[UncleMeat]

This isn't really a property of cryptocurrencies, but a property of signed transactions. We could absolutely have traditional banking transactions online where you don't give the information to the PoS that is sufficient to create a new transaction. In fact, this is exactly what chips are doing in an in-person transaction. The hard part here is getting everybody to have the right equipment and software to sign these transactions when purchasing stuff online.

Cryptocurrency does not actually solve this problem. It just gives people a greater incentive to push through the pain of solving this problem.