A new knapsack-type public key cryptosystem is introduced. The system is based on a novel application of arithmetic in finite fields, following a construction by Bose and Chowla. By appropriately choosing the parameters, one can control the density of the resulting knapsack, which is the ratio between the number of elements in the knapsack and their sue in bits. In particular, the density can b...

This paper deals with the collapsing knapsack problem. In the literature, to solve the problem, a method incorporating a reduction from the problem to the 0-1 knapsack problem has been proposed. In this paper we show an alternative reduction which produces coefficients smaller than those by the previous. rlOUS. The improvement makes it possible to solve the resulting 0-1 knapsack problem faster...

In this paper we break a knapsack based two-lock cryptosystem proposed at ICICS’03 [7]. The two-lock cryptosystem is a commutative encryption algorithm that is very useful for the construction of the general t-out-of-n oblivious transfers and millionaire protocol. However, our analysis shows that the proposed knapsack based two-lock cryptosystem is extremely insecure. The serious flaw is that t...

Knapsack problem is a typical computer algorithm of NP complete (Nondeterministic Polynomial Completeness) problem. The research of solving this problem has great significance not only in theory, but also in application, for example, resource management, investment decisions and so on. For solving this problem, scholars have developed a number of algorithms, however, they are all have some draw...

In this paper we study and solve two different variants of static knapsack problems with random weights: The stochastic knapsack problem with simple recourse as well as the stochastic knapsack problem with probabilistic constraint. Special interest is given to the corresponding continuous problems and three different problem solving methods are presented. The resolution of the continuous proble...

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem arises in a number of other contexts, e.g. it is a relaxation of general mixed-integer programming. We show how strong inequalities valid for the semi-continuous knapsack ...

The need of totally secure online auction has led to the invention of many auction protocols. But as new attacks are developed, auction protocols also require corresponding strengthening. We analyze the auction protocol based on the well-known mathematical public-key knapsack problem for the design of asymmetric public-key knapsack trapdoor cryptosystem. Even though the knapsack system is not c...

We address in this paper the problem of modifying both profits and costs of a fractional knapsack problem optimally such that a prespectified solution becomes an optimal solution with prespect to new parameters. This problem is called the inverse fractional knapsack problem. Concerning the l1-norm, we first prove that the problem is NP -hard. The problem can be however solved in quadratic time ...

We consider the minimization version of the multi-dimensional knapsack problem with bounded integer variables. We propose a greedy approximation algorithm that runs in O(mn) time and has a guarantee of m + 1, where n is the number of items and m is the number of knapsack constraints. The guarantee of the algorithm can be improved in case of easy coefficients in the constraints associated with s...

It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...