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Volume 22 Issue 5
Sep.  2000
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Liu Shengli, Zheng Dong, Wang Yumin. FINDING SECURE ELLIPTIC CURVES OVER GF(2n) AND THEIR BASE POINTS[J]. Journal of Electronics & Information Technology, 2000, 22(5): 824-830.
Citation: Liu Shengli, Zheng Dong, Wang Yumin. FINDING SECURE ELLIPTIC CURVES OVER GF(2n) AND THEIR BASE POINTS[J]. Journal of Electronics & Information Technology, 2000, 22(5): 824-830.

FINDING SECURE ELLIPTIC CURVES OVER GF(2n) AND THEIR BASE POINTS

  • Received Date: 1998-12-28
  • Rev Recd Date: 1999-09-09
  • Publish Date: 2000-09-19
  • 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.
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  • 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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