable Gate Array,FPGA)中进行了实现和测试。结果表明,该方法能达到较理想的效果。The ECC(Elliptic Curve Cryptography)is an asymmetric cipher which plays an increasingly important role in the field of information security.Most of the current research on ECC is aiming at Weierstrass curves,and less research is aiming at Twisted Edwards curves.In view of the efficiency and safety of scalar multiplication on Twisted Edwards curves,the Twisted Edwards curves are converted to Montgomery curves and the Montgomery scalar multiplication is used to perform fixed point-plus and pointdouble operation in each loop,thus it can resist the SPA(Simple Power Analysis).Finally,the method is implemented and tested on a FPGA(Field Programmable Gate Array)model JFM7K325T of FUDAN Microelectronics.Results indicate that the proposed method can achieve a fairly ideal effect.

关 键 词：椭圆曲线密码 标量乘法 Edwards曲线 Weierstrass曲线 

分 类 号：TN791[电子电信—电路与系统]