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Use is made of the elliptic coordinates for the ease of treating ellipse shaped boundary, while the analytical results for the components in the Cartesian coordinates are provided for convenience of application.

分析引入椭圆坐标,以助于处理问题的边界条件,并最终给出直角坐标下各分量的对应结果,以便于实际应用。

IGMs are a kind of experimentally new-identified optical mode, standing with apparent potential in design and application. However, the mathematical expression of IGMs under Elliptic Cylindrical coordinates, preventing us from understanding IGMs instinctively, stands a formidable challenge in application. The pure mathematical expressions of IGMs are composed by a great deal of calculation, which also bids us no help in common use. I am, therefore, prompted to build an easier mathematical approach in this study.

Ince- Gaussian modes为在实验中可见的一种崭新型态的光学模态,对於我们在应用和设计上的实现,拥有许多潜力;然而,由於IGMs是在椭圆圆柱座标系下的数学来表示,造成了我们无法直觉的去了解,也成了我们在使用上的一大考验; IGMs的不易亲近,也让我们无从进一步去了解其物理特性,若纯粹以数学出发,又包含了庞大的运算,无法达到普遍的运用,是故我希望能在这篇论文使用简单的数学描述来达成对IGMs较平易近人的理解。

So the research of elliptic curve in this paper has an important value.

本文研究椭圆曲线密码算法,具有重要的理论意义和应用价值。

This article deals with the design and implementation of a cryptosystem based on elliptic curve .

本文主要完成了一个基于椭圆曲线的加密系统的设计和实现。

In this dissertation the elliptic curve cryptosystems and the related algorithms are investigated.

本文主要研究椭圆曲线密码和其中的有关算法。

In chapter three, the elliptic curve cryptography is studied.

第三章着重研究椭圆曲线密码系统。

This paper presents the encryption algorithm based on elliptic curve of the basic working principles.

本文首先给出基于椭圆曲线加密算法的基本工作原理。

Both of them were based on Elliptic Curve Cryptosystem and had high security.

两种算法均基于椭圆曲线密码体系,具有较高安全性。

This is all pretty elementary, and doesn't even refer to the group law on the elliptic curve.

这两个命题都是初级的,甚至连椭圆曲线的群定律都不用。

Elliptic curve cryptography is an important subject in the field of public key cryptography.

椭圆曲线密码体制是公钥密码学领域的一个重要课题。

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