橢圓曲線密碼體制中點(diǎn)的數(shù)乘的一種快速算法
A fast algorithm for the point multiplication in elliptic curve cryptosystems
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摘要: 該文基于橢圓曲線密碼體制,提出了橢圓曲線上點(diǎn)的數(shù)乘的一種快速算法.該算法通過引入2~k進(jìn)制序列,縮短了乘數(shù)的相應(yīng)序列長(zhǎng)度,從而大大減少了點(diǎn)的數(shù)乘中的加法運(yùn)算次數(shù),并且分析了k的最佳選取,使得我們提出的算法比通常點(diǎn)的數(shù)乘算法效率提高了60％以上。
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關(guān)鍵詞:
- 橢圓曲線; 快速算法; 密碼學(xué)
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]盧開澄,計(jì)算機(jī)密碼學(xué)(第二版),北京,清華大學(xué)出版社,1998,241-243.[5]四川大學(xué)數(shù)學(xué)系高等數(shù)學(xué)教研室,高等數(shù)學(xué)(第一冊(cè)),北京,高等教育出版社,1995,170-172. -
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