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If the starting point and ending point of the curve are the same, a complete ellipse is drawn

如果曲线的起点和终点相同，就可以画出一个完整的椭圆。

Through point-by-point scanning measurement for elliptic cylinder by phase method, the height difference between neighbouring isohypses is:△z≈4.5mm, and measuring accuracy is±1mm.

用相位法对椭圆柱面样品进行逐点扫描测量，测得相邻等高线高差△z≈4.5mm，测量精度为±1mm。

The algorithm has been realized on PC by assembly language. Hence the problem of how to choose a base point and how to code data into a point over an elliptic curve is resolved completely.

在PC机上用汇编语言实现的结果表明，该基点选取算法适于微机实现且实际可行，从而全面解决了椭圆曲线密码体制中基点选取及如何把数据编码为椭圆曲线上点的问题。

Besides, how to achieve fast point multiplication will influence the performance efficiency of the whole encryption system; in this article, for different situations, signed binary method and rolling window method are respectively applied to perform quick operation of elliptic curves point multiplication.

在密码层上实现了基于大素数域GFp=2~(192-2~(64)-1的密钥交换、ELGamal加密和椭圆曲线数字签名。

In the process of elliptic curve digital signature verification, the elliptic curve scalar multiplication and the elliptic point addition, which are under different coordinates, need to be calculated twice and once, respectively. With operands allocation, the two operations in the thesis are using the shared registers and arithmetic units as well as the same modular inverse process. No extra resource is needed for the introduction of point addition. Hence the resource utilization efficiency is optimized.

论文对这两种不同坐标系下的计算进行了寄存器和运算单元的统一调度，使它们的求逆运算共用同样的流程，减小了控制状态机的复杂度，并且在实现标量乘法的基础上，没有增加额外的运算单元或寄存器，点加运算的所有计算资源均和标量乘法公用，最大限度的提高了资源利用率。

This article first introduces the math foundation required by ECC,including the addition rule for elliptic curve point defined over finite field.Then , the principle of ECC is discussed and its security and efficiency of ECC are analyzed.Third, a cryptosystem is designed through analyzing the security requiration, choosing the elliptic curve domain parameters,denoting field element,elliptic curve and elliptic curve point,choosing associate primitves and schemes andpartitioning functional module.Forth, how to develop a crytosystem based on elliptic curve encryption algorithm is investigated.Fifth, a cryptosystem we have developed by us and the testing result is described.

本文首先介绍了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；其次探讨了ECC的原理，分析了ECC的安全性和有效性；第三，设计了一个基于ECC的加密系统，包括系统的安全需求分析，域参数选择，域元、椭圆曲线、点的表示，原语和方案的选择，及整个系统的模块功能划分；第四，在设计的基础上，研究如何开发一个基于椭圆曲线的加密系统；第五，描述了一个我们已经设计与开发的基于椭圆曲线的加密系统，并给出了相应的测试结果。

Elliptic curves discrete logarithm ; elliptic curve domain parameter ; point group ; base point ; quadratic remainder ; quadratic congruence equation

椭圆曲线离散对数；椭圆曲线域参数；点群；基点；平方剩余；二次同余方程

Elliptic Curve.Cryptosystem Scalar multiplication. Point add. Point double. FPGA.

公钥密码体制，椭圆曲线密码体制，标量乘，点加，倍点，FPGA

For a monotone twist map the well-known Birkhoff fixed point theoremsays that the circles with rational rotation number will break up whence a finitenumber of pairs of periodic points arise,half of which are elliptic and the othershyperbolic.Moreover,around each elliptic periodic point a few of new invariantcurves will appear and make a picture of phase space with a self-similar structure.Again one may ask is there a similar picture for higher dimensional Hamiltoniansystems?

对于单调扭转映射，著名的Birkhoff不动点定理指出，在通有情况下旋转数为有理数的不变曲线一般会破裂，在原来的不变曲线附近会产生有限多对周期点，其中一半是双曲的，一半是椭圆的，而在椭圆型周期点的周围又会产生一圈圈的不变曲线，使得椭圆周期点附近的动力学行为和整个相空间的动力学行为十分相象，换句话说，整个相空间具有无限嵌套的自相似结构，自然又产生了一个问题：对于自由度数目大于2的高维哈密顿系统，其相空间是否有类似的图象？

Finally indicated:the light compensation point of Elodea nuttallii between 10 ℃-20 ℃ is in a declining trend, and reaches the lowest point at about 20 ℃,and then between 20 ℃-30 ℃ within the gradual increase.

结果表明：伊乐藻的光补偿点在10℃-20℃范围内呈下降趋势，并在20℃左右时达到最低点，在20℃-30℃范围内逐渐上升。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。