We analyze a two-country economy with complete markets, featuring two national currencies as well as a global (crypto)currency. If the global currency is used in both countries, the national nominal interest rates must be equal and the exchange rate between the national currencies is a risk-adjusted martingale. Deviation from interest rate equality implies the risk of approaching the zero lower bound or the abandonment of the national currency. We call this result Crypto-Enforced Monetary Policy Synchronization (CEMPS). If the global currency is backed by interest-bearing assets, additional and tight restrictions on monetary policy arise. Thus, the classic Impossible Trinity becomes even less reconcilable.