Fast Multiplication on a Family of Koblitz Elliptic Curves
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    Abstract:

    Fast point multiplication on a family of Koblitz elliptic curves in characteristic 3 is considered. Such curves are suitable for establishing provable secure cryptographic schemes with low bandwidth. By utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, it is shown that there is a fast point multiplication method without precomputation on the curves, which is 6 times faster than the ordinary repeated-double-add method. The idea of the fast method is independent of the optimization of finite field arithmetic and the choice of coordinate expression for points of the elliptic curves.

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胡磊,冯登国,文铁华.一类Koblitz椭圆曲线的快速点乘.软件学报,2003,14(11):1907-1910

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History
  • Received:September 12,2002
  • Revised:December 31,2002
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