Mathematical Modeling and Adaptation Strategies in the Confrontation Between Cryptocurrencies and Quantum Computers

<ns0:p>This article is dedicated to studying the resilience of cryptocurrency systems (CCS) under new threats associated with the development of quantum computing. A differential game model is introduced, allowing for the formalization of the interaction between CCS and quantum computers (QC), as well as the analysis of their mutual influence. The research methodology is based on the application of differential game theory to model the dynamics of resource allocation between the parties and to evaluate their strategies under conditions of uncertainty and competition. Various scenarios of confrontation between CCS and quantum computing were considered during the modeling process, which made it possible to identify key patterns and factors that significantly affect the effectiveness of cryptographic protection, as well as the computational capabilities of attackers utilizing QCs. Special attention is given to the analysis of different methods for protecting digital assets under potential quantum threats. The results of the study may serve as a foundation for developing new cryptographic security standards and adaptive protection strategies that will remain effective amid the rapid growth of quantum computing capabilities</ns0:p>