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Subject: Digital Cash One point of digital cash is to allow electronic payments, so printing it on paper would not be useful as other than a novelty. People would have to scan the bit patterns back in, which would be inconvenient. How big will a piece of digital cash be? An electronic "dollar bill" in the simple scheme of Chaum's consists of two parts: (x, f(x)^(1/e). X is a random number, f(x) is a one-way function like MD5, and e is the exponent which could be taken to represent the denomination of the bill. MD5 takes 64 bytes as an input "chunk" so that would be a natural size for x. f(x)^(1/e) is f(x) "signed" by the bank using exponent e, so that would be about the size of the bank's modulus n, say 1024 bits or 128 bytes. Probably there would be some control information as well. So the total size of an electronic banknote would be 128 + 64 + a few, or about 200 bytes, maybe a little more. To print this you'd have to Ascii-encode it, which generally expands things by 1/3, so you'd get about 270 to 300 characters per bill/coin. This would be around four or five lines of text, comparable to a PGP key (and looking about as interesting - totally jumbled letters and numbers). "Forgery" is in one sense hard and in one sense easy. It's hard because to create new dollar bills because you have to forge a signature using the bank's public key (n, e). This is equivalent to breaking at least some uses of RSA. But it's easy to reproduce existing electronic dollars, and you don't even need a Xerox machine. Just "copy dollar1 dollar2" on your PC, and repeat the process. Presto, plenty of dollars, all exactly the same. Send one to the butcher, one to the baker, and you've still got plenty more where those came from. Keeping this kind of re-use from occurring is one of the things that makes electronic cash tricky. Chaum's simple scheme has the receiver of cash calling the bank or sending the cash there right away. The bank has a list of "serial numbers" for all the cash that's ever been deposited, which it compares against to see if this is a re-use. The first person to deposit a dollar with a given serial number gets credit for it; the others are told that it's worthless. Another area that people seem a little unclear about is the difference between electronic cash and electronic checking accounts. A checking account could be managed by simple RSA-signed messages (e.g. created with PGP) saying, please transfer $X.00 to account number XYZ. If you wanted to buy something from someone, you'd find out what his account number is with the bank, write up a little note like this, sign it using your public key with PGP, and email it to the person that you wanted to buy from. He'd send it on to the bank and his account would get credited. Again, you'd want to put a serial number on your check so that the guy couldn't send it again tomorrow and get another $X.00. Or, you could just send it directly to the bank and request the bank to notify the seller that the funds had been transferred. This would seem to avoid the re-use problem. The difference between this system and electronic cash is that the bank knows exactly what is going on. It sees all transactions, so it knows which accounts are making payments to which other accounts. This is true of ordinary paper checking accounts as well, of course. Electronic cash is designed so that not even the bank can tell who is paying whom. I withdraw some cash, say, $100.00, and I pay you $35.00 by mailing you the electronic bills. You deposit them. The bank has no way of determining which particular withdrawal produced those bills which you are depositing. This is, more or less, how real cash works. Hal 74076.1041@compuserve.com