The effect of cryptocurrency security protocol on the medium of exchange properties were studied. Notably, cryptocurrencies make use of cryptography as holders of coins store their currencies such as Bitcoin at an address on a decentralized ledger that is linked to both a private and public key. If the device storing a private key is lost or dam-aged, the coins will be lost permanently. Consequently, the currency loss creates condi-tions where private money circulates. It is also likely to impact whether the supply of pri-vate money over time would be socially efficient. Intermediaries can be valuable firms that help individuals avoid uncertainty from holding cryptocurrency by providing safe-keeping of tokens. We consider that there may be different types of intermediaries who offer different services including safe-keeping and providing transactions services. Notably, we find financial intermediation improves the volume of decentralized trade regardless of the type of bank. However, the largest gains occur when banks only provide safe-keeping for tokens that are borrowed. With banks pro-viding safekeeping for all tokens, token loss will be eliminated but a steady-state equilib-rium only exists when total token production is capped. Lastly, in order to study the effect of monetary policy on price movements ofcryptocurrency, we use a standard Vector Autoregression (VAR) framework to identify shocks to the stance of monetary policy. We find that positive shocks to the size of themoney stock cause the prices of both Bitcoin and Ethereum to increase. From this per-spective, our results do indicate that investors have sought out access to cryptocurrencies as central banks have adopted easy monetary policies since the end of the Great Financial Crisis.