查询词典 elliptic motion

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。

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。

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 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。

This thesis consists of three chapters .In chapter one , the distributions of the last exit time and the corresponding results of Brownian motion in Markov process are introduced ,and previous remarkable achievements on the excursion of Brownian motion are numerated too ,also ,we introduce the main results and the history of elliptic diffusion process; In chapter two ,we summarily describe the excursion in Markov process and the result of the first hitting time of the elliptic diffusion process ; In last chapter ,we study estimates for the distributions of above three maximum excursions and minimum excursion in the elliptic diffusion process on R (d≥3), which leads the excursion of Brownian motion on ball on R (d≥3) to become a particular case .

全文共分三章，第一章介绍对称Markov过程中布朗运动的未离时分布及相关研究结果，列举了前人对布朗运动的游程问题的研究成果，并用较多篇幅介绍了一类特殊且非常重要的扩散过程——一致椭圆扩散过程的研究历史和本文的主要研究结果；第二章介绍Markov过程有关停时及游程的概念，叙述了一致椭圆扩散过程的定义，并给出了一致椭圆扩散过程有关首中时的结果；第三章是本文的核心部分，详细讨论了暂留一致椭圆扩散过程关于R~d(d≥3)上球的三类极大游程和极小游程的分布估计，使得布朗运动关于球的游程问题成为特例。

The simulation study mainly concentrates on the following aspects: the relations of attack angle versus caudal fin motion, the phase difference of heaving and pitching motion of caudal fin motion, swimming velocity and body motion, body wave length and body motion, heaving amplitude and body motion, Strouhal Number and body motion.

具体研究内容包括：最大击水角度对尾鳍运动的影响；尾鳍摆动—平动运动相位差对尾鳍运动的影响；游动速度对鱼体运动的影响；鱼体波波长对鱼体运动的影响；尾鳍后缘最大摆幅对鱼体运动的影响；斯德鲁哈尔数对鱼体运动的影响。

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。

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。

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。

I think people in this lifetime in a rebirth.

我觉得人在这一生里其实也在轮回。

He had to tie her hands together.

他不得不把她的双手绑在一起。