My definition of digital currency

It is a coin, made of encryption bits. Central payment clearing is optional. 

The serial numbers of every digital coin and the digital wallet it came from are known only to the digital wallets exchanging the digital coin. It is up to the payees to voluntarily aggregate payments and look for fraud. It is up to them to insure digital wallets have a physical counterpart that it difficult to counterfeit, like smart card that are tamper proof.

So when a shopkeeper accepts a MasterCharge digital payment, he is looking over the card construction, then collecting wallet id and coin ids. He may check personal ID.  Beyond that, he can spend the stuff without ever checking with MasterCharge. But the shopkeeper has some prior agreement with MasterCharge to clear accounts. Or his deposit bank may require clearing accounts, mainly for fraud detections, are their duplicate bitcoin IDs out there.

 I think Bitcoin keeps the chain of transactions between account clearings. That way they can ultimately reconstruct the accounts  and discover any cheats. They have to do that because the ultimate central banker is a web bot without a second job. But JP Morgan could skip even that step assuming the smart cards were very counterfeit proof. When the frauds are discovered, they split the difference with an insurance payment, and one of the duplicates deleted.

So in the libertarian version, if I risk it, I can collect digital coin payments in my digital wallet and never report my wealth, for decades! The only way to find my wealth would be to interrogate a large number of payer wallets, and get a representative sample. In a cokmpletely libertarian version of digital coin, the system need only know the wallets are valid,  but they remain anonymous.