A Novel Model for Distributed Denial of Service Attack Analysis and Interactivity

Abstract

A Distributed Denial of Service (DDoS) attack is a type of cybercrime that renders a target service unavailable by overwhelming it with traffic from several sources (attack nodes). In this paper, we focus on DDoS attacks on a computer network by spreading bots throughout the network. A mathematical differential equation model is proposed to represent the dynamism of nodes at different compartments of the model. The model considers two levels of security, with the assumption that the recovered nodes do not return to the same security level. In previous models, the recovered nodes are returned to be suspect on the same security level, which is an unrealistic assumption. Moreover, it is assumed that the attacker can use the infected target nodes to attack again. With such epidemic-like assumptions of infection, different cases are presented and discussed, and the stability of the model is analyzed as well; reversing the symmetry transformation of attacking nodes population is also proven. The proposed model has many parameters in order to precisely describe the infection movement and propagation. Numerical simulation methods are used to solve the developed system of equations using MATLAB, with the intention of finding the best counteraction to control DDoS spread throughout a network.

Keywords

• computer networks
• differential equations
• dynamic equilibrium
• network servers
• non-linear dynamical systems
• non-linear equations