最优带仲裁认证码

本文研究带仲裁认证码（亦称A^2-码）。一个A^2-码，当它的欺骗攻击成功概率达到信息论下界且密钥长度也达到最小时称为是最优的。本文给出最优A^2-码的组合结构的特征，从而将构造最优A^2-码的问题归结为构造相应的一类组合设计的问题。     

搜索三个目标

本文通过建立简洁而有效的搜索方法 ,证明了对于无穷多个n来说 ,三个目标的最优搜索问题的最小试验次数等于信息论下界 .同时也研究了上述问题的修正情形 ,证明了对于所有整数n来说 ,对应的最小试验次数或者等于信息论下界或者超过信息论下界 1次并且对于无穷多个区间 ,信息论下界均是可以达到的 .     

带有仲裁认证码的组合论下界

本文给出了带有仲裁认证码的组合论下界,并利用带有约束的t-设计,给出了敌方的r阶欺骗攻击成功的概率达到下界的带有仲裁认证码的组合结构。     

构作正交空间中的一类Cartesian认证码

利用正交几何构作出一类Cartesian认证码,并且计算了它们的参数.假定信源和编码规则都按等概率分布选取,求出了认证码的成功的模仿攻击概率PI和成功的替换攻击概率PS.本文构作的Cartesian认证码的成功的模仿攻击概率PI均达到了其下界.     

基于有限域上的辛几何构造带仲裁的多接收认证码

在通信中,发方发送信息给一群收方.但是,发方或者部分收方有时会联合欺骗群组中的某个成员.多接收认证码能够有效地阻止这种欺骗攻击.本文的目的是研究多接收认证码的构造问题.运用有限域上的辛几何这一工具,构造了一类带仲裁的多接收认证码,并证明其合理性.然后,充分运用辛空间的子空间结构及其计数原理,计算了相关参数以及被各类攻击成功的最大概率.最后,对该多接收认证码所受到的来自发方的假冒攻击进行仿真.     

基于有限域上的辛几何构造带仲裁的多接收认证码北大核心CSCD

在通信中,发方发送信息给一群收方．但是,发方或者部分收方有时会联合欺骗群组中的某个成员．多接收认证码能够有效地阻止这种欺骗攻击．本文的目的是研究多接收认证码的构造问题．运用有限域上的辛几何这一工具,构造了一类带仲裁的多接收认证码,并证明其合理性．然后,充分运用辛空间的子空间结构及其计数原理,计算了相关参数以及被各类攻击成功的最大概率．最后,对该多接收认证码所受到的来自发方的假冒攻击进行仿真．     

两类组合设计及其在认证码中的应用

W．Ogata等定义了两种新的组合设计：外差族（EDF）与外平衡不完全区组设计（E-BIBD）．本文首先用有限域中的分圆类给出EDF的一个构造；接着用EBIBD构造出具有完善保密性的最优分裂A-码，然后证明了由满足一定条件的两个EBIBD通过上述方法构造出的两个认证码是同构的.     

对称多胞形的极值性质及其应用

凸多胞形现代理论的主要成就是被称之为Dehn-Sommerville关系的上界定理和下界定理,它们属于凸多胞形的经典组合理论.本文建立了关于对称凸多胞形的两个极值定理,它们可视为凸多胞形度量理论中的上界定理和下界定理,另外给出了两个极值定理的一个应用.     

对称多胞形的极值性质及其应用

凸多胞形现代理论的主要成就是被称之为Dehn-Sommerville关系的上界定理和下界定理,它们属于凸多胞形的经典组合理论．本文建立了关于对称凸多胞形的两个极值定理,它们可视为凸多胞形度量理论中的上界定理和下界定理,另外给出了两个极值定理的一个应用．     

各阶欺骗概率相等的最优认证码

本文研究各阶欺骗概率相等的、一般阶的最优认证码的构造。利用有限域上高次抛物线、M-序列和线性校验办法分别构造了一类保密最优认证码和两类Cartesian最优认证码。     

混水平均匀设计的构造

我们用离散偏差来度量部分因子设计的均匀性,本文的目的在于寻找一些构造混水平均匀设计的方法,这些方法比文献中已有的方法更简单且计算成本更低.我们得到了离散偏差的一个下界,如果一个U 型设计的离散偏差值达到这个下界,那么该设计是—个均匀设计.我们建立了均匀设计与组合设计理论中一致可分解设计之间的联系.通过一致可分解设计,我们提出了一些构造均匀设计的新方法,同时也给出了许多均匀设计存在的无穷类.     

Branch and bound algorithm for a transfer line design problem: Stations with sequentially activated multi-spindle heads

In this paper, a new transfer line balancing problem is considered. The main difference from the simple assembly line balancing problem is that the operations are grouped into blocks (batches). All the operations of the same block are carried out simultaneously by one piece of equipment (multi-spindle head). Nevertheless, the blocks assigned to the same workstation are executed in series. The line cost consists of the sum of block and workstation costs. At the considered line design stage, the set of all available blocks is given. The aim is to find a subset from the given set of available blocks and to find a partition of this subset to workstations such that each operation is executed once and the line cost is minimal while all the precedence, cycle time, and compatibility (operation inclusion and block exclusion) constraints are respected. A new lower bound based on solving a special set partitioning problem is presented and a branch and bound algorithm is developed. The experimental results prove the quality of the lower bound and applicability of the suggested branch and bound algorithm for medium sized industrial cases.     

Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

Uniform supersaturated design and its construction

Supersaturated designs are factorial designs in which the number of main effects is greater than the number of experimental runs. In this paper, a discrete discrepancy is proposed as a measure of uniformity for supersaturated designs, and a lower bound of this discrepancy is obtained as a benchmark of design uniformity. A construction method for uniform supersaturated designs via resolvable balanced incomplete block designs is also presented along with the investigation of properties of the resulting designs. The construction method shows a strong link between these two different kinds of designs     

On complexity of round transformations

A modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well. In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose “necessary” security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F^′ attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F^′ is useful only from the theoretical point of view.     

预知工件大小上界的平行机排序问题

平行机排序问题广泛出现并应用于各领域,如通讯网信道分配的负载均衡,大型计算中的并行计算,柔性制造系统的任务编排等等.研究了预知工件大小上界的半在线平行机排序问题.考察了仅预知工件大小上界和既预知工件大小上界又预知最优目标值的两类半在线模型.基于资源分配公平性和提高服务质量的考虑,针对每类模型都分别考察了两个目标:C_(max)(极小化机器最大负载makespan)和C_(min)(极大化机器最小负载).在不同的目标下,针对m台平行机的一般情况均给出了问题的下界并设计了半在线算法,某些情况下设计的算法是最优算法.     

Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

The equitable location problem on the plane

This paper considers the problem of locating M facilities on the unit square so as to minimize the maximal demand faced by each facility subject to closest assignments and coverage constraints. Focusing on uniform demand over the unit square, we develop upper and lower bounds on feasibility of the problem for a given number of facilities and coverage radius. Based on these bounds and numerical experiments we suggest a heuristic to solve the problem. Our computational results show that the heuristic is very efficient, as the average gap between its solutions and the lower bound is 4.34%.     

Supersaturated Design with More Than Two Levels

gO. IntroductionA fractional factorial design is called supersaturated if the number of factors includedexceeds the limitation for keeping all the factors estimable, ignoring interactions. Sincesupersaturated designS can accommodate large nUInbers of factors, they are thought usefulin screening experhoellts.The research work on tWO-level supersaturated design was st8lted in the late fifties andearly staies (see [1,101). The subject has been gaining more and more renewed interest inthe last …     

A multicut L-shaped based algorithm to solve a stochastic programming model for the mobile facility routing and scheduling problem

This paper considers the mobile facility routing and scheduling problem with stochastic demand (MFRSPSD). The MFRSPSD simultaneously determines the route and schedule of a fleet of mobile facilities which serve customers with uncertain demand to minimize the total cost generated during the planning horizon. The problem is formulated as a two-stage stochastic programming model, in which the first stage decision deals with the temporal and spatial movement of MFs and the second stage handles how MFs serve customer demands. An algorithm based on the multicut version of the L-shaped method is proposed in which several lower bound inequalities are developed and incorporated into the master program. The computational results show that the algorithm yields a tighter lower bound and converges faster to the optimal solution. The result of a sensitivity analysis further indicates that in dealing with stochastic demand the two-stage stochastic programming approach has a distinctive advantage over the model considering only the average demand in terms of cost reduction.