关于三分Cantor集的构造的一个基本性质及其应用

本文提出了三分 Cantor集的构造的一个基本性质 .作为应用 ,给出了计算三分 Cantor集的简明的初等的计算方法 ,另外还得到了一列有趣的对数不等式     

Basic Calculus on Time Scales and some of its Applications

The study of dynamic systems on time scales not only unifies continuous and discrete processes, but also helps in revealing diversities in the corresponding results. In this paper we shall develop basic tools of calculus on time scales such as versions of Taylor’s formula, l’Hôspital’s rule, and Kneser’s theorem. Applications of these results in the study of asymptotic and oscillatory behavior of solutions of higher order equations on time scales are addressed. As a further application of Taylor’s formula, Abel-Gontscharoff interpolating polynomial on time scales is constructed and best possible error bounds are offered. We have also included notes at the end of each section which indicate further scope of the calculus developed in this paper.     

α-对角占优矩阵的性质及其应用

本文引入矩阵的弱可达性的概念,得到α-对角占优矩阵的一些基本性质。利用它们 建立了判定α-双对角占优矩阵为广义严格对角占优矩阵的若干充要条件.     

Orlicz函数的基本性质及其应用

讨论了一类凸函数的基本性质,并应用这些基本性质证明了Orlicz-Lorentz空间上的一个插值定理.     

On Finite Forms of Certain Bilateral Basic Hypergeometric Series and Their Applications

In this paper we derive finite forms of the summation formulas for bilateral basic hypergeometric series 3ψ3,4ψ4 and 5ψ5.We therefrom obtain the summation formulae obtained recently by Wenchang CHU and Xiaoxia WANG.As applications of these summation formulae,we deduce the well-known Jacobi's two and four square theorems,a formula for the number of representations of an integer n as sum of four triangular numbers and some theta function identities.     

Basic formulas and languages: PART II.Applications to E0L systems and forms

This paper (the second of two parts) settles the decidability status of several properties of derivations in E0L systems (forms). In particular we show that the so called “one-to-many simulation” among E0L forms is decidable, solving in this way an open problem from [6]. We use a more general mathematical framework, based on the theory of well-quasi orders, developed in Part I of this paper [2].     

Surface Bundles with Nonvanishing Signature

Using the theory of Lefschetz fibrations and recent advances in mapping class group theory, surface bundles over surfaces with nonzero signature and small base genus are constructed. In particular, a genus-5 fibration over the surface of genus 26 with nonzero signature is given –- improving former results on the possible base genera for surface bundles over surfaces with nonzero signature.     

Signature classes of transportation polytopes

Signature algorithms solve certain classes of transportation problems in a number of steps bounded by the diameter of the dual polyhedron. The class of problems to which signature algorithms may be applied—the signature classes of the title—are characterized, and the monotonic Hirsch conjecture is shown to hold for them. In addition, certain more precise results are given for different cases. Finally, it is explained why a supposed proof of the Hirsch conjecture for all transportation polytopes is incomplete and apparently irremedial.Dedicated with affection to Philip Wolfe on the occasion of his 65th birthday.     

利用生物特征数据的签名方案研究

研究了基于生物特征的密钥提取,利用模糊提取器将不可精确再生和非均匀分布的生物特征数据生成为可应用于经典密码体系的密钥,密钥的产生和用户的认证紧密结合,使认证和密钥产生这两个密码操作统一在一个密钥原语中实现.并将生物特征数据生成的密钥应用于短签名等经典的数字签名方案,从而达到更高的安全性和实用性.     

Efficient Rabin-type Digital Signature Scheme

Rabin's cryptosystem was proved to be as hard as factorization. However, Rabin's digital signature schemes is probabilistic. This paper shows two efficient Rabin type digital signature schemes, a basic scheme and an improved scheme. Both schemes run much faster than Rabin's scheme. They are deterministic and the size of a signature is much smaller than that of a signature in Rabin's scheme. Furthermore, it is proved that, by applying the technique of Bellare and Rogaway, the proposed scheme is secure against chosen plaintext attack. More precisely, breaking the proposed digital signature scheme by chosen plaintext attack is as hard as factoring N.     

Signature invariants of covering links

We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.

     

一种灵活的基于身份的签名方案

在基于身份的密钥提取过程中,使密钥生成器在私钥中嵌入随机数,从而使得密钥提取具有较好的灵活性,使得用户对一个身份可具备多个私钥,这无疑会增加密钥使用的安全性;基于这种新的密钥提取思路,给出一个基于身份的签名体制,新的密钥提取方式使得它具有更好的安全性和灵活性;新的基于身份的签名体制中具有最少对运算,因此,与类似的方案相比,其具备较好的计算效率;新签名体制的安全性依赖于k-合谋攻击问题(k-CAAP)的困难性,其在适应性选择消息和ID攻击下具备强不可伪造性,并且其安全性证明具有紧规约性.     

两个无证书签名方案的分析与改进

无证书密码体制结合了基于身份密码体制和传统公钥密码体制的优点,受到了密码和信息安全研究者的极大关注.对梁景玲等提出的消息可恢复的无证书签名方案和侯红霞等提出的无证书短签名方案进行安全性分析,发现两个方案都不能抵抗公钥替换攻击.通过修改签名者密钥生成算法,增加对用户公钥的有效性验证,提高了梁等方案的安全性.通过在签名阶段将用户公钥绑定进HaSh函数,弥补了侯等方案的安全缺陷.     

Index Calculation Attacks on RSA Signature and Encryption

At Crypto ’85, Desmedt and Odlyzko described a chosen-ciphertext attack against plain RSA encryption. The technique can also be applied to RSA signatures and enables an existential forgery under a chosen-message attack. The potential of this attack remained untapped until a twitch in the technique made it effective against two very popular RSA signature standards, namely iso/iec 9796-1 and iso/iec 9796-2. Following these attacks, iso/iec 9796-1 was withdrawn and ISO/IEC 9796-2 amended. In this paper, we explain in detail Desmedt and Odlyzko’s attack as well as its application to the cryptanalysis of iso/iec 9796-2. AMS Classification: 11T71, 14G50, 94A60     

对一群签名方案的分析与改进

通过对夏祥盛等人的动态门限群签名方案的研究,指出该方案的若干不足,其中最主要的不足是通过伪造和不可追踪性,并对该方案进行了改进．与现有群签名方案不同,新方案中用户的秘密数由用户自己选取,从而避免了双线性对的计算,大大提高了效率．分析说明改进的群签名方案几乎克服了原方案的所有缺点．     

可证明安全的基于证书聚合签名方案

对刘云芳等人提出的基于证书聚合签名方案进行安全性分析,指出方案不能抵抗类型Ⅱ敌手攻击,并给出两种攻击方法,在此基础上提出了一个新的可证安全的基于证书聚合签名方案,利用Diffie-Hellman困难问题,在随机预言模型下证明了新方案是存在性不可伪造的.另外,新方案的聚合签名长度是固定常数,与签名者的数量无关,在签名验证中只需要4个对运算和n个标量乘运算,因此,新方案的签名验证效率得到很大提高.     

Computation of Signature Symmetric Balanced Realizations

A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of the algorithm is shown.