Crypto-currency is an implementation of E-Cash. I think most expected a company would create a centralized system like what Paypal is but Friedman does say "without record" and certainly you need only the email addresses for sending money if both are on Paypal and in good standing.

Cryptocurrency is a fusion of several ideas: Signatures, peer-to-peer, and distributed ledger and some way to issue such currency (now that we have other methods apart from proof of work).