密码的

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 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。

Hybrid schemes in a KEM-DEM structure is regarded as the most natural approach to public key encryption with IND-CCA security and practical efficiency. Traditional KEM is realized by public key scheme, which only provides confidentiality security for session key used by DEM. In 2005, combining the idea of signcryption with the KEM-DEM model hybrid encryption, Alexander proposed a signcryption KEM-DEM model hybrid signcryption primitive.

KEM-DEM结构的混合密码体制是获得IND-CCA安全最实际有效的方法，传统的KEM由公钥加密方案实现，仅提供DEM使用的会话密钥的保密性安全。2005年Alexander等人将签密的概念与KEM-DEM结构的混合密码体制相结合，提出了Signcryption KEM-DEM结构的混合签密。

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

Then she called me to her small warehouse, to give me a +-S of the Black Dragon, she said that her friend did not want to play a miracle, a miracle to go to the world, and her friend have a Black Dragon King, many people would like to to, but I just so emotional for her, he decided to give me this, so now my account number and password, to my brother's number to his friend to the reputation of this equipment, I turned to the account number and password him, then he has been connected to my account, I feel a bit wrong at the time, for its account of my other junk a dragon and a few stones for to its eternal friends, the next line after the number to the eternal look at the small warehouse, was to see the Running out of Time, Running out of Time and then disappeared, I find the whole continent can not find him.

然后她叫我去小仓库等她，要给我一套+-S的黑龙，她说她朋友不想玩奇迹了，要去奇迹世界了，她朋友有这样一套黑龙王，很多人都想要，但是我刚才对她这么意气他决定把这套送给我，所以现在要我的帐号和密码，上我的号以弟弟的名誉向他朋友要这套装备，我又把帐号和密码给了他，然后他一直连接我的帐号，我当时觉的有点不对劲，换号把我帐号里的另外一套垃圾龙和几个石头换到朋友的永恒号上，之后下线上永恒的号去小仓库看看，果然见到暗战，然后暗战就消失了，我找个整个大陆都找不到他。

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。

Coding and non-coding sequences are expected to have very different patterns of sequence changes because of the following characteristics of coding sequences: biased codon composition, higher conservation, absence of stop codons and frameshifts, higher fraction of synonymous than nonsynonymous substitutions, higher frequency of substitutions corresponding to changes of chemically similar amino acids, higher proportion of mutable contexts.

我们可以预期可转录的序列及不可转录的序列会有相当不同的序列改变特徵，因为可转录的序列有以下特色：偏颇的密码子组成，较高的保存度，有终止密码子和移码的出现，相较於异义取代有较高比例的同义取代，较高的频率出现化学结构相似的胺基酸取代，较高比例的可变之前后序列。

For the application of 64 Codons, each step from DNA chain to mRNA chain, t RNA, ribosome, peptides, and to protein, has its specific permutable calculation model between chemical reactants and products, none of which has an objective permutable relationship with that in the 43 Table of Triplet Codes.

在生物遗传学的解释上，不预先测定给定生命体的 DNA 碱基顺序及其蛋白质的氨基酸顺序并把两者作比较，就把 DNA 和密码表两者指导合成的多肽链的氨基酸顺序称为该生命体遗传得来的氨基酸顺序，并以此将密码表称为生命的元素周期律在一切生命体中通用，是完全错误的。

To prevent such an outbreak from happening, it is imperative that administrators refrain from logging onto a suspect machine using their own accounts. Logging on using the workstation's local administrator account can also have the same effect; most corporate workstations are ghosted from the same image and could have the same local admin account and password.

要防止此类病毒爆发事件的发生，紧急的办法是不要实用管理员自己的用户名和密码登陆系统，用工作站的本地管理员用户一样也会有此类事件发生，很多的工作站的系统都是通过同一个镜像文件并利用ghost方式进行的安装，因此用户名和密码相同也是肯定的

In fact, with more than one in 10 people having 50 or more separate online accounts to log into, many are not only using the same password for everything, but also writing all their passwords down in one handy place, such as the noticeboard in their office, a document on their desktop, or a Post-it note stuck to their computer.

事实上，超过10%的人在网上有50个以上的注册帐户，他们中的多数人不仅到处都用唯一的密码，还将所有的私人密码记录在熟悉的地方，诸如办公室的通告栏，桌上的便签，或者在放在他们电脑里。

What would he tell Judith and the children?

他将怎样告诉朱迪丝和孩子们呢？

I this is at that time, the opinion with peacockish true girl is full of in a heart.

这就是当时的我，一个心中布满虚荣的女孩子真实的想法。