Computing the order of the Jacobian of Koblitz hyperelliptic curve

The hyperelliptic curve cryptosystem system is built over hyperelliptic curve based on the discrete logarithm problem.By virtue of fast group operation on the Koblitz hyperelliptic curve,there is a way to realize digital signature and identity authentication in a limited bandwidth and memory network environment.Using the Newton formula,a new method to fast compute of the order of the Jacobian of Koblitz hyperelliptic curve is given in this paper,which can be achieved without factoring or solving polynomials, and rapidly realization.Then a new way is proposed to find safe hyperelliptic curves.At last some examples are shown.