Bimal Kumar Mishra

Dynamic model of worms with vertical transmission in computer network

An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduction number is greater than one, the infected nodes exists and the worms persist at an endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. We have analyzed the behavior of the susceptible, exposed, infected and recovered nodes in the computer network with real parametric values.

Stability analysis of a predator–prey model in wireless sensor network

Limited availability of energy within the network motes in wireless sensor network became a critical issue; therefore, making a perfect use of energy is necessary. A widely employed energy-saving technique is to place motes in sleep mode, corresponding to low-power consumption as well as to reduce operational capabilities. In this paper, we propose a mathematical model based on predator–prey dynamics to analyse the impact of energy conservation in the context of worm attacks in such network. We analyse the system to obtain different equilibrium points and then found the conditions for their stability. Lastly, some numerical simulations are given to illustrate the analytical results.

Mathematical model on vulnerability characterization and its impact on network epidemics

Mathematical modeling and accurate representation of malware spread in a network is a difficult process because of our lack of understanding of several features that form the basis of such spread. Models have been used to analyze and predict the behavior of epidemic spread in networks over the years, to gain a better understanding of the process. The aim of this paper is to understand the process of emergence of vulnerabilities and its relationship with a network epidemic. Eighteen years of vulnerability emergence data has been used in this work. The data includes the total count of vulnerabilities emerging every month. The pattern reveals several important characteristics of the process including frequency peaks at seasonal locations. A steady state distribution of the process is defined. The transition of vulnerability into an exploit is characterized. Finally an interface between this vulnerability model and epidemic models is established through a description of the relationship between the epidemic force of infection and types of vulnerabilities. The paper concludes with several results that can be useful in our attempts to better approximate the spread of malware in networks.

Cyber Attack and Control Techniques

We have developed an Susceptible-Exposed-Infectious-Undetected-Recovered (SEIUR) model. The main feature of this model is the introduction of undetected class. This class is introduced due to the use of un-updated version of antivirus. Optimal control technique is one of the most efficient techniques to plan strategies for better implementation of resources. We have formulated the model and also developed some theoretical results supported by numerical simulation for implementation of control variable in the model.

Probabilistic e-epidemic model on computer worms

In epidemiology, several mathematical models are developed by using the system of differential equations and many of them have used the parameters traditionally as deterministic variables. In this paper, the variables, which are used in the system, are considered as random variables with specified distributions because the equations with random coefficients are well suited in describing the real behavior of the parameters as compared to deterministic coefficients. A stochastic spectral representation of the parameters is used. Numerical methods and polynomial chaos method are used to solve and simulate the system of equations and analysis of the spread of worms in computer network with respect to time is done.

Computing the Spreading Power of a Business Portal to Propagate the Malicious Information in the Network

This paper predicts the malicious object prone site from the set of multi business portals of an organization or company. Graph theory is used to solve this problem as the diverted traffic of customers is interdependent among all the business portals. At first the interconnected business portals are represented in the form of a graph and its corresponding adjacency matrix. Later the centrality and eigenvectors were computed to find the degree of a business portal to propagate the malicious information, helping to cure the business portal by taking available security measures to avoid further infection.

Dynamics for Proactive Defense through Self-hardening in the Presence or Absence of Anti Malicious Software

In computer networks, the computers can be categorized into two categories, one is susceptible or healthy and another is infected. The susceptible computers can have the Anti Malicious Software (AMS) or can not have to protect themselves from the malicious objects. In addition they can have a costly action to self-harden themselves against the malicious objects for proactive defense. The utility cost of being susceptible or infected is the major concern of this paper. The paper considers the role of AMS and the self-hardening action to find out the lifetime utility of a computer. This lifetime utility is beneficial to take the decision, whether the self-hardening/AMS has to be implemented in the computer network or not as it is costly action to protect the computer network from malicious objects.