I think that very few would have the initiative to lay out the money for a no-transaction cash system. With credit cards and checks there is a transaction trail that you can follow to spot and get rid of fraud. I trust that for "transaction" above you mean "audit". You still have transactions and you still have audits. It's just that this information does not allow for the derivability of the customer's transaction. Assume four accounts in the books of an issuing bank: one asset account, cash, and two liability accounts, one for a customer and one suspension account for digital banknotes issued by not yet redeemed. The withdrawal transaction posts a debit to a customers demand deposit account (decreasing it) and a credit to the suspension account (increasing it). Now suppose the customer buys something from a merchant, and the merchant redeems the digital banknote cash. The deposit transaction posts a debit to the suspension account (decreasing it) and a credit to the cash account (also decreasing it). As you can see, there are perfectly good journal entries for each of the two transactions just described. What is missing is an audit trail to determine which debit to the suspension account corresponds to which credit to the suspension account. An assurance that these match up is provided by two properties. First, for each banknote issued there is one and only feasibly computable modification of it that is acceptable for redemption. (In Chaum's scheme this is the unblinding.) Second, a database of the banknotes as redeemed is kept, which prevents multiple redemption. Will it be a replacement to ATM and credit cards or would it be a concurrent working solution? Concurrent, of course. There's very little point to scrap any existing system as a system. Individual merchants may decide not to support older systems eventually, but that is a different issue. Nonetheless, I have argued at length at other times that digital cash will not be viable as a physical retail system very soon. Where digital cash is immediately useful is online as a retail level wire transfer system. Chaum: Such a verification procedure might be acceptable when large amounts of money are at stake, but it is far too expensive to use when someone is just buying a newspaper. Maybe a physical newspaper today, but the cost of networking is dropping and the cost of computation is dropping. I personally don't expect that off-line digital cash techniques will ever actually be economically most efficient. Existing alternates (e.g. credit cards) work well enough today, and by the time PDA's work well enough and are cheap enough to be universal, the cost of an online verification will be down in the fractions of a cent. Eric