The cutting stock problem and integer rounding

An integer programming problem is said to have the integer round-up property if its optimal value is given by the least integer greater than or equal to the optimal value of its linear programming relaxation. In this paper we prove that certain classes of cutting stock problems have the integer round-up property. The proof of these results relies upon the decomposition properties of certain knapsack polyhedra.This research was partially supported by National Science Foundation grants ECS-8005350 and 81-13534 to Cornell University.     

Lattice basis reduction: Improved practical algorithms and solving subset sum problems

We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of theL ³-algorithm of Lenstra, Lenstra, Lovász (1982). We present a variant of theL ³-algorithm with deep insertions and a practical algorithm for block Korkin—Zolotarev reduction, a concept introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC1 + computer.Corresponding author.     

一种新型的安全云存储模型

针对云存储中的数据安全访问控制问题,设计了一个以云服务器为中心节点,支持不同权限多用户访问的安全高效的云存储模型。该模型利用椭圆曲线公钥密码设计具有语义安全的可搜索加密算法,并结合关键字相关度定义和保序加密算法提高数据检索准确性,降低系统通信负担;通过代理加密思想、用户访问控制列表和用户——数据访问控制矩阵实现不同权限用户的访问控制,安全灵活解决动态用户密钥管理问题。最后通过对模型安全性和模型效率两个方面对比分析,对模型可行性给出了证明。     

The Collapsing 0–1 Knapsack Problem

The Collapsing 0–1 Knapsack Problem is a type of non-linear knapsack problem in which the knapsack size is a non-increasing function of the number of items included.An algorithm is developed and computational results included.     

Efficient scalar multiplication for elliptic curves over binary fields

Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.     

Hyperelliptic Curves with Compact Parameters

We present a family of hyperelliptic curves whose Jacobians are suitable for cryptographic use, and whose parameters can be specified in a highly efficient way. This is done via complex multiplication and identity-based parameters. We also present some novel computational shortcuts for these families.     

基于广播加密的多策略非对称叛逆者追踪方案

双线性映射叛逆者追踪方案不能抵抗叛逆者攻击,且计算量与用户数量相关,计算效率很低。为了减少计算量、存储量和通信量,提高安全性能,基于离散对数难题,提出多策略、多服务、非对称公钥叛逆者追踪方案,进行了安全性证明和效率分析。该方案通过改变门限值t实现了多策略广播,可灵活运用于不同的网络广播领域。分析表明,方案具有更高的计算效率和更短的密文长度,同时该方案被证明可实现面向多服务、抗共谋性、完全撤销性、完全可恢复性和黑盒追踪性。     

Constant approximation for fault-tolerant median problems via iterative rounding

In this paper, we study the fault-tolerant matroid median and fault-tolerant knapsack median problems. These two problems generalize many fundamental clustering and facility location problems, such as uniform fault-tolerant k-median, uniform fault-tolerant facility location, matroid median, knapsack median, etc. We present a versatile iterative rounding framework and obtain a unifying constant-factor approximation algorithm.