Koblitz型超椭圆曲线Jacobian阶的计算

超椭圆曲线密码体制是基于超椭圆曲线上的离散对数问题的困难性而建立起来的.由于Koblitz型超椭圆曲线Jacobian群中有快速的群运算,因此这类曲线常被用来实现在带宽和存储受限的环境中的数字签名和身份认证.本文基于牛顿公式提出了一个快速计算Koblitz型超椭圆曲线Jacobian的阶的新方法,该方法不需分解多项式或去求多项式的根,可以快速实现.这为寻找安全的超椭圆曲线提供了新的方法.

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.