Peer-to-Peer

In some environments, it doesn't make sense to place all the power and responsibility on a central server. Peer-to-peer networks can also trade bills, although they must take some extra precautions to prevent counterfeiting. Anyone can hand over a bag of bits to another player, but there's no simple way to prevent them from counterfeiting by handing over the same bits to other people.

The best approaches can only reduce the load on the central bank because there's no way to eliminate it. All of the notes must run through a central location to check for counterfeiting, and the security of the system is directly proportional to the time between checks. Banks may check only a fraction of the bills chosen at random, but they can't eliminate the check altogether.

A transaction in this scheme will look something like this:

The notes grow each time they're spent in this scheme forming a chain of custody for the cash. Counterfeiting, if it happens, can be identified by looking at the chain of custody. If two bills with the same serial number appear, the counterfeiter can be identified by walking up the chain of custody to find the person who spent it twice.

The role of the bank depends upon the nature of the game. In the most extreme case, there's no need to look for counterfeiting because the game comes to a grand conclusion when everyone turns in their notes and their pieces, perhaps to claim a share of a purse. If there's one final judgement, then everyone can search for cheating at that point. There's no need for auditing along the way.

Often, waiting for the end of the game can be a mistake. Some games come with no ending. Others could be wrecked by some jerk counterfeiting like crazy.

Auditing can take any number of forms. Complete audits every n turns would require everyone to turn in their bills and receive new ones. This also saves overhead because the new replacements would not have a potentially long chain of digital signatures to be checked. The auditing will also clean house and add efficiency.

Another strategy is to recall bills selectively. Every so often, the bank will ask all bills with a serial number ending in, say, a 3 to be turned in. If this value is chosen at random, the cheaters won't be able to time their counterfeiting for maximal effect.

Making Change

Digital cash systems in peer-to-peer environments work more efficiently if the peers can split notes and make change. Requiring people to head to the bank to make change may help auditing, but it may be too onerous in any peer-to-peer environment.

Another solution lets users split the bills themselves. The simplest approach is to allow users to insert a message into the chain of digital signatures that says, in effect, "This bill has been split into n pieces and this is piece number i." Everyone who accepts the bill afterwards will treat it as being worth only 1/nth of the original denomination.

If n=10, then adding digits to the serial number is an efficient solution. A player with bill number 1045 would split into ten parts by creating new serial numbers 10450,10451,¼,10459.

Removing the Central Bank

There's no reason why there should be only one central bank for each game. While it may be efficient in some cases, it can be a bottleneck or an imposition on others. Some games may want to allow multiple banks or even allow each player to run their own bank.

In the most extreme case, each player also acts as their own bank. Instead of withdrawing cash from a central location, they simply mint it themselves. This temptation is not as dangerous as it sounds because players can place limits on each other.

For instance, if a board game begins by giving each player $100, then each player could begin with the right to issue 100 notes with serial numbers between 0 and 99. If someone notices a bill with a serial number outside of this range, then there's evidence of counterfeiting or at least inflationary spending.

Multiple banks do not change the transaction process. Each player still checks the validity of the chain of signatures and looks for potential duplicate serial numbers. In some sense, the issuer's name or number is just another part of the serial number for the bill.

Multiple Audits

Separating the auditors from the company is one tradition from the business world that can work here. There's no reason why the same person needs to maintain the bank and audit the transactions.

One simple solution is to allow any player to recall bills at any time. Well, subject to some rational limit. One player may ask all players to turn in a particular subset of bills at one time. Demanding all that end with the serial number `5' would pull in one tenth of the notes and uncover any cheating from that set.

The auditor can either return the notes to circulation or replace them with new notes drawn on a new bank. Having multiple players issue new notes will make things more confusing, but reduce the ability for individual players to create havoc. If another player may recall notes at any time, cheating can be discovered faster.

The downside of these multiple audits can be confusion. What happens to the status of a note if it isn't returned? It will not be valid, but what if this happened because of a software glitch or a communications failure? Is there a failsafe process? Adding all of the layers of audits discourages some cheating but certainly increases the complexity of the game.

Conclusion

Digital cash systems are just more specialized versions of the process for controlling the proliferation of objects. Every digital game must stop people from duplicating desirable objects, and cash is often the most desirable object. There's no reason why other objects can't be defined with the same system if the rules of physics apply. It may not make sense to split apart a suit of armor, but there's no reason why a flagon of beer can't be split into n different parts.

The schemes in this chapter offer a rudimentary form of privacy that may not be ideal in all cases. While a distributed mechanism doesn't let any one player pay too much attention to another, all the transactions are essentially in the clear. If you can see all of the bills, you can know who did business with whom. This can be a problem because people can pick up the data as the bills circulate.

Lessons