用级联方法构造高阶相关免疫函数

相关免疫函数在密码通信、计算机安全等诸多领域有着广泛的应用 .自TSiegen thaler提出该概念以来 ,找到简便易行的构造相关免疫函数的方法一直是一个十分活跃的研究领域 .本文用级联的方法 ,从低阶相关免疫函数来构造高阶的相关免疫函数 ,由此得到几种构造任何阶相关免疫函数的简便方案 ,推广了文献 [4,5]的结果     

级联Bent函数的编码性质(英文)

考虑由Bent函数级联而成的布尔函数 ,讨论其平衡性、非线性度及严格雪崩准则等编码性质 ,分别得到这类级联函数为Bent函数和满足严格雪崩准则的条件     

Socially Structured Games

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power. We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core. We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera.      

Balanced Confidence Regions Based on Tukey's Depth and the Bootstrap

We propose and study the bootstrap confidence regions for multivariate parameters based on Tukey's depth. The bootstrap is based on the normalized or Studentized statistic formed from an independent and identically distributed random sample obtained from some unknown distribution in R ^q . The bootstrap points are deleted on the basis of Tukey's depth until the desired confidence level is reached. The proposed confidence regions are shown to be second order balanced in the context discussed by Beran. We also study the asymptotic consistency of Tukey's depth-based bootstrap confidence regions. The applicability of the method proposed is demonstrated in a simulation study.     

A Note on Balancedness of Dominating Set Games

In this paper we consider the balancedness of dominating set games, introduced by Velzen 2003. We establish a new kind of 0-1 program formulation to model the domination problem on graphs, and give a strong connection between LP relaxation of this 0-1 program and the cost allocation problem concerning the core of a dominating set game. Duality theory on Lagrange dual is the main technique in our proof. In particular, we use this insight to give the equivalence of the balancedness for two different dominating set games. Supported by NSFC (No. 10371114) and KRF-2003-002-C00038