Here is an excerpt from a description of one version of Chaum's digital cash, which I posted on Nov. 25:
There are lots of proposals for electronic cash in the literature, mostly very complex. I think one of Chaum's simpler proposals would be adequate for email "banking". This proposal, from the beginning of his paper "Untraceable Electronic Cash" in Crypto 88(?), goes like this:
1. Alice chooses a random x and r, and supplies the bank with B=r^3*f(x) mod n, where f is a one-way function (like MD5), and n is the modulus for the bank's public key.
2. The bank takes the third root of B (e.g. via an RSA decryption) and sends it back to Alice: D = r * f(x)^(1/3), and withdraws one dollar from her account.
3. Alice extracts C = f(x)^(1/3) by dividing D by r. (Note that division can be done mod n without knowing the factors of n, but it's rather complicated.)
4. To pay Bob one dollar, Alice gives him (x, C).
5. Bob can verify that C = f(x)^(1/3), but he still has to send (x, C) to the bank in order to make sure that x hasn't been used before. Otherwise Alice could spend (x, C) twice. The bank increases Bob's account by one dollar.
This scheme is pretty simple and provides untraceability - the bank saw B and D but not C, so although it can verify that (x, C) is legit, it can't correlate that with Alice's withdrawal.
The main disadvantage of this approach is that Bob has to send (x, C) to the bank right away (or at least before sending Alice anything in return for her cash) to verify that the cash hasn't been used before. But in email, where turnarounds of a day or more aren't unusual, this should be tolerable.
Alice and Bob could be pseudonyms, using anonymous addresses to communicate with each other and with the bank.
Different denominations of cash could correspond to different exponents than "3" in the example above. (That is, $1 would use C=f(x)^(1/3), $2 would use C=f(x)^(1/5), $4 would use C=f(x)^(1/7), and so on.)
Technically, this would be quite easy to implement, using the code in PGP for the arithmetic, and MD5 for the one-way function. We'd need to define a few message formats. The RFC1113 ascii encoding from PGP could be used as well.
The "social" problems are more challenging, it seems to me. What is the backing for this electronic money? Why do people care what their bank balances are? Is this stuff really worth anything?
One possibility is to base digital cash on real money. People would open a pseudonymous account via email, then postal-mail dollars to the bank, enclosing their account number so the bank would know whom to credit with the deposit. Later, if someone wanted to withdraw "real money" from their account they would have to give a real postal address where it could be mailed. Now the electronic money is worth real dollars. Even if people didn't deposit or withdraw very often, it still has value because of the backing.
Unfortunately, this approach would currently be illegal (at least, unless you actually were a real bank!). If there were some way the bank itself could be anonymous, it might survive, but I don't see how to mail it money while keeping the anonymity. Still, we could consider experimenting with this on a small scale with accounts of no more than a few dollars. As long as it was clearly an experiment I doubt that any prosecutions would result even if it attracted government attention, because the expense involved in court costs would be so disproportionate to the few dollars involved in this technically illegal act.
Another approach would be not to try backing the digital cash at all, or rather backing it implicitly by the determination of various people to accept it and perform services or supply goods in return for it. Tim's offer to Xerox papers in return for digital cash would be one example. Perhaps others could provide some other services. It would be great if some shareware author would accept digital cash as a symbol of support for crypto anonymity.
One problem that I see with this approach is how you determine the size of the money supply. Or, in other words, how does new digital cash get started circulating? How do people get new accounts, and how much money is in them?
If these problems can be solved, a big advantage of this approach is that the banker can be anonymous. He would be known only by his anonymous address and his public key(s). This would provide some safety in the event that even a small-scale experiment like this was targetted for a crackdown.
Another issue is the prospect of multiple "banks", each issuing their own (incompatible) cash. How would they compete? Perhaps in terms of rapid turnaround? Some might choose to be anonymous, others would go public. The latter would have the advantage that people might trust them more, but OTOH there is more chance of your bank account disappearing after a crackdown for a public bank than an anonymous one.
Lots to think about here!
Hal 74076.1041@compuserve.com