We observed few important facts that concerns with the new proposal of knapsack cipher 0/255, recently published by Pham [1]. The author claimed that the time complexity for solving new improved trapdoor knapsack is O(256). In this paper, we show that the knapsack cipher 0/255 can be solved in the same time that is required for solving the basic knapsack-cipher proposed by Merkle and Hellman [2...

The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack problem appears difficult in comparison with the linear Knapsack problem, we prove that its complexit...

— Recently, Hwang et al. introduced a knapsack type public-key cryptosystem. They proposed a new algorithm called permutation combination algorithm. By exploiting this algorithm, they attempt to increase the density of knapsack to avoid the low-density attack. We show that this cryptosystem is not secure, as it based on basic Merkel-Hellman knapsack cryptosystem and because of the superincreasi...

We present a highly efficient incremental algorithm for propagating bounded knapsack constraints. Our algorithm is based on the sublinear filtering algorithm for binary knapsack constraints by Katriel et al. and achieves similar speed-ups of one to two orders of magnitude when compared with its lineartime counterpart. We also show that the representation of bounded knapsacks as binary knapsacks...

A new secure knapsack cryptosystem based on the Merkle-Hellman public key cryptosystem will be proposed in this paper. Although it is common sense that when the density is low, the knapsack cryptosystem turns vulnerable to the low-density attack. The density d of a secure knapsack cryptosystem must be larger than 0 9408 . to avoid low-density attack. In this paper, we investigate a new Permutat...

We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0–1 knapsack set, the mixed 0–1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a common presentation of the inequalities based on covers and packs and highlight the connections among them. The focus of the paper is on recent re...

The 0/1 Knapsack Problem is an optimization problem solved using various soft computing methods. The solution to the 0/1 Knapsack Problem (KP) can be viewed as the result of a sequence of decisions. Simple Genetic Algorithm (SGA) effectively solves knapsack problem for large data set. But it has problems like premature convergence and population diversity. Dual Population Genetic Algorithm (DPG...

Integer packing problems have traditionally been some of the most fundamental and well-studied computational questions in discrete optimization. The paper by Aouad Segev studies incremental knapsack problem, where one wishes to sequentially pack items into a whose capacity expands over finite planning horizon, with objective maximizing time-averaged profits. Although various approximation algor...

Merkle and Hellman proposed a first knapsack cryptosystem. However, it was broken because the density is not sufficiently high. In this paper, we propose a a new trapdoor in modular knapsack PKC. Proposed scheme can use the message encoding. This method can use the method of enlarging messages over a finite field in order to realize a high density over 1. Keywords— Knapsack public-key cryptosys...