Efficient algorithms for the Jacobian variety of hyperelliptic curves $y^2=x^p-x+1$ over a finite field of odd characteristic $p$
Efficient algorithms for the Jacobian variety of hyperelliptic curves $y^2=x^p-x+1$ over a finite field of odd characteristic $p$
复制标题
在奇数特征 $p$ 的有限域上计算雅可比变体超椭圆曲线 $y^2=x^p-x 1$ 的高效算法
DOI：
10.1007/978-3-642-57189-3_6
复制
发表时间：
2000
影响因子：
0.7
通讯作者：
K. Sakurai
中科院分区：
文献类型：
--
作者：
I. Duursma;K. Sakurai
我们开发了由奇数特征p的有限场f p n上方程y2 = xp-x+1定义的高纤维曲线的雅各布的有效算法。我们首先确定曲线的ZETA函数，该曲线产生了Jacobian的顺序。我们还研究了Frobenius操作员，并使用它来表明，对于场扩展序列，y2 = xp-x+1在有限的场f p n，n prime to p to p的有限场f p n上，雅各布式具有环状基团结构。我们此外，通过使用具有较小特征值的Frobenius以外的有效运算符，提出了一种在Jacobian中更快的标量乘法的方法。
We develop efficient algorithms for the Jacobian of the hyperelliptic curve defined by the equation y2=xp-x+1 over a finite field F p n of odd characteristic p. We first determine the zeta function of the curve which yields the order of the Jacobian. We also investigate the Frobenius operator and use it to show that, for field extensionsequation y2=xp-x+1 over a finite field F p n , of degree n prime to p, the Jacobian has a cyclic group structure. We furthermore propose a method for faster scalar multiplication in the Jacobian by using efficient operators other than the Frobenius that have smaller eigenvalues.