Antagonistic Differential Game of Critical Infrastructure Migration Management to Post-Quantum Cryptography Under HNDL Conditions

Advances in quantum computing have created a serious threat to modern asymmetric cryptosystems protecting heterogeneous critical information infrastructures (CIIs). During this transition period, the primary threat is the “Harvest Now, Decrypt Later” (HNDL) temporal strategy of attackers, which requires the forced migration of CIIs to post-quantum cryptography (PQC) algorithms. However, such migration is associated with nonlinear “technological friction.” This will manifest as a drop in the performance of legacy systems, such as SCADA. In the context of deep cross-industry integration, this can trigger avalanche-like cascading CII failures. This article presents a model of a zero-sum differential game between a CII defender and an attacker (APT group). Using Pontryagin’s maximum principle and the Forward–Backward Sweep Method (FBSM) iterative algorithm, a saddle point was found that determines the equilibrium trajectories of limited resource allocation over a given planning horizon for the CII transition to PQC. The results of the computational experiment demonstrated that isolated sectoral migration is ineffective. It is shown that optimal control requires cross-sector synchronization to prevent cascading degradation of the CII. The proposed mathematical framework provides a practical toolkit for strategic IT budget planning and national security risk management in anticipation of quantum supremacy (Q-Day).