As far as the issue of receipts in Chaumian ecash, there have been a couple of approaches discussed.
The simplest goes like this. If Alice will pay Bob, Bob supplies Alice with a blinded proto-coin, along with a signed statement, "I will perform service X if Alice supplies me with a mint signature on this value Y". Alice pays to get the blinded proto-coin Y signed by the mint. Now she can give it to Bob and show the signature on Y in the future to prove that she upheld her end. A slightly more complicated one starts again with Bob supplying Alice with a blinded proto-coin, which Alice signs. Now she and Bob do a simultaneous exchange of secrets protocol to exchange their two signatures. This can be done for example using the commitment scheme of Damgard from Eurocrypt 93. Bob gets the signature necessary to create his coin, and Alice gets the signed receipt (or even better, perhaps Bob's signature could even constitute the service Alice is buying). I would be very interested to hear about a practical application which combines the need for non-reversibility (which requires a degree of anonymity) with the need to be able to prove that payment was made (which seems to imply access to a legal system to force performance, an institution which generally will require identification). CP --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]