基本运算

Based on the research results of Chaos theory, in this dissertation, it has made detailed analysis of the chaotic signal generator. Firstly, the characteristic and various detection methods of chaotic signal are recommended. Secondly, with the aid of software, such as MATLAB, PSPICE, EWB, etc, discussion of the process of generating chaotic signal proceeds. Through simulation, the output result of several kinds of chaotic circuit are analyzed and compared. Thirdly, aiming at Chuas chaotic circuit, through debugging, the impacts by components and parts in the circuit, such as operation amplifier, capacity, inductor, etc, has been further investigated. And then provides a new scheme to implement Lorenz chaotic system, the circuit design and analysis are presented in detail and it can be realized by the hardware of programmable arrays FPGA, the experimental results indicate that this scheme has the advantages of easy operation, flexible design and high efficiency. An application example in secure communications is also provided. Finally, through picking up the characteristic parameter-Lyapunov exponent of the Chaos we can analyze the performance of different chaotic signal generators.

本文在混沌理论研究成果的基础上，对混沌信号的产生做了详细的分析，涵盖以下内容：首先介绍了混沌的定义，混沌信号的基本特性和各种判别方法，特别是对简单的一维Logistic映射的硬件实现问题做了初步探索；其次对混沌信号的产生方法进行讨论，借助于MATLAB、PSPICE、EWB等仿真软件，对几种混沌电路输出的混沌信号进行了分析比较，并在此基础上针对典型三阶连续自治系统Chua's电路作进一步实验研究，通过混沌电路调试，深入研究电路中各元器件，特别是运算放大器、电容、电感等对混沌信号时域以及频谱的影响；再次研究连续混沌系统的数字化硬件产生，设计了Lorenz混沌电路在现场可编程门阵列FPGA上实现的新方案，在保密通信中的应用实验结果表明该方案具有操作简单、设计灵活、效率高等优点；最后针对不同混沌系统，采取不同算法，提取混沌特性参数Lyapunov指数，进而对不同的混沌信号发生器的性能进行了分析。

The soundness and completeness theorem of this method were proved at last. This part consists of the following points: 1. The properties of the indecomposable extremely simple form of LP were discussed, the theorem shown that every logical formula of LP was equals of a generalized conjunction normal form. 2. The method for judging a logical formula is a indecomposable extremely simple form or not was discussed, the necessary and sufficient conditions of a logical formula with not more than three implicative connective being a indecomposable extremely simple form was given. 3. The α-resolution fields of the indecomposable extremely simple form of LP were discussed, some elementary results were obtained. 4. The automated reasoning method based on the resolution principle of classical logic was discussed, the author given a method to describe the set of clauses by using a matrix, and translated the resolution of two clauses to column operations of this matrix.

二、关于格值命题逻辑系统LP中α-自动推理方法的研究 1、对LP中不可分极简式的性质进行了研究，证明了LP中任何一个格值逻辑公式等值于一个广义合取范式； 2、对LP中不可分极简式的判定方法进行了研究，讨论了含有不超过3个蕴涵运算的格值逻辑式为不可分极简式的充分必要条件； 3、对LP中不可分极简式的α-归结域进行了研究，得到了一些基本结果； 4、对经典逻辑中基于归结原理的自动推理方法进行了研究，给出了用符号矩阵表示子句集合的一种方法，把不同的归结过程转换成矩阵的列变换。

Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.

本文首先介绍了椭圆曲线密码的有关基本概念；其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算，对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析，给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法，并对IEEE P1363 标准给出的标量乘法做了改进，使得标量乘法的运算效率提高了近10%；最后介绍了利用复乘计算标量乘法的方法，对已有的方法进行总结归纳，得出完整的计算过程，并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法，得出一类普遍的结果，并给出了进一步用复乘加快标量乘法的思路。

Therefore, from the most basic computing element is introduced, and MATLAB ordered three of its use.

因此，从最基本的运算单元出发，介绍MATLAB的命令及其用法3。

In the last section ,according to the basis theory of rough set ,we propose the definition of an approximation space which is basing on the convex cone that contain the origin ,and define the upper and the lower approximation of convex cone ,then discuss some operation properties.

文章的最后是基于粗糙集的基本理论，提出了可利用含原点的凸锥构造一个近似空间，定义了此空间的上、下近似，总结了一些运算性质。

Based on the rule that all the coordinate value of the basic vector is integral in coordinate plane, an algorithm for approaching the reference vector in coordinate plane was drawn out, which is easy to be realized by arithmetic and rounding operation.

本文根据基本矢量在两相坐标平面的坐标都是整数的规律，总结得到了在两相坐标平面下对参考电压矢量进行逼近的算法，该算法只需要进行简单的四舍五入与加减运算，易于实现。

In this thesis, the basic concepts of cryptogram including number theory and modular arithmetic are introduced.

本文介绍了密码学的基本概念，包括数论的基础知识和模运算的概念。

In chapter two, some necessary and basic materials of the finite field arithmetic theory and elliptic curve cryptosystems theory are introduced.

第二章给出有限域运算和椭圆曲线密码体制理论的基本知识和相关性质。

With the emphasis on the results obtained by the author, the basic scheme of the finite field theory and elliptic curve cryptosystems theory is sketched.

全文在强调作者所取得研究成果的同时给出了有限域运算理论和椭圆曲线密码体制理论的基本框架。

This paper brought forward some new design schemes based on the principle and signal processing algorithm of velocity detector, and introduced the hardware construction of the velocity detector based on Depolarizer and S3C2410A microprocessor. The high-efficient ARM program of radical 4-FFT was designed according to the architecture characters of ARM core. In the process of code designing, the instruction scheduling and register allocation were controlled subtly, and the fixed-point number's storage format and computing method of float number were provided. Barrel shifter and 5-lever pipeline were fully utilized and the pipeline interlock was avoided.

针对多普勒测速仪的基本原理和信号处理算法提出了新的设计方案，介绍了由多普勒收发前端和三星S3C2410A处理器构成的测速仪的硬件结构；并结合ARM内核设计特点实现了基4时间抽取快速傅里叶变换算法，针对大多数ARM处理器硬件上不支持浮点运算，提出了把浮点数以定点数格式存储和计算的方法，充分利用桶型移位器和5级流水线，避免了流水线互锁问题。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。