椭圆点

其次介绍了ECC的数学基础，对有限域上椭圆曲线点的运算规则进行了详细描述。

Then , this paper introduces the math foundation required by ECC , including the addition rule for elliptic curve point defined over finite field .

等弧长椭圆曲线点的放样与实践

Setting-up and Practice of Equal Segmental Arc of Ellipse Curve Points

其中重点研究了投影椭圆边缘点的提取以及边缘点的匹配。

And the emphases are the projection elliptical edge extraction and matching edge point .

最后给出了明文嵌入算法在椭圆曲线点的存储及传输中的应用。

Finally we provide its applications on storage and transmission of points on elliptic curves .

强震危险地点的判定及强震预测&利用椭圆脐点突变模式

Judgement of strong earthquake hazard area and prediction of strong earthquake ── by elliptic umbilic catastrophe model

提高椭圆曲线点积运算的效率是椭圆曲线研究的一个核心问题。

To improve the efficiency of the algorithm of point multiplication on elliptic curves is a key problem .

椭圆夹杂点热源问题的研究

The Study on the Thermoelastic Problem of an Elliptical Inclusion with a Point Heat Source in the Matrix

实现了算法的快速优化，其原理与有限域算术优化和椭圆曲线点的坐标表示的选取无关，其运算速度是通常的重复加倍&点加算法的6倍。

The idea of the fast method is independent on the optimization of finite field arithmetic and the choice of coordinate expression of points of elliptic curves .

具体包括不同尺度椭圆分割点取值研究，多尺度算法搜索区域面积研究和最短路径查询时间研究等。（3）二树椭圆最短路径算法研究及其性能分析。

Including study on value of split point between different scale ellipses , and study on shortest path query time as well as searching area of multi-scale algorithm . ( 3 ) Two-tree ellipse shortest path algorithm and its performance analysis .

在对水平位移观测资料的误差分析中，用误差椭圆替代点位中误差来计算观测的误差量，以便确定是边坡位移还是测量误差。

In error analyses for horizontal displacement measurement data , the observed errors are calculated with error ellipse instead of point root - mean - square errors , so as to judge whether they are just slope displacement or the measuring errors .

由于椭圆量子点本征态的特征，使得沿椭圆长轴方向布置的导线对本征态的影响很小，每个束缚态都得以稳定地驻留于量子点中并反映在电导曲线上。

Due to the character of eigen states in elliptic dot , the influence of connecting lead to the eigen states is quite small , every bound state can sit stable in the dot and show their existence in the conductance curve .

提高椭圆曲线上点加运算的速度在整个基于FPGA设计的椭圆曲线密码应用系统实现中极为关键。

The speed of point addition on elliptic curve is critical in elliptic curve application cryptosystem design based on FPGA device .

抵抗SPA和DPA的椭圆曲线上点的标量乘法

Scalar Multiplication on ECC Resistant Against SPA and DPA

在此，我们结合几何图形给出了Fp上椭圆曲线的点加和倍点的数学描述。

Herein below , in accordance with the geometric figures , we bring forward a new mathematical description of point addition operation and point doubling operation on the elliptic curve based on the field F_p .

在有限素整数域Fp上定义了一条椭圆曲线及点群运算规则，并由此构造出一种椭圆曲线密码体制。

An elliptic curve is defined over a finite field GF ( p ) for a given set of operation rules .

为了提高椭圆曲线上点的数乘的运算效率，本文提出了椭圆曲线离散对数（ECDLP）上一种改进的快速冗余算法。

For the operational efficiency on the numerical multiplication of points on elliptic curves to be heighten , in this paper , a better fast redundant binary algorithm for the elliptic curves discrete logarithm problem ( ECDLP ) is presented .

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

椭圆曲线上点的数乘中窗口最佳长度的选取

Best of all windows for point multiplication in elliptic curve cryptosystems

正二测轴测图中椭圆的八点比例作图法

A Method in Proportion to drawing ellipses in dimetric projection

过椭圆外一定点作其法线的求解分析及其几何逼近作图

Solution analysis and geometric approach graphic method of ellipse normal

关于椭圆内整点问题

On the lattice - point problem in a ellipse

椭圆曲线上点的数乘的一种固定窗口算法

Fixed window algorithm of scalar multiplication in elliptic curves

圆与定压缩系数椭圆截面三点初步定心

Preliminary three points centering for circle and fixed compressibility factor ellipse cross - section

椭圆曲线上点的标量乘法

Scalar Multiplication of the Point on Elliptic Curve

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 .

通过对边缘点集的归一化运算，有效地正则化了提取椭圆的边缘点集的病态性；

With normalization of the digital edge set , the ill-posed problem is effectively regularized .

椭圆上特殊点的准确作图原理简析

A Brief Analysis of the Principle of Drawing Graphs Accurately on Special Points of Ellipses

椭圆曲线上点的标量乘和加法运算是椭圆曲线密码算法的核心运算。

Scalar multiplication and point addition in elliptic curves are core operations in elliptic curve cryptosystem .

标定圆上的点集与像椭圆上的点集，之间的对应关系是常用来标定摄像机参数的方法。

Points on the circle and points on the ellipse , the corresponding relationship between them were used to calibrate the camera parameters .

该算法比经典算法减少了点的加法的计算次数，从而加快了椭圆曲线上点的数乘的运算速度。

The algorithm can greatly reduce the number of elliptic point addition , so the efficiency of scalar multiplication in elliptic curves is improved .