查询词典 elliptic function of the third kind

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。

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。

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。

A new technique is presented for maximizing the band-edge selectivity of elliptic filters, and then the equal ripple parameter of the quasi-elliptic function can be calculated when the band-edge selectivities of the elliptic function and quasi-elliptic function are the same.

提出了标准椭圆函数的边带优化方法，在此基础上使标准椭圆函数与修正后的准椭圆函数在边带上的衰减相等，得到准椭圆函数的等波纹系数。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

This paper first analyses and summarizes the ststus quo and evolution trend of encryption, some common used cryptograph are introduced, including the algorithms used in symmetric cryptosystem and asymmetirc cryptosystem. We describe the theory of each algorithms and compare the elliptic curve cryptosystem with the other two asymmetric cryptosystems to show the advantages of this algorithm. Second, the principle of ECC is discussed, including the math foundation of ECC, basic conception of elliptic curves, constructiong idea of ECC, operation on the elliptic curve and so on. Third, the current attacks of ECC were analyzed deeply, and an algorithm based on limited prime number field was constructed. We analyzed its realizability in theory, and implement it by using certain function of MIRACL software package. Latter half in this paper, the implementation model of a simple elliptic curve encryption system which based on GF has been introduced. The paper also put a deep analysis on the algorithm of point addition and point multiplication.

本文首先对密码技术的发展现状及其发展趋势进行了分析和综述，详细的介绍了私钥密码系统和公钥密码系统的发展，说明各种算法的原理和优缺点，并给出了一些典型的密码体制的简要分析，重点将椭圆曲线算法与其它几种公钥密码算法比较，说明椭圆曲线算法的优势；其次，探讨了椭圆曲线密码体制的原理，包括椭圆曲线密码的数学基础、基本概念、椭圆曲线密码体制的构造思想等问题；第三作者对椭圆曲线的攻击现状作了详细的分析，针对所使用的大素数域F_p，设计了素数域上安全椭圆曲线产生的算法，从理论上做了可实施性分析，从软件上做了具体实现；在本文的后半部分，提出了一个简单的基于有限素数域上的椭圆曲线加密方按算实现模型，并对SECES中设计的点加和点乘运算进行了深入分析。

The main task of this article contains:compares algorithm and encryption and decryption between the widely-used public key encryption system RSA and ECC;(2) directing against present elliptic curve attack algorithm, uses SEA algorithm to perform choosing of safe elliptic curve and to achieve based on prime field elliptic curve"s ELGamal encryption and decryption and digital signature;(3) discusses elliptic curve"s application on smart card and proposes two identification plans based on EEC.

2针对目前已有的椭圆曲线攻击算法，使用SEA算法实现了安全椭圆曲线的选取，实现了基于大素数域上的椭圆曲线的ELGamal加解密和数字签名。(3)讨论了椭圆曲线在智能卡上的应用，并提出了两种基于ECC的身份认证方案。

An elliptic rotating field is produced when an induction motor operates in asymmetry, this paper proposes a model of jointed motion to describe the motion of an elliptic rotating vector and states that the elliptic rotating vector is jointed with two components, the main one rotates forward at a uniform speed while the adjunctive one jointed at the topend of the main one rotates backward around the joint point at a double speed, both make the elliptic rotating vector rotate at swinging amplitude, speed and direction.

感应电机不对称运转时产生椭圆旋转磁场，本文建立了描述椭圆旋转矢量的接合运动模式，说明椭圆旋转矢量是由一个主矢量带动一个付矢量一起旋转构成的接合矢量，主矢量以匀速旋转，付矢量链接在主矢量顶端同时绕着链接点相对主矢量以二倍速反向旋转，两者共同构成的一个单向椭圆旋转矢量。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Along with the time development, the computer technology more and more thorough various trades and occupations, have provided thorougher and a convenient service for the general users In order to realize raises department's working efficiency, uses the resources fully, reduces the nonessential manpower, physical resource and financial resource goals and so on disbursement, presented various information management system The paper will design university student's dormitory information management system's Web and realizes using the solution The university student's dormitory information management system is one safe and the highly effective proprietory system, designs specially for the information engineering institute This system has used many technologies, for instance JSP, JDBC, Web service and so on The proprietory system use's database is SQL the Server 2000 databases The university student's dormitory information management system's major function includes: May realize to the student's dormitory information inquiry function, including fast inquiry function and classified inquiry function; To the student's dormitory information's input function, the revision function, deletes the function and the statistical function Realizes the dormitory Control section through the system above function regarding the student's dormitory information current management, namely facilitates the dormitory administrative personnels to keep abreast of the student lodging situation and the billeting situation comprehensively promptly; Has provided some simple data inquiry for the user and outputs each kind of information and so on

随着时代的发展，计算机技术越来越深入各行各业，为广大的用户提供了更为周到和便捷的服务。为了实现提高部门的工作效率，充分利用资源，减少不必要的人力，物力和财力的支出等目的，出现了各种各样的信息管理系统。论文将设计一个高校学生公寓信息管理系统的Web应用解决方案并予以实现。高校学生公寓信息管理系统是一个安全和高效的专用系统，专为信息工程学院设计。这个系统使用了很多技术，比如JSP，JDBC ，Web服务等。专用系统使用的数据库是SQL Server 2000 数据库。高校学生公寓信息管理系统的主要功能包括：可以实现对学生公寓信息的查询功能，包括快速查询功能和分类查询功能；对学生公寓信息的录入功能，修改功能，删除功能和统计功能。通过系统上述功能实现公寓管理部门对于学生公寓信息的日常管理，即方便公寓管理人员及时全面地掌握学生住宿情况及公寓分配情况；为用户提供了一些简单的数据查询并输出各种信息等。

Panorama Many people are dancing in a large sitting room.

在一个大客厅里，许多人在跳舞。

We fully understand how a microwave oven cooks food, it is first necessary to talk ...

我们充分理解一个微波炉煮的食物，这是首先要谈。。。