有理点

寻找对椭圆曲线公钥体制（ECC）有用的椭圆曲线，关键在于求有限域上椭圆曲线有理点群的阶。

The key to finding a useful elliptic curve for Elliptic Curve Cryptosystem ( ECC ) is to compute the order of elliptic curve rational points group over a finite field .

关于圆周上有理点的稠密性

The density of rational points on the circle

本文研究了有限域F~q上几类超曲面Fq&有理点的个数，并对其中某些超曲面，计算出他们的zeta函数。

In this paper , we studied the number of F_q-rational points for several hypersurface over finite filed F_q , and obtained Zeta functions for some of the hypersurface mentioned above .

超椭圆曲线密码体制所基于的除子类群，又称Jacobian群，其结构与运算比有理点群要复杂得多。

The divisor class group , often called Jacobian group , based on which hyperelliptic curve cryptosystems are constructed , is much complicated than the elliptic curve rational point group .

以椭圆曲线上的有理点构成的Abel群为背景结构，实现各种密码体制已是公钥密码学领域的一个重要课题。

Implementing various cryptosystems , based on the Abel group composed of the points on elliptic curves , has already developed into an extremely important subject in cryptology research .

椭圆曲线Weierstrass方程存在一个系数与椭圆曲线上有理点群的标量乘法无关[4]，从而出现了一系列相应的攻击方法。

Since there are some coefficients in the Weierstrass equations of the ellip-tic curves which are independent with the scalar multiplication on the group consisting of the rational points of the curves [ 4 ] , a series of relative attack methods are proposed .

椭圆曲线有理点扭子群的明显分类

Explicit Classification for Torsion Subgroups of Rational Points of Elliptic Curves

一类缺项级数在有理点上值的超越性

The Transcendence of the Values of Certain Gap Series in Rational Points

方法利用椭圆曲线上的有理点以及同余数的相关信息。

Methods Using some facts of rational points of elliptic curves and congruent numbers .

有理点的个数及其估计；有限域上的基；

Number of rational points and their estimates ;

主要的理论工具为椭圆曲线有理点群的指数和估计。

Important tool in the proof is an estimate of character sums along elliptic curves .

插值细分曲线有理参数点的精确求值卫星定位值间的内插最初用的是推算航行法。

EXACT EVALUATION OF THE INTERPOLATORY SUBDIVISION CURVES AT RATIONAL PARAMETER VALUES Interpolation between satellite positions was initially carried out by dead-reckoning procedures .

关于一类Müntz有理逼近的点态估计

On Pointwise Estimate for a Class of M ü ntz Rational Approximation

重心有理插值配点法分析压杆稳定问题

Stability Analysis of Bar Using Barycentric Rational Interpolation Collocation Method

而采用重心有理插值配点法求解微分方程，具有计算公式简单、精度高、数值稳定、计算节点适应性好等优点。

Adopting barycentric rational interpolation collocation method to solve differential equations has the advantage of simple calculation formula , high precision , numerical stability and good adaptability to calculate nodal etc. The work of this paper includes discussion of the selection of interpolation points and barycentric weights .

对于电报方程的求解，我们采用重心有理插值配点法，对时间域和空间域上的节点均采用重心有理插值来近似未知函数，将初边值条件也进行相同的离散。

For the calculation of telegraph equation , we use barycentric rational interpolation collocation method . For the nodes of time domain and space domain , we approximate the unknown functions with rational interpolation . And we discrete the initial boundary value conditions with the same method .