Game-Theoretic Defense Against Hardware Trojans with Multi-Level Strategies

Abstract

Hardware Trojans are malicious circuit modifications that can be covertly inserted during the design or fabrication of integrated circuits, enabling leakage, performance degradation, or mission failure after deployment. Because exhaustive testing against all Trojan classes and activation behaviors are prohibitively expensive, effective defense requires reasoning about the strategic interaction between an IC buyer/tester and a potentially malicious manufacturer. In this paper, we model Hardware Trojan insertion and testing as a two-player zero-sum security game with multi-level attacker and defender intensities. We first derive the Mixed-Strategy Nash Equilibrium (MSNE) under classical expected-utility assumptions and identify parameter regimes in which the game reduces to a smaller equilibrium over the remaining dominant strategies. Recognizing that real decision-makers exhibit bounded rationality, loss aversion, and distorted probability perceptionespecially under low-probability, high-impact threats-we then incorporate Prospect Theory to obtain a ProspectTheoretic MSNE (PT-MSNE) formulation. The resulting equilibrium conditions are nonlinear and are computed numerically under simplex constraints. Extensive simulations quantify how behavioral parameters reshape equilibrium mixing, shift the security-cost tradeoff, and alter defensive investment relative to the rational benchmark, providing actionable insights for designing robust and cost-effective Trojan testing policies under uncertainty and human bias.