Re: Brand e-cash implementation?
Brands has a web page at <URL:http://www.cwi.nl/~brands>. I don't know of any implementations of his technology. The last time I heard from him was early this year and at that time he apparently was still looking for backers. BTW he has a new paper out as of July 95, available above, which discusses some problems and attacks on some earlier papers. He had proposed a notion called "secret key certificates" in which some problems have been found. Basically a secret key certificate is just like a public key certificate (a signature by someone on a public key as in PGP) except that realistic-looking but ultimately worthless secret key certificates can be faked up (simulated) by anyone. No one can distinguish a fake secret key certificate from a real one. However, they are worthless because the faking process requires you to choose a random public key, and you can't figure out what the secret key is. Brands has (re)expressed his digital cash technology in terms of these secret key certificates. But Berry Schoenmakers of CWI has shown a way in which a faked-up secret key certificate can be used to spend a coin which was never withdrawn. However, to do so, you have to go through the withdrawal protocol in a particular incorrect way. You force the bank to act as an "oracle" for a certain discrete log problem when you do the withdrawal. The data you get from the incorrect withdrawal protocol allows you to spend the fake coin. So this is not actually a dangerous attack, because you in effect have to withdraw a coin in order to spend the fake one. You can't make any money from it. Still it was not anticipated and that is a bit worrisome. I'm not sure why Brands' various proofs of correctness (which are one of the big selling points of his technology) did not anticipate this attack. (In effect this is a different form of a blind signature than what Brands planned for, since you withdraw one thing and get another. I was thinking Brands should write this up under the title "Unanticipated Blinding for Signatures", a pun on Chaum's "Blinding for Unanticipated Signatures", one of his credential papers.) Brands has a workaround to prevent this attack, but it hurts the provability of his scheme. "A rigorous prove [sic] of the effectiveness of the measure may be hard to provide, though, since one must hereto prove that the CA cannot be used as an oracle to perform the cryptographic action in the showing protocol with respect to simulated public keys." So this may be a setback in Brands' attempts to get his thesis finished and accepted. As for the question of whether any digital cash scheme offers "true" anonymity, I think you have to be more specific. Virtually all cash advocates will claim that they can offer this. In the debate I had earlier with Lucky Green I argued that Chaum's ecash does offer a certain kind of anonymity. The extent to which it does not is largely not technical but a product of not allowing anonymous bank accounts. With anonymous accounts Chaum's technology offers as much anonymity as any system that I have studied. There is one technical problem with Chaum's ecash which Lucky mentioned, but I believe it applies to all systems. That is that the spender of the cash can "mark" it or at least recognize it when it is later deposited. If the spender wanted to attack the receiver of the money and it is deposited non-anonymously then this will be a problem. However, as we discussed here several months ago, Chaum's paper "Transferred Cash Grows in Size" from a recent Crypto proceedings shows that by colluding with the bank a payor of cash can recognize it at any later stage of the payment chain. So this kind of anonymity is very hard to achieve. Chaum's paper applied to off-line cash, though, so perhaps an online system could do it. But you'd have to blind the coins twice, once when they pass from bank to payor and once when they go from payor to payee, and I don't see how to do this. Hal Finney
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Hal