REESSE 1公开密钥密码体制

本文给出了互素序列的定义和杠杆函数的概念，介绍了REESSE1公开密钥密码体制及其密钥生成、加密、解密、数字签名和身分验证五个算法。文章对加密和解密算法进行了有关推导和证明，对REESSE1公钥体制的安全性进行了初步分析。另外，作者还给出了一个用于公钥密码体制中求模逆元的新递归算法。     

REESSE 2公开密钥密码体制

作者综合利用超递增序列、杠杆函数和HASH函数的特性提出了能有效地抵御“极小点”攻击和“LOB-L3归约基”攻击的REESSE2公开密钥密码体制，详细描述了该体制的数学基础、密钥生成算法、加密算法和解密算法。文章对REESSE2体制的安全性和优越性做了分析，并归纳了提高公钥密码体制安全性的两条途径。     

基于REESSE3+算法的改进算法

REESSE3+算法是苏盛辉教授于2014年提出的一个8轮迭代的分组密码算法。本文在REESSE3+算法的基础上做出了一些改进,提出了一种新的改进算法。由于REESSE3+算法受到了来学嘉教授提出的IDEA算法的启发,采用了3个不相容的群运算来保证其安全性,因此采用来学嘉教授提出的马尔科夫密码模型来对REESSE3+(16)算法和16位输入的改进算法进行比较。通过实验发现,在面对差分攻击时,16位输入的改进算法比原REESSE3+(16)算法更加安全。     

融入中国剩余定理及Montgomery算法的快速RSA算法研究

利用中国剩余定理和Montgomery模乘算法的思想,改进了RSA密码体制.改进后的中国剩余定理算法在时间效率上有较大提高,而且加入Montgomery模乘算法使模乘速度及安全性都有较大的提高,更加适合于高速的RSA密码体制.     

REESSE对称密钥密码体制

笔者在IDEA体制的基础上给出了REESSE对称密钥密码体制,新体制分组长度被扩展为128比特,轮函数做了改变,速度加快,密钥长度仍为128比特。文章阐述了REESSE对称体制的算法、加密子密钥和解密子密钥,对算法的正确性进行了证明,对体制的安全性做了简单分析。     

基于量子粒子群的全参数连分式混沌时间序列预测

针对传统混沌时间序列预测模型的复杂性、低精度性和低时效性的缺点, 在倒差商连分式基础上提出全参数连分式模型, 并利用量子粒子群优化算法优化模型参数, 将参数优化问题转化为多维空间上的函数优化问题. 以二阶强迫布鲁塞尔振子和三维二次自治广义Lorenz 系统为模型, 通过四阶Runge-Kutta 法产生混沌时间序列, 并利用基于量子粒子群优化算法的全参数连分式、BP 神经网络和RBF 神经网络分别对混沌时间序列进行单步和多步预测. 仿真结果表明, 基于量子粒子群优化算法的全参数连分式结构简单、精度高、效率高, 该预测模型可被推广和应用.

     

二元非张量积型连分式插值

首先,基于新的二元非张量积型逆差商递推算法,分别建立奇数与偶数个插值节点上的二元连分式插值格式,并得到被插函数的两类恒等式。接着,利用连分式三项递推关系式,分别确定渐近式的分子和分母的次数,即特征定理,并给出推导分子、分母的递推算法。同时,研究表明所提连分式的分子、分母次数分别小于相应的二元Thiele型插值连分式分子、分母次数,这主要是因为所提连分式插值减少了对冗余的插值节点的采用。然后,从计算复杂性的角度出发,所提二元有理函数插值的计算量小于相同插值节点上的径向基函数插值的计算量。最后,数值算例表明所提二元连分式插值方法有效且可行,同时也揭示了即使插值节点集合不变,所提插值连分式的表达式也会随着插值节点顺序的改变而改变。     

矩阵序列结构算法在单变量系统降阶问题中的应用

本文指出了单位模阵与连分式的一种对应关系。根据这一事实,把矩阵序列结构算法用于系统降阶问题。其结果包含了第一,第二 Cauer 形连分式降阶法,有效地克服了连分式降阶法在 Routh表首列出现零元素时遇到的困难。这种方法既便于手算,也适合在计算机上运算,它还具有在一次施行结构算法过程中同时获得各阶降阶模型的特点。     

复杂系统的模型简化——带偏连方式法的计算及改进

本文探讨了用于模型简化的带偏连分式法,提出了一个带偏连分式展开和反演的具体算法,并根据可调参数法的思路,对带偏连分式法作了进一步改进,改进后的方法逼近精度较好,应用灵活,在频率特性上,既能实现整个频段上有侧重的逼近,又能实现在某些特定频率处较精确的拟合。最后通过例题进行了计算比较。     

四素数RSA数字签名算法的研究与实现

RSA算法中模数和运算效率之间一直存在矛盾,目前一些认证机构已采用模数为2048bit的RSA签名方法,这必然会影响签名效率。针对这一问题,提出四素数CRT-RSA签名算法,并使用安全杂凑函数SHA512来生成消息摘要,采用中国剩余定理结合Montgomery模乘来优化大数的模幂运算。通过安全性分析和仿真实验表明,该签名算法能抵抗一些常见攻击,并且在签名效率方面具有一定优势。     

区间分数阶系统的鲁棒稳定性判别准则:0 < α < 1

针对同元阶次在0和1之间的区间分数阶系统,提出了类似Kharitonov定理的鲁棒稳定性判别准则. 研究了区间分数阶系统分母的主分支函数值集不包含原点所需满足的条件.根据除零原理, 给出了区间分数阶系统鲁棒稳定的顶点和棱边条件. 定义了由分母函数系数构成的矩阵,通过检验矩阵是否在负实轴上存在特征值来检验棱边条件. 最后,通过对两个数值算例的分析说明了这种方法的有效性.     

Dynamics of the Binary Euclidean Algorithm: Functional Analysis and Operators

We provide here a complete average-case analysis of the binary continued fraction representation of a random rational whose numerator and denominator are odd and less than N . We analyze the three main parameters of the binary continued fraction expansion, namely, the height, the number of steps of the binary Euclidean algorithm, and finally the sum of the exponents of powers of 2 contained in the numerators of the binary continued fraction. The average values of these parameters are shown to be asymptotic to A _i log N , and the three constants A _i are related to the invariant measure of the Perron—Frobenius operator linked to this dynamical system. The binary Euclidean algorithm was previously studied in 1976 by Brent who provided a partial analysis of the number of steps, based on a heuristic model and some unproven conjecture. Our methods are quite different, not relying on unproven assumptions, and more general, since they allow us to study all the parameters of the binary continued fraction expansion. Received February 9, 1998; revised March 15, 1998.     

Relation between powers of factors and the recurrence function characterizing Sturmian words

In this paper we use the relation of the index of an infinite aperiodic word and its recurrence function to give another characterization of Sturmian words. As a by-product, we give a new proof of the theorem describing the index of a Sturmian word in terms of the continued fraction expansion of its slope. This theorem was independently proved in [A. Carpi, A. de Luca, Special factors, periodicity, and an application to Sturmian words, Acta Inform. 36 (2000) 983–1006] and [D. Damanik, D. Lenz, The index of Sturmian sequences, European J. Combin. 23 (2002) 23–29].     

Simultaneous expansion and inversion of the Cauer continued fractions of certain transfer functions

The main aim of this paper is to apply Evelyn Frank's algorithm for the continued fraction expansion of a rational transfer function into Cauer's first and second forms. The very essence of the algorithm itself is an inversion procedure for a continued fraction into a sequence of reduced-order rational transfer functions. This algorithmic scheme is well-suited for efficient computerization. However, it has (like its counterpart, the Routh algorithm) one drawback in that it involves divisions. Hence one might encounter rational quantities while working with integer coefficients. To overcome this, the present algorithm is carefully modified in order to compute the elements in a precise fraction-free manner. The time and Markov parameters of the system are also obtained by the orthogonality properties of the corresponding Cauer continued fractions. The specific methods are discussed in detail and illustrated by explicit numerical examples.     

On the martingale approximation of the estimation error of ARMA parameters

The aim of this paper is to prove a theorem which is instrumental in verifying Rissanen's tail condition for the estimation error of the parameters of a Gaussian ARMA process. We get an improved error bound for the martingale approximation of the estimation error for a wide class of ARMA processes.     

Numeration and discrete dynamical systems

This survey aims at giving both a dynamical and computer arithmetic-oriented presentation of several classical numeration systems, by focusing on the discrete dynamical systems that underly them: this provides simple algorithmic generation processes, information on the statistics of digits, on the mean behavior, and also on periodic expansions (whose study is motivated, among other things, by finite machine simulations). We consider numeration systems in a broad sense, that is, representation systems of numbers that also include continued fraction expansions. These numeration systems might be positional or not, provide unique expansions or be redundant. Special attention will be payed to β-numeration (one expands a positive real number with respect to the base β > 1), to continued fractions, and to their Lyapounov exponents. In particular, we will compare both representation systems with respect to the number of significant digits required to go from one type of expansion to the other one, through the discussion of extensions of Lochs’ theorem.