域GF(2n)上安全椭圆曲线及基点的选取
FINDING SECURE ELLIPTIC CURVES OVER GF(2n) AND THEIR BASE POINTS
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摘要: 该文系统地介绍了如何利用Weil定理来寻找特征为2的域上的安全椭圆曲线。提出了一种求曲线的基点的算法。求基点的算法中涉及求域元素的迹的问题。该文在最后还提出了一种求域GF(2l)的扩域GF(2lk)上元素的迹的快速实现方法。
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关键词:
- 椭圆曲线密码体制; 基点; 迹
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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