椭圆曲线密码体制中点的数乘的一种快速算法
A fast algorithm for the point multiplication in elliptic curve cryptosystems
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摘要: 该文基于椭圆曲线密码体制,提出了椭圆曲线上点的数乘的一种快速算法.该算法通过引入2~k进制序列,缩短了乘数的相应序列长度,从而大大减少了点的数乘中的加法运算次数,并且分析了k的最佳选取,使得我们提出的算法比通常点的数乘算法效率提高了60％以上。
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关键词:
- 椭圆曲线; 快速算法; 密码学
Abstract: In this paper, a new fast algorithm for the numerical multiplication of the points on elliptic curves is presented. By introducing 2k sequence representation for number, the length of numerical multiplication is shortened, so that the number of addition operation on elliptic curves is decreased greatly. Moreover, the optimal choice of k is analyzed and the efficiency of the algorithm presented is improved about 60. -
N. Kobliz, Elliptic curve cryptosystem, Mathematics of Computation, 1987, 48(177), 203-209.[2]V. Miller.[J].Uses of elliptic curve in cryptography, Advances in Cryptology-CRYPTO85, LNCS,218, Berlin, Springer-Verlag.1986,:-[3]N. Demytko.[J].A new elliptic curve based analogue of RSA, Advances in CryptologyEUROCRYPT93 Proceedings, Springer-verlag.1994,:-[4]卢开澄,计算机密码学(第二版),北京,清华大学出版社,1998,241-243.[5]四川大学数学系高等数学教研室,高等数学(第一册),北京,高等教育出版社,1995,170-172. -
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