Mike Ingle:
After-the-fact detection probably won't fly, because organized multiple spending could kill it. There are people who are dumb enough to write their PIN numbers on their ATM cards.
Nevertheless, millions use ATM cards, with substantially less loss to fraud than with credit cards. Improvement in privacy and reduction of incidence of fraud over credit cards are sufficient goals for a digital cash system. For Pretty Good Digicash, which would probably far exceed those goals, how about a "mostly offline" system as follows: * Modify offline cash to be "stochastically online", so that 1 out of every N coin transactions are checked for double spending online, and the remainder of the coins are kept offline. The chances of getting away with K+1-spending a coin are (1-1/N)^K. The chances of getting away with K+1-spending each of M different coins are (1-1/N)^MK. In general, with a fixed upper limit on coin denominations, the chances of getting caught at the scene of double-spending increase exponentially with the amount double-spent. This means penny-ante fraud will be easy to get away with (at the scene), but large scale fraud quickly becomes impractical. This also means that most low-value transactions will be offline and most high-value transactions online. Note that above formulae are the odds of getting the goods before being caught. Even if by chance all coins are kept offline during the fraudulent transactions, the odds of two making it back to the bank increase exponentially with the number of times they change hands. Thus even penny-ante double-spenders will soon be caught, with odds quickly approaching certainty, after the fact. The double-spender's 'nym is then revealed, and its reputation damaged or destroyed. * N is the credit rating of the customer. 'Nyms with good, solid credentials and/or long-standing reputations can be trusted to spend large amounts of digital cash per online check. New 'nyms, 'nyms with bad credit ratings, and anonymous spenders have lower N and are thus checked more often. Attempting to defraud via rapid turnover of penny-ante double-spending 'nyms won't pay, because the odds of a new 'nym getting caught online can be placed as high as needed to make this strategy a loser. At the first sign of double-spending, or if other signs of bad credit accumulate, credit rating N is lowered for the customer. N should be set by credit rating agencies so that (Max coin denomination)*MK*(1-1/N)^MK is less than the 'nym's accumulated "reputation capital", so that it does not pay to build a reputation and then "cash in the reputation chips" with a spectacular act of digicash fraud. Since the reputation capital of most customers will dwarf the average size of their purchases, in practice the vast majority of purchases will be offline, with only a few (mostly large) purchases held up for online verification (which need not take any longer than online verification of credit cards today). I envision a decentralized credit-rating system, so that the integrity of ratings cannot be jeopardized by corrupting one or a related few credit rating agencies with false information. (The IP paradigm: an economy should be able to route around node failures). Nick Szabo szabo@netcom.com HEx symbol: N :-)