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This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列,主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等,得到如下主要结果:(1)系统讨论椭圆曲线-线性同余序列的一致分布性质,即该类序列是渐近一致分布的,并给出了它的非线性复杂度下界;(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ),这两类序列具有&优&的密码性质,也正面回答了Goubin等提出的公开问题;(3)利用椭圆曲线及其挠曲线构造一类二元序列,其周期为4p(其中椭圆曲线定义在有限域F_p上),0-1分布基本平衡,线性复杂度至少为周期的四分之一;(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计,并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性;(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布;(6)讨论椭圆曲线-子集和序列的一致分布;(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布,线性复杂度等性质。

The general decoding method for Turbo codes provided by the invention adopts enhanced Max-Log-MAP algorithm, makes use of Max-Sum semiring property in the generalized distribution law and combines and simplifies measure and calculation of forward and backward status of traditional binary Turbo codes, which means combining grid graph of traditional binary Turbo codes in nature to ensure that the status measure and calculation of the traditional binary Turbo codes have the same calculation expression way with that of the duobinary Turbo codes so that a general decoding device can both decode the traditional binary Turbo codes and duobinary Turbo codes.

本发明提出的Turbo码通用译码方法采用增强型Max-Log-MAP算法,利用广义分配率中的Max-Sum半环性质,对传统二进制Turbo码的前向和后向状态度量计算进行合并简化,从本质上也就是对传统二进制Turbo码的网格图进行合并,使得传统二进制Turbo码的状态度量具有和双二进制Turbo码一样的计算表达方式,从而使得通用译码装置对于传统二进制Turbo码和双二进制Turbo码都可实现。

Definition of tree ADT, FirstChild-NextSibling Representation, Tree traversals, Applications of trees, Definitions and properties of binary trees, Traversal of trees, Recursive functions of trees, Threaded binary trees, Binary search trees, AVL trees, Splay trees, B-trees, Application of binary trees.

树的定义,树的兄弟表示法,树的遍历,树的应用;二叉树的定义和基本特性,遍历二叉树,二叉树的递归操作,线索二叉树;二叉排序树,平衡二叉树,Splay树,B-树,二叉树应用。

And another construction methods for perfect and quasi-perfect binary array pairs are presented with the help of the relationships among the perfect, quasi-perfect and double quasi-perfect binary array pairs. On the other hand, a new kind of discrete signal is presented in this paper, which is the punctured binary sequence pair and the punctured binary array pair.

另一方面,本文提出了一种新的离散信号,即屏蔽二进序列偶和阵列偶,建立了完整的屏蔽二进序列偶和阵列偶的理论体系,它包括最佳屏蔽二进序列偶理论、最佳屏蔽二进阵列偶理论、准最佳和双准最佳屏蔽二进阵列偶理论,以及屏蔽二元互补序列偶理论。

With the help of these conditions, computer efficiently searches out many quasi-perfect and double quasi-perfect punctured binary array pairs. The relationships among perfect punctured binary array pair, quasi-perfect and double quasi-perfect punctured binary array pair is presented. Specially, when first and second dimension period of the punctured binary ar

定义了非周期屏蔽二元序列偶的自相关函数、屏蔽二元互补序列偶和最佳屏蔽二元互补序列偶,给出并证明了屏蔽二元互补序列偶的变换性质;和它存在的组合允许条件,用计算机搜索出若干最佳屏蔽二元互补序列偶;给出了屏蔽二元互补序列构造出新的屏蔽二元互补序列偶的四种构造方法;并且,给出了利用不同长度的二元互补序列和屏蔽二元互补序列偶构造出新的屏蔽二元互补序列偶的四种构造方法。

Blend various advantages of the coding project of the parameter audio frequencies in the meantime, carried on adjustment on the coder structure, have to a certain signal more the mold piece of coding result, if wave structure analytical transformation short time of the mold piece, double the composition examine and double the transformation short time mold piece etc. is an options to bring into coder, from user while coding according to small together source voice document of small together characteristics, decide whether use and how use, but these vivid constitutions can through a code flow in define several good to mark ratio in advance tell a decoding machine especially, constituting decoding machine is little with complications to without direct influence.

同时融合多种参数音频编码方案的优点,在编码器结构上进行了调整,将只对某类信号有较好编码效果的模块,如谐波结构分析模块、双变换短时成分检测与双变换短时模块等,作为选项纳入到编码器中,由使用者在编码时根据小同源声文件的小同特点,来决定是否使用和如何使用,而这些灵活的设置都可以通过码流中预先定义好的几个标示比特位来告知解码器,对解码器本身的构成与复杂度少没有直接的影响。

The analytical properties of arithmetic coding are investigated, which include the nested intervals property of arithmetic coding, the convergence of arithmetic coding, the concepts of an arithmetic code number and of arithmetic code mapping.

这些分析性质丰富了算术编码的理论,在本文一些重要结论的证明中得到了应用,并简化了证明。

Referring to HMIS public data coding criterion, parts coding management module was designed and established, and parts coding automatic generation function was realized. According to the data collection methods in the reliability theory, maintenance record collection principle was determined, and maintenance record management module was established. Then, by using reliability theory and mathematical statistics method, data statistic analysis and malfunction analysis modules were established, and components failure data statistics, choosing of life distribution law, and predicting of maintenance period were realized.

参照HMIS公用数据编码规范,设计并建立了零件编码管理模块,实现零件编码自动生成功能;根据可靠性理论中数据的收集方法,确定了维修记录收集原则,建立了维修记录管理模块;继而,利用可靠性理论及数理统计方法中对数据的统计分析,建立了数据统计分析、故障分析模块,实现了对零部件故障数据的统计、寿命分布规律的选择及对维修周期的预测。

Information theory and coding, right Shannon source coding theorem simulation, verification of the Shannon coding theorem.

信息论与编码中,对香农信源编码定理的仿真,验证了香农编码定理的可行性。

Basic image coding VC procedures, including Shannon theorem, Huffman coding, bitplane coding in accordance with the importance...

最基本的图像编码VC程序,包括香农定理、霍夫曼编码、位平面编码(按照比特位的重要性编码)等。

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