Stackelberg Games for the “Active Deception” Strategy in the Process of Critical Infrastructure Migration to Post-Quantum Cryptography

The coming era of quantum supremacy has created an existential threat to critical information infrastructures (CIIs). This threat is realized through delayed attack vectors of the “Harvest Now, Decrypt Later” (HNDL) class. Existing security paradigms dictate forced migration to post-quantum cryptography (PQC) algorithms. However, in the context of legacy architectures, and in particular in the ICS and SCADA segments, such a strategy generates quantum technological friction. This friction can trigger cascading failures of legitimate CII services. This article proposes addressing the PQC transformation problem not as a linear IT modernization task, but as a general-sum differential Stackelberg game. The concept of “active deception” (Cyber Deception) is described as a Leader (Defender) strategy, i.e., the variable redistribution of budgets between real cryptographic migration and the generation of resource-intensive decoy infrastructures. Using the Forward-Backward Sweep Method algorithm, optimal software controls are obtained for three typical architectural profiles, calibrated using statistical data from the critical information infrastructure of the Republic of Kazakhstan. Numerical simulations have demonstrated that in high-inertia and strategic networks, maximizing active deception creates the necessary “temporal buffer”, minimizing the damage from an HNDL compromise while maintaining operational continuity. The results support the need to revise rigid cryptographic transition regulations in favor of flexible, mathematically sound hybrid strategies.