Anonymous Transactions
One of the fashionable things about ecash is (or at least was back in the mid 90’s when ecash was fashionable, and pre-September 11) that it can provide anonymity: neither the bank, or the merchant, or the government can track how you spend your money. Lucre provides anonymity to the degree that you can’t do any correlations at all except by traffic analysis. This potentially allows vast amounts of money laundering, and the benefit is somewhat questionable.
It should be trivial to do away the anonymity in lucre by requiring the blinding factor to be 1. Other possibilities are only issuing particular variants of the currency to suspected launderers: so any currency marked with a big “D” that’s spent anywhere is likely to be drug money, and you can see where the money goes, but not where it came from. You can’t do this with a great deal of secrecy from the person you’re trying to spy on, which makes their choice “accept that the bank can see what I’m doing, or don’t use ecash”, but that’s going to happen anyway. To a point, it trades off law enforcements ability to easily monitor criminal activity and trace it, to the ability to stop criminals from being able to accept money. Except that it doesn’t really work that well.
What benefits does anonymity provide? It means you don’t have to keep track of accounts, but I think you have to do that to keep your bank in the black anyway. Since you have to track transactions anyway, it doesn’t give you an excuse to use significantly less storage, either. On the upside, it avoids embarrassment, if you know you’re never going to get a statement, but that can be arranged by never giving out statements. Non-anonymity might be a lie, in that you can do money laundering in someone else’s name anyway, and get the cash yourself with good assurance, without having any of your accounts ever used — but knowing who your launderer is is probably more important anyway (Drew buys a car from Joe, using Laura’s cash – police track down Joe, ask for his receipts, start wondering who this Laura is…)
Probably better to provide something that’s anonymous, then remove the anonymity if it’s not valuable, though — doing it the other way around would probably be hard.