Research On Malware Propagating Laws And Containing Policies In Heterogeneous Wireless Sensor Networks

Heterogeneous wireless sensor networks(HWSNs)are a kind of wireless sensor networks(WSNs),that is to say,HWSNs are also a multi hop self-organizing intelligent network,which are composed of a great many of heterogeneous sensor nodes(HSNs).Compared with WSNs,the heterogeneity of HWSNs is mainly reflected in three aspects.First,the HSNs of HWSNs have different battery energy,computing resources,communication resources,and storage resources.Second,HWSNs have the different network topology.Third,the communication link between HSNs is different.Therefore,HWSNs have the advantages of strong adaptability,high availability,and high reliability,and HWSNs have been deployed more and more widely than WSNs in many practical applications.Malware is a program with malicious intent and serious destructive on network,system or data.Because HWSNs are characteristic in terms of network,low configuration and weak defense mechanism,which are vulnerable to malware propagation.Once malware propagates itself in HWSNs through network vulnerabilities or HSN system's vulnerabilities,it will quickly propagate throughout the whole HWSNs.Then,malware will destroy the normal work of HWSNs by injecting malicious data,breaking data transmission,blocking the network,or exhausting the resource of HSNs.This paper is devoted to exploring the propagating laws and containing policies of malware in HWSNs.The main contributions of this paper are listed as follows.(1)We predict the propagating laws of malware in HWSNs based on cellular automata and the static Bayesian game.Firstly,according to the discrete characteristics of cellular automata,the elements of HWSNs are mapped with the characteristics of cellular automata.Secondly,according to the transition function of cellular,the differential equations of HSNs states transformation are established,and a malware propagation model is constructed based on cellular automata.Thirdly,based on the static Bayesian game,the malware propagation dynamics in HWSNs is accurately predicted,through which malware and HSNs would determine their optimal actions by the Bayesian Nash equilibrium(BEN),then the BEN is applied to this malware propagation model.Finally,we verify that this malware propagation model can effectively predict the propagating laws of malware in HWSNs by data analyses,by which we obtain the dynamic evolution trend of HSNs in various states with time.(2)Considering the heterogeneity of the incubation period for malware,we construct a study malware propagation model based on cellular automata,and then analyze the stability of the model.Firstly,considering the heterogeneity of the incubation period for malware,HSNs infected by malware have many states,including susceptible,infectious,exposed,recovered and death,and we propose a malware propagation model based on cellular automata.Secondly,according to the transition function of cellular,the differential equations describing this malware propagation model are proposed to present the transition relationship between HSNs in different states.Thirdly,we calculate the equilibrium point of this malware propagation model and attain the basic regeneration number governing the stability of the equilibrium points using the next generation matrix.And then we prove that the malware-free equilibrium point of the malware propagation model is locally asymptotically stable,and attain the threshold for whether malware will diffuse or die out in HWSNs.Finally,via experimental simulation,we verify that when the basic regeneration number is less than 1,the malware propagation model converges to the malware-free equilibrium point,and malware will die out.(3)Using the optimal control theory,we construct the optimal control strategy to control the malware propagation in HWSNs.Firstly,consiering the heterogeneity of HSNs' s degree and the heterogeneity of the incubation period for malware,we propose a new malware propagation model to describe the state dynamics of HSNs in HWSNs by extending the classical SIR model.Secondly,we prove the existence of an optimal control problem with installing antivirus on HSNs to minimize the sum of the cumulative propagation probabilities of HWSNs at a low cost based on this malware propagation model,and then we further derive an optimal control strategy for the problem using the optimal control theory.Thirdly,the optimal control strategy based on this malware propagation model is transformed into a corresponding Hamiltonian by the Pontryagin's Minimum principle,and the corresponding optimality system is derived.Finally,the experimental results verify that the optimality control system is validated in suppressing the malware propagation.(4)Considering the malware attack correlation,we evaluate the steady-state availability of HWSNs based on semi-Markov chain theory.Firstly,considering the malware attack correlation,and the characteristics of malware hiding and acting,we propose a new malware propagation model by adding the HSN's states of threatened and active based on epidemic theory.Secondly,considering that the HSN's IDS and malware are two agents,we establish an SADG(Stackelberg attack-defence game)to predict the optimal propagation probability of malware.Thirdly,considering the heterogeneity of HSNs and malware attack correlations,we derive the state transition probability matrix of an HSN based on semi-Markov chain.We further derive the steady-state availability of an HSN,and the steady-state availability of HWSNs with various topologies,including the star topology,cluster topology,and mesh topology.Finally,we obtain some important factors to improve the steady-state availability of HWSNs by the data analyses.