A Game Theoretic Study of Attack and Defense in Cyber-Physical Systems

Chris Y. T. Ma, Nageswara S. V. Rao, David K. Y. Yau

Agenda

Motivation System model Boolean attack and defense System with robustness Conclusion

Motivation

Cyber-physical systems Model a number of engineering infrastructure systems

Physical – hardware components Cyber – computations, communications

Susceptible to attacks

Motivation

Our objectives Use of game theoretic formulations to capture the

attack and defense of cyber-physical systems Study the survival of the cyber-physical systems using

different utility functions

Motivation

Our observations Pure strategy Nash Equilibrium (NE) may not exist Cost boundaries (budgets) may determine the NE

outcome The presence of NE does not mean the system

survives

System Model

System Model

Boolean Attack and Defense

Special case of attacks where the cyber and physical parts can be attacked or defended as whole units

Successful attack on either cyber or physical part will disrupt the whole system

Boolean Attack and Defense

Boolean Attack and Defense

System with Robustness

General case when resources are not represented as one whole unit

Consider different benefit functions

System with Robustness

The players’ best response functions

System with Robustness

General Benefit and Cost Functions

General Benefit and Cost FunctionsOne-space cases

Observation Pure strategy Nash Equilibrium is rare, most likely to

exist when the attacker has tight budget

General Benefit and Cost FunctionsOne-space cases

General Benefit and Cost FunctionsTwo-space cases

Observations Resource allocation is non-trivial even without an

attacker, and greedy approach may be sub-optimal, e.g., the S-shaped benefit function

The NE results are sensitive to the parameters of the payoff functions in the two spaces

General Benefit and Cost FunctionsTwo-space cases

Observations

System ACyber space: Ba

Physical space: Ba

NE: X

System BCyber space: Bb

Physical space: Bb

NE: X

System CCyber space: Ba

Physical space: Bb

NE: ?

General Benefit and Cost FunctionsTwo-space cases

Conclusions

Presented a game theoretic formulation of the interplay between a rational attacker and a rational defender in cyber-physical system security

Studied the presence (or absence) of pure strategy Nash Equilibrium using different payoff functions