Counting Points on the Jacobian Variety of a

نویسندگان

  • E. Furukawa
  • M. Kawazoe
  • T. Takahashi
چکیده

Counting the order of the Jacobian group of a hyperelliptic curve over a nite eld is very important for constructing a hyperelliptic curve cryptosystem (HECC), but known algorithms to compute the order of a Jacobian group over a given large prime eld need very long running times. In this note, we propose a practical polynomial-time algorithm to compute the order of the Jacobian group for a hyperelliptic curve of type y 2 = x 5 + ax over a given large prime eld F p , e.g. an 80-bit eld. We also investigate the order of the Jacobian group for such curve and determine the necessary condition to be suitable for HECC, that is, to satisfy that the order of the Jacobian group is of the form l 1 c where l is a prime number greater than about 2 160 and c is a very small integer. Moreover we show some examples of a suitable curve for HECC obtained by using our algorithm.

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تاریخ انتشار 2002