• Journal of the Korea Institute of Information Security & Cryptology
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• v.1 no.1
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• pp.16-28
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• 1991

Knapsack public-key cryptosystems are based on the knapsack problem which is NP-complete. aii of the knapsack problem, are known to be insecure. However, the Chor and Rivest knapsack cryptosystem based on arithmetic in finite field is secure against all known cryptosystem based on arithmetic in a finite field is secure against all known cryptanalytic attacks. We suggest a new msthod of attack on knapsack cryptosystem which is based on the relaxation of a quadratic 0-1 integer optimization problem. We show that under certain condirions some bits of the solution of knapsack problem can be determined by using persistency property of linear relaxation. Also we propose a new Chor-Rivest system, this new cryptosystem reduces the number of calculation of discrete logarithms which are necessary for the implemention in a multi-user system.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.9
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• pp.883-892
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• 1991

In this thesis explanation of new knapsack algorithm for public key system difficulty test and parallel architecture for implementation are suggested. Past Merkle-Hellman’s knapsack is weak in Shamir or Brickell`s attack by the effects of mapping into other easy sequenoes. But linearly shift knapsack system compensates them.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.127-130
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• 1991

The multi-divisional knapsack problem is defined as a binary knapsack problem where each of mutually exclusive divisions has its own capacity. We consider the relaxed LP problem and develop a transformation which converts the multi-divisional linear knapsack problem into smaller size linear knapsack problems. Solution procedures and a numerical example are presented.

• Journal of Korean Institute of Industrial Engineers
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• v.40 no.4
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• pp.396-403
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• 2014

The multi-divisional knapsack problem is defined as a binary knapsack problem where each mutually exclusive division has its own capacity. In this paper, we present an extension of the multi-divisional knapsack problem that has generalized multiple-choice constraints. We explore the linear programming relaxation (P) of this extended problem and identify some properties of problem (P). Then, we develop a transformation which converts the problem (P) into an LP knapsack problem and derive the optimal solutions of problem (P) from those of the converted LP knapsack problem. The solution procedures have a worst case computational complexity of order $O(n^2{\log}\;n)$, where n is the total number of variables. We illustrate a numerical example and discuss some variations of problem (P).

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.25-29
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• 2001

We present a two dimensional linear programming knapsack problem with the extended GUB constraint. The presented problem is an extension of the cardinality constrained linear programming knapsack problem. We identify some new properties of the problem and derive a solution algorithm based on the parametric analysis for the knapsack right-hand-side. The solution algorithm has a worst case time complexity of order O($n^2logn$). A numerical example is given.

• Management Science and Financial Engineering
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• v.14 no.1
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• pp.91-96
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• 2008

Robust knapsack problem appears when dealing with data uncertainty on the knapsack constraint. This note presents a generalization of the cover inequality for the problem with its lifting procedure. Specifically, we show that the lifting can be done in a polynomial time as in the usual knapsack problem. The results can serve as a building block in devising an efficient branch-and-cut algorithm for the general robust (0, 1) IP problem.

• The Transactions of the Korea Information Processing Society
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• v.2 no.4
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• pp.611-618
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• 1995

In the high information societies, the requirement of encryption security is increasing so as to protect information from the threat of attacks by illegal changes of data, illegal leakage of data, disorder of data sequences and the unauthorized sender and an unauthorized receiver etc. In this paper, multivariable knapsack crytosystem is proposed for security of computer communication. This system is securer and simpler than the conventional knapsack cryptosystems. And, proposed cryptosystem composed what represented each element of superincreasing vector with multivar able polynomial after transforming it of ciphervector. For the deciphering of ciphertext, the plaintext is determined by using the integers of secret and the superincreasing vector of secret key. Thus, the stability of this cryptosystem is based on the difficulty of obtaining the root that ciphervector becomes the superincreasing vector, in substituting the integers of secret for ciphervector to represent with the miltivariable polynomial. The propriety of proposed multivariable knapsack cryptosystem was proved through computer simulation.

• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.2
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• pp.43-50
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• 2011

We consider the separation problem of the rank-1 Chvatal-Gomory (C-G) inequalities for the 0-1 knapsack problem with the knapsack capacity defined by an additional binary variable, which we call the fixed-charge 0-1 knapsack problem. We analyze the structural properties of the optimal solutions to the separation problem and show that the separation problem can be solved in pseudo-polynomial time. By using the result, we also show that the existence of a pseudo-polynomial time algorithm for the separation problem of the rank-1 C-G inequalities of the ordinary 0-1 knapsack problem.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.11
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• pp.2291-2302
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• 1994

This paper shows the implementation and design of special processor for linearly shift knapsack public key cryptography system. We highten the density of existing knapsack vector and shift the vectors linearly in order to implement the structure of linearly shift knapsack system which has the stronger cryptosystem. As it needs the parallel processing at each path according to the characteristics of this system. we propose the pipelined parallel structure and implement this system into VLSL. Also we evaluate this system and compare with other systems. The processing speed of this system is 550kb/s when dimension is 100. It is possible to use this system at the place of requiring high speed security to enlarge the structure of it.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.225-228
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• 2004

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We prove via the ellipsoid method the equivalence between the fully polynomial approximability and a certain pseudo-polynomial separability of the gknap polytope.