论文标题:椭圆曲线上点的标量乘法
Scalar Multiplication of the Point on Elliptic Curve
论文作者 张宁
论文导师 肖国镇,论文学位 硕士,论文专业 密码学
论文单位 西安电子科技大学,点击次数 476,论文页数 50页File Size279k
2005-01-01论文网 http://www.lw23.com/lunwen_36433337/ 椭圆曲线密码; 标量乘法; 复乘; 边信道攻击
elliptic curve cryptosystem; scalar multiplication; complex multiplication;side channel attack
椭圆曲线公钥密码是目前公钥体制中比特安全最高的一种密码体制,是公认的下一代通用的公钥密码系统。本文主要考虑了椭圆曲线密码的快速实现的内容—点的标量乘法。本文首先介绍了椭圆曲线密码的有关基本概念;其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算,对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析,给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法,并对IEEE P1363 标准给出的标量乘法做了改进,使得标量乘法的运算效率提高了近10%;最后介绍了利用复乘计算标量乘法的方法,对已有的方法进行总结归纳,得出完整的计算过程,并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法,得出一类普遍的结果,并给出了进一步用复乘加快标量乘法的思路。
Elliptic Curve Cryptosystem (ECC) has the highest bit security among Public-Key Cryptosystems. This thesis mainly has a study of the fast implementation problems of the ECC—the scalar multiplication of the point. Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.
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