<p class="Abstract"><span id="docs-internal-guid-d3fe8e21-7fff-17fc-df0e-00893428243c"><span>The Merkle-Hellman (MH) cryptosystem is one of the earliest public key cryptosystems, which is introduced by Ralph Merkle and Martin Hellman in 1978 based on an NP-hard problem, known as the subset-sum problem. Furthermore, ant colony optimization (ACO) is one of the most nature-inspired meta-heuristic optimization, which simulates the social behaviour of ant colonies. ACO has demonstrated excellent performance in solving a wide variety of complex problems. In this paper, we present a novel ant colony optimization (ACO) based attack for cryptanalysis of MH cipher algorithm, where two different search techniques are used. Moreover, experimental study is included, showing the effectiveness of the proposed attacking scheme. The results show that ACO based attack is more suitable than many other algorithms like genetic algorithm (GA) and particle swarm optimization (PSO).</span></span></p>

In this paper, we propose a pair-dependent rejection rate of packet information between routers in the framework of the minimal traffic model applied to scale-free networks. We have shown that the behavior of the transition point from the phase where the system balances the inflow of new information packets with successful delivery of the old ones to the congested phase depends on the underlying mechanism of packet rejection. It is possible to achieve larger values for the critical load by varying the rejection of the packets issued from a given node by its neighbors. We have proposed an asymmetric protocol, where we found the existence of a whole interval where the packet rejection is strongly beneficial to the overall performance of the system. We have also shown that for the dynamic protocol, the transition point is shifted toward higher values permitting the network to handle more traffic load, despite the fact that the critical load decreases when increasing the rejection parameter.

In this paper, we introduce the effect of neighbors on the infection of packets by computer virus in the SI and SIR models using the minimal traffic routing protocol. We have applied this model to the Barabasi–Albert network to determine how intrasite and extrasite infection rates affect virus propagation through the traffic flow of information packets in both the free-flow and the congested phases. The numerical results show that when we change the intrasite infection rate [Formula: see text] while keeping constant the extrasite infection rate [Formula: see text], we get normal behavior in the congested phase: in the network, the proportion of infected packets increases to reach a peak and then decreases resulting in a simultaneous increase of the recovered packets. In contrast, when the intrasite infection rate [Formula: see text] is kept fixed, an increase of the extrasite infection rate results in two regimes: The first one is characterized by an increase of the proportion of infected packets until reaching some peak value and then decreases smoothly. The second regime is characterized by an increase of infected packets to some stationary value.

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In this paper, we propose a new model for computer virus attacks and recovery at the level of information packets. The model we propose is based on one hand on the susceptible-infected (SI) and susceptible-infected-recovered (SIR) stochastic epidemic models for computer virus propagation and on the other hand on the time-discrete Markov chain of the minimal traffic routing protocol. We have applied this model to the scale free Barabasi–Albert network to determine how the dynamics of virus propagation is affected by the traffic flow in both the free-flow and the congested phases. The numerical results show essentially that the proportion of infected and recovered packets increases when the rate of infection [Formula: see text] and the recovery rate [Formula: see text] increase in the free-flow phase while in the congested phase, the number of infected (recovered) packets presents a maximum (minimum) at certain critical value of [Formula: see text] characterizing a certain competition between the infection and the recovery rates.