It would be quite a twist if a technology whose most ardent fans are motivated by distrust of central banks became a key tool for those banks.

But it would address some of the concerns connected to Bitcoin and its many privately created rivals. To the degree that the value of existing cryptocurrencies fluctuates wildly, they are ill-suited as a medium of exchange. Central banks have spent hundreds of years learning how to keep the value of money stable.

And to the degree Bitcoin and the like facilitate tax evasion, money laundering and fraud, they will be a target of global law enforcement. Central banks are used to building systems that allow enforcement of those laws.

It’s clear that central banks weighing use of blockchain technology don’t share the more anarchist impulses of some of the most die-hard cryptocurrency enthusiasts. But there may be more commonality than it might seem. As Mr. Warsh argues, if people really do believe that digital currencies in some form are the future of money, it would behoove central banks to treat them as more than a novelty.

“Congress gave the Fed a monopoly over money,” Mr. Warsh said. “And if the next generation of cryptocurrencies look more like money and less like gold — and have less volatility associated with them so they would be not just a speculative asset but could be a reliable unit of account — as a purely defensive matter I wouldn’t want somebody to take that monopoly from me.”

In other words, if cryptocurrency enthusiasts are correct that this technology could become a better way of carrying out even routine transactions, the Fed and its counterparts are the institutions that have the most to lose.