特征3有限域上椭圆曲线的co-Z Montgomery算法

发布时间：2018-05-16 07:32

本文选题：椭圆曲线 + Montgomery算法　；参考：《计算机学报》2017年05期

【摘要】：椭圆曲线公钥密码是公钥密码体制的主流方向之一.由于密钥短、计算速度快,该体制在智能卡和手机存储卡等受限的环境中得到了广泛的应用.椭圆曲线密码体系中最耗时的运算是标量乘.标量乘需要安全、有效、快速的实现算法.Montgomery算法是计算椭圆曲线标量乘的算法之一,它能够有效地抵抗简单能量分析.在Montgomery算法结构的基础上,文中首次利用统一Z坐标技巧和循环中间阶段不计算Y坐标的技巧,改进了有限域GF(3~m)上椭圆曲线的点加和倍点公式,构造了抵抗简单能量攻击的co-Z Montgomery算法.设I,M,C分别表示有限域上的求逆、乘法、立方.当域上的平方和乘法使用相同的算法时,理论分析表明每轮循环中,co-Z Montgomery算法比仿射Montgomery算法快I+C-5 M,比射影Montgomery算法快C+2 M,比使用"Selected Areas in Cryptography"2012上快速点加、倍点公式的Montgomery算法快2C+M.在文章"特征3有限域上椭圆曲线的Montgomery算法"的模拟实验环境下,结果表明该算法比上述算法分别快26.3%、19.0%、20.6%;Sage云平台的实验结果表明该算法比上述算法分别快24.1%、20.1%、23.1%.
[Abstract]:Elliptic curve public key cryptosystem is one of the main directions of public key cryptosystem. Because of the short key and fast computing speed, this scheme has been widely used in the limited environment such as smart card and mobile phone memory card. The most time-consuming operation in elliptic curve cryptosystem is scalar multiplication. Scalar multiplication needs to be implemented safely, efficiently and quickly. Montgomery algorithm is one of the algorithms to calculate scalar multiplication of elliptic curves, which can effectively resist simple energy analysis. On the basis of the structure of Montgomery algorithm, the technique of unified Z-coordinate and the technique of not calculating Y-coordinate in the middle stage of the cycle are used for the first time to improve the formula of point addition and point doubling of elliptic curve on the finite field GFN 3m. The co-Z Montgomery algorithm to resist simple energy attack is constructed. Let I _ M _ M _ (C) denote the inverse, multiplication, and cubic of finite fields, respectively. When the square sum multiplication in the domain uses the same algorithm, the theoretical analysis shows that the co-Z Montgomery algorithm in each cycle is faster than the affine Montgomery algorithm I C-5 M, the projective Montgomery algorithm C 2 M, and the Montgomery algorithm which uses the "Selected Areas in Cryptography" 2012 fast point addition and double point formula is faster than the Montgomery algorithm. In this paper, the Montgomery algorithm of elliptic curve on the finite field of feature 3 is simulated. The results show that the algorithm is 26.3and 19.019.019.020.6Sage cloud platform faster than the above algorithm, respectively. The experimental results show that the algorithm is 24.1and 20.1and 23.1faster than the above algorithm, respectively.
【作者单位】：中国科学院信息工程研究所;中国科学院DCS中心;
【基金】：国家自然科学基金(61502487,61272040) 国家“九七三”重点基础研究发展规划项目基金(2013CB338001)资助
【分类号】：TN918.1

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