基于不经意传输协议的隐私保护推荐算法研究

在当今的网络购物环境下,相互竞争的两家购物网站会为了自身利益,会考虑在某一领域开展合作.而合作的前提条件就是不能泄露自己的核心信息给对方,即合作下的隐私保护问题,基于不经意传输协议(Oblivious Transfer Protocol,OT协议)设计了一个安全两方协同计算协议方法,有效地解决了二个参与方在协同过滤推荐中的隐私保护问题,并给出了协议的安全性及正确性证明.     

关于非线性等式约束优化问题的一点注记

给出了一种求解非线性约束优化问题的算法.利用Lagrange函数,将非线性约束优化问题转化为无约束优化问题,从而得到解决.方法仅仅依靠求解一个线性方程组来求解,因此使得计算量减小,计算速度变快.在一定条件下,给出算法的收敛性证明.数值试验表明方法是有效的.     

不等式约束优化全局收敛的滤子线性方程组算法

设计了求解不等式约束非线性规划问题的一种新的滤子序列线性方程组算法,该算法每步迭代由减小约束违反度和目标函数值两部分构成.利用约束函数在某个中介点线性化的方法产生搜索方向.每步迭代仅需求解两个线性方程组,计算量较小.在一般条件下,证明了算法产生的无穷迭代点列所有聚点都是可行点并且所有聚点都是所求解问题的KKT点.     

在具有局部内存与共享主存的并行机上并行求解线性方程组

求解线性方程组是解许多问题的核心,因此有效地求解线性方程组在科学与工程计算中是非常重要的.并行计算机的问世,使求解问题的速度和解题规模大幅度地提高.同时也使计算方法产生了变化.在传统的串行机上,LINPACK数学软件是求解线性方程组的有效软件包,然而在并行机上求解此问题,就需要设计出适合该机的并行算法.算法的优劣会对并行机的效率产生很大的影响,这里考虑的重点是并行计算一矩阵A的LU分解,亦即存在一排列矩阵P,使AP=LU.由于是在具有局部内存与共享主存的并行机上求解问题,因此算法的设计要有分布式计算的特点,又要利用共享主存的     

凸二次函数优化问题在快速多极边界元法中的应用

利用快速多极边界元法(FMM-BEM)求解大规模工程问题最终结为稀疏线性方程组的求解,因此,采用更好的方法求解线性方程组可以提高边界元法的计算效率.本文利用最优化数值技术处理,将稀疏线性方程组的求解等价为求解一个凸二次函数极小化的问题,并利用最优化理论及相关数学理论证明了其解的存在唯一性,为该理论的形成和发展奠定了理论基础.     

柯西矩阵的三角分解及应用

1 引 言 矩阵分解具有非常重要的应用.例如,可以利用矩阵的LU分解回代求解线性方程组Ax=b.对于在有理函数的计算中经常遇到的以柯西矩阵为系数的线性方程组的求解问题,需要做柯西矩阵的三角分解.     

基于块子空间迭代算法的GPU加速

利用块Krylov子空间方法结合GPU(图形处理单元)对线性方程组求解进行加速.利用GPU进行计算具有并行度高的好处,并能提高计算效率.数值算例说明,块算法在GPU上的运行效率要高于非块算法在CPU上的运行效率.但是对于块算法,谨慎地选择块的大小对于提升整个问题求解的速度也是非常重要的.     

约束优化无罚函数非单调SQP算法

本文研究求解非线性约束优化问题.利用非单调无罚函数方法,提出了一个新的序列二次规划算法.该算法在每次迭代过程中只需求解一个QP子问题和一个线性方程组.在一般条件下,算法具有全局收敛性,数值结果表明,计算量小于单调且含罚函数的传统算法.     

不等式约束优化的一个超线性收敛FSSLE算法

本文针对不等式约束优化问题,提出了一个可行序列线性方程组(FSSLE)算法.该算法每次迭代只需求解四个具有相同系数矩阵的线性方程组,因而计算量较小.在没有假设算法产生的聚点是孤立点和近似乘子列有界的条件下,证明了算法具有全局收敛性.在一般条件下,证明了算法具有超线性收敛性.     

有限网络的一个性质

借助实例提出一个有关有限网络研究的基本问题：对装置的任意电路网络是否总能经有限次改变状态后,从全＂关闭＂状态变为全＂开启＂状态.利用无向图作为网络的数学模型,并利用邻接矩阵,可把该基本问题归结为证明二元域Z2上一个特殊的线性方程组是否有解的问题.基于二元域Z2的运算性质及此域上线性方程组的理论,可严格证明上述线性方程组...     

Wide minimal binary linear codes from the general Maiorana–McFarland class

Designs, Codes and Cryptography - Minimal linear codes form a special class of linear codes that have important applications in secret sharing and secure two-party computation. These codes are...     

Privacy-preserving vertically partitioned linear program with nonnegativity constraints

We propose a simple privacy-preserving reformulation of a linear program with inequality constraints and nonnegativity constraints. By employing two random matrix transformation we construct a secure linear program based on the privately held data without revealing that data. The secure linear program has the same minimum value as the original linear program. Component groups of the solution of the transformed problem can be decoded and made public only by the original group that owns the corresponding columns of the constraint matrix and can be combined to give an exact solution vector of the original linear program.     

Computing payoff allocations in the approximate core of linear programming games in a privacy-preserving manner

We investigate privacy-preserving ways of allocating payoffs among players participating in a joint venture, using tools from cooperative game theory and differential privacy. In particular, we examine linear programming games, an important class of cooperative games that model a myriad of payoff sharing problems, including those from logistics and network design. We show that we can compute a payoff allocation in the approximate core of these games in a way that satisfies joint differential privacy.     

Privacy-preserving horizontally partitioned linear programs

We propose a simple privacy-preserving reformulation of a linear program whose equality constraint matrix is partitioned into groups of rows. Each group of matrix rows and its corresponding right hand side vector are owned by a distinct private entity that is unwilling to share or make public its row group or right hand side vector. By multiplying each privately held constraint group by an appropriately generated and privately held random matrix, the original linear program is transformed into an equivalent one that does not reveal any of the privately held data or make it public. The solution vector of the transformed secure linear program is publicly generated and is available to all entities.     

非同类机极小化最大完工时间的保密排序问题

提出并研究了一类非同类机的极小化最大完工时间的保密排序问题Rm||Cmax.该问题的模型参数分为若干组,每个组都由一个不愿意共享或公开自己数据的单位所拥有.基于随机矩阵变换构造了一个不泄露私有数据且与原问题等价的安全规划模型,求解该安全模型可以获得问题的最优解,而且各单位的隐私数据仍然保持不被泄露.     

三方相互体谅讨价还价模型

对于较重要的三方合作利益分配博弈问题,将相互体谅作为基本遵循并基于适应性预期模型,建立三方相互体谅讨价还价模型.运用这个模型,可以把三方相互体谅讨价还价达成均衡,归结为单调有界数列收敛与常系数非齐次线性差分方程组求解的结合运用.三方相互体谅讨价还价属于不完全信息动态合作博弈.对模型求解,一般地揭示三方相互体谅讨价还价达成均衡的过程与结果,阐明讨价还价有满足初始条件的唯一解和充要条件,以及充要条件的经济含义和数学意义.三方相互体谅讨价还价模型是对于两方相互体谅讨价还价模型的拓展,可以为建立更多方相互体谅讨价还价模型提供借鉴.     

Authentication and authenticated key exchanges

We discuss two-party mutual authentication protocols providing authenticated key exchange, focusing on those using asymmetric techniques. A simple, efficient protocol referred to as the station-to-station (STS) protocol is introduced, examined in detail, and considered in relation to existing protocols. The definition of a secure protocol is considered, and desirable characteristics of secure protocols are discussed.This work was done while Whitfield Diffie was with Northern Telecom, Mountain View, California.     

Privacy-preserving linear programming

We propose a privacy-preserving formulation of a linear program whose constraint matrix is partitioned into groups of columns where each group of columns and its corresponding cost coefficient vector are owned by a distinct entity. Each entity is unwilling to share or make public its column group or cost coefficient vector. By employing a random matrix transformation we construct a linear program based on the privately held data without revealing that data or making it public. The privacy-preserving transformed linear program has the same minimum value as the original linear program. Component groups of the solution of the transformed problem can be decoded and made public only by the original group that owns the corresponding columns of the constraint matrix and can be combined to give an exact solution vector of the original linear program.     

Existence and uniqueness of coexistence states for an elliptic system coupled in the linear part

In this paper, we discuss the existence, uniqueness and stability of coexistence states for an elliptic system coupled in the linear part. The linear part of this system is co-operative. Our approaches are based on the maximum principle and some properties of linear cooperative system.     

Existence and Stability of Positive Solutions for an Elliptic Cooperative System

By discussing the properties of a linear cooperative system, the necessary and sufficient conditions for the existence of positive solutions of an elliptic cooperative system in terms of the principal eigenvalue of the associated linear system are established, and some local stability results for the positive solutions are also obtained.