Models of information influence for assessing information systems security
3. Simulating dissemination of destructive information influence within the information system
When modelling and analysing the process of dissemination of DII we regarded the IS as a two-dimensional cellular automaton. A two-dimensional cellular automaton is a set of finite automata (subjects of the IS) allocated on the reference frame and marked
with integer coordinates ( ji, ). Each automaton can have certain properties and be in
one of the states S ∈i,j {S1,S2,..,Sk}. The state of a finite automaton ( ji, ) at a certain
moment in time t +1 is determined as follows [8, 9]:
), ), , ( ), ( ( ) 1 ( , , t F S t N i j t Si j + = i j (3)
where F is the rule for the transition of state of the automaton; N( ji, )is the point neighbourhood ( ji, ); t is a step on the axis of time.
In the cellular automaton model each cell changes its state while interacting with a limited number of other cells, normally adjacent ones with the same side or vertex. Therefore, it is easy to see the connection between the processes occurring on the micro level and the processes of spatial interaction between the elements [8].
To describe the process of dissemination of DII within the IS the following model is suggested. Information interaction within the IS is presented as a two-dimensional cellular automaton, whose grid is a two-dimensional array, where each cell is
numbered with an ordered pair ( ji, ). Each cell is an information system subject. The
nearest neighbours of each cell are considered the cells that have a common vertex with the one observed (Moore neighbourhood). Thus, each cell has 8 nearest neighbours. To eliminate the tip effect, the grid of the cellular automaton is topologically twisted into a torus [8], i.e. the first line is considered to be the continuation of the last one, and the last one precedes the first one. The same applies to the columns [9].
Each cell may be in one of the following states: S0 - initial state; S1 - the subject developed a reaction to the DII, but does not distribute it; S2 - the subject took in the DII, but does not disseminate it; S3 - the subject developed a reaction to the DII and distributes it; S4 - the subject took in the DII and disseminates it. Depending on the state and the inner properties, a cell may or may not disseminate the DII (by influencing the neighbouring cells). The state and behaviour of cells change according to the rules set for the suggested model. This rules consider the inner parameters of the IS subjects and their state. A state transition graph is presented in Fig. 3.
Figure 3 - State transition graph
The subject may either take in the destructive information influence or resist it. Depending on the inner parameters, the subject may also disseminate the DII within the IS, or not.
In our study we used the following modelling algorithm: initial stage - main properties of the IS subjects are determined; first stage (corresponds to the origin on the time axis) t=0- the whole grid consists of cells in state S0, except for certain cells that
initiate the DII; second stage - the DII is disseminated along the time axis t= +t 1, the
inner parameters of the subjects are determined basing on the suggested model; cells with the value of DII dissemination equal 1 pass on the information to the neighbouring cells.
3.1 Results
Fig. 4 demonstrates the functioning of the automaton when most subjects are neutral to the DII. Fig. 5 demonstrates the functioning of the automaton when most subjects are negative to the DII. Fig. 6 demonstrates the functioning of the automaton when most subjects are positive to the DII. Figures “a” demonstrate the functioning of the automaton when the subjects take in the DII from other subjects. Figures “b” demonstrate the functioning of the automaton when the subject can resist the DII.
a b
Figure 4 - Distribution of cells according to the discrete time (most subjects are neutral to the
a b
Figure 5 - Distribution of cells according to the discrete time (most subjects are negative to the
DII)
a b
Figure 6 - Distribution of cells according to the discrete time (most subjects are positive to the
DII)
Analysis of Figures 4-6 shows that
- the character of dissemination of the DII within the IS is practically exponential; - when the subjects are neutral to the DII (Fig. 4a), just a small number of initiators can successfully perform the DII;
- when the subjects are negative or positive to the DII (Fig. 5a and 6a), the DII does not influence their state;
- when the subjects can resist the DII (Fig. 4B, 5b, and 6b), the number of subjects in states S3 and S4 is similar, irrespective of their initial state.
The suggested model demonstrates the connection between the process of dissemination of DII within the IS and the changes in the states of the IS subjects resulting from the interaction of interconnected subjects.
4. Conclusion
The suggested model of conflict interaction between the information system and the adversary, and the obtained analytical relations for approximate estimate of probability and lower probability of information security violation, demonstrates that it is not necessary to determine the specific type of distribution density for the duration of each possible state of the parties of the conflict. This model can be successfully applied to
various problems concerning the security of ISs. The suggested model of dissemination of destructive information influence within the information system shows the connection between dissemination of destructing information influence and the process of state transition of the information system subjects. It is very important for studying security problems of information systems based on modern information technologies. Using both models together allows for a comprehensive study of the main factors effecting the security of modern information systems.
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Igor Goncharov - Ph.D., CEO JSC “NGO “Infosecurity”
Nikita Goncharov - Information Security Specialist JSC “NGO “Infosecurity” Pavel Parinov - Information Security Specialist JSC “NGO “Infosecurity”