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To raise the efficiency of scalar multiplication on elliptic curve,a scalar multiplication algorithm based on double base number system over binary field was improved.

为了提高椭圆曲线标量乘法效率,对二元域上椭圆曲线的基于双基数的标量乘法进行改进。

In the elliptic curve binary field,it needs less computation amount for that the Montgomery algorithm only computes the x coordinate in the whole course and gets the y coordinate in the last step.

在椭圆曲线二进制域上,Montgomery算法利用在计算kP过程中只需计算x坐标,在最后才恢复y坐标的特性,使该算法的计算量更少。

Next it gives out some prove and illustrations to the algorithms used in the hardware design, aiming at each calculation modules referred in ECC., which concludes the basic mathematic calculation over binary field and the point multiplication algorithm over elliptic curve.

接下来我们会针对ECC中涉及的各个运算模块,对硬件设计中所用到的一些特殊算法给出相应的证明或者说明,这包含一些二元域上的基本数学运算算法和椭圆曲线上的点乘算法。

The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.

具体安排如下:第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型,证明了该边值问题弱解的存在唯一性,在此基础上研究了自然电位测井电阻率识别问题:然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法,利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响,取得了满意的结果。

A class of boundary value problem for elliptic equation with two parameters is considered.

由解的结构指出,在两参数一定的情况下,相应问题的解只具有二个边界层。

The meshless method for a kind of semi-linear elliptic boundary value problem is discussed.

讨论了一类半线性椭圆边值问题的无网格方法。

The Neumann Problem of Laplace equation is an important elliptic boundary value problem and has extensive applications.

Laplace方程的Neumann问题作为一类重要的椭圆边值问题,有广泛的运用背景。

At last we apply the results to a kind of fourth order elliptic boundary value problem and Duffing equation.

最后我们将所得结论应用到一类四阶椭圆型微分方程和Duffing方程,给出了它们的解存在唯一的一些结果。

The article deals with the discontinuous boundary value problem for nonlinear elliptic complex equations of second order.

讨论了二阶非线性椭圆型方程在多连通区域上的间断边值问题。

In chapter four, the coefficient which is not large for nonsymmetric and indefinite elliptic boundary value problems is considered.

本文主要考虑低阶项的系数不是很大的情况下的非对称不定椭圆边值问题。

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