Behavioral and Strategic Modeling of Trojan Insertion and Testing Under Imperfections

The presence of hardware Trojans in Integrated Circuits (ICs) poses a serious security concern for cyber-physical systems (CPS), and mitigating such threats has become increasingly critical. In this paper, we address the problem of testing Integrated Circuits (ICs) for the presence of hardware Trojans, considering the hierarchical classification of Trojans, the inherent imperfections of testing processes—including different detection probabilities and false alarm probabilities—and the strategic and behavioral characteristics of IC buyers and manufacturers. We demonstrate that these factors significantly influence the design of Trojan insertion and detection strategies. Under a hierarchy of Trojan types and testing imperfections, we first analytically characterize Trojan insertion and testing strategies at the Nash Equilibrium (NE), assuming the buyer (defender) and the malicious manufacturer (attacker) are strategic and rational. Subsequently, we extend this analysis to account for behavioral irrationalities (cognitive biases), examining the impact of these biases on strategic decision-making. Our results highlight the asymmetric effects of detection probabilities, false alarms, and behavioral irrationalities on the defender and attacker utilities. Finally, extensive simulation results are presented to validate the analytical findings and provide deeper insights into optimal Trojan insertion and testing strategies.