域GF(2n)上安全橢圓曲線及基點的選取
FINDING SECURE ELLIPTIC CURVES OVER GF(2n) AND THEIR BASE POINTS
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摘要: 該文系統(tǒng)地介紹了如何利用Weil定理來尋找特征為2的域上的安全橢圓曲線。提出了一種求曲線的基點的算法。求基點的算法中涉及求域元素的跡的問題。該文在最后還提出了一種求域GF(2l)的擴域GF(2lk)上元素的跡的快速實現(xiàn)方法。
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關鍵詞:
- 橢圓曲線密碼體制; 基點; 跡
Abstract: This paper systematically introduces how to find secure elliptic curves with the help of Weil theorem, and proposes an algorithm to find base points in the curves. Finally, an efficient method of finding the trace of any element in GF(2lk), which is involved in the algorithm of finding base points, is given. -
Menezes A,Okamoto T,Vanstone S A.Reducing elliptic curve logarithms to logarithms in a finite field,IEEE Trans.on IT,1993,IT-39(5):1639-1646.[2]Koblitz N.A Course in Number Theory and Cryptography,Beijing:Springer-Verlag World Publishing Corp.1990,150-170.[3]Beth T,Schaefer F.Non supersingular elliptic curves for public key cryptosystems.Advances in Cryptology-EUROCRYPT91,Berlin:Springer-Verlag,1992,317-327.[4]McEliece J.Finite Field for Computer Scientists and Engineers,Boston:Kluwer Academic,1987,97-105. -
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