Abstract
The present paper addresses the problem of modeling the resilient operation of a cryptocurrency exchange (CEX) under delayed quantum attacks of the harvest-now-decrypt-later type. The proposed model diverges from extant approaches in its conceptualization of the quantum threat. Whereas extant approaches treat the quantum threat as an external shock, the proposed model conceptualizes the accumulation of cryptographically vulnerable data as an internal state variable of the system. The framework under consideration is formulated as a system of nonlinear differential equations linking the exchange’s liquidity, the intensity of post-quantum cryptography (PQC) adoption, and the volume of accumulated threat. The analytical conditions for asymptotic stability are derived. The resolution of the system enables the identification of a region of admissible defense strategies, which is interpreted in the paper as a “survival dome.” Numerical simulations demonstrate that both delayed and excessively aggressive migration strategies toward post-quantum cryptography may lead to the degradation of the exchange. The findings indicate that a balanced and adaptive transition strategy, aimed at mitigating quantum risks, can preserve liquidity while minimizing long-term losses. The findings establish a theoretical framework for the development of migration strategies for financial platforms undergoing a transition to post-quantum security standards.