Illegal, copying of data is a problem in many areas. Despite various efforts in copy protection and copyright enforcement the problem still exists, and with the growing use of digital means of storing and distributing data the problem seems to be getting worse.

Storing a unique, invisible marking in each distributed object is a possible way of dealing with the problem of illegal copying. That way, if an illegal copy is found somewhere, it is possible to find the original holder of the object. This type of scheme is called fingerprinting.

The thesis deals with codes for fingerprinting of digital data in the context of several users colluding to create an untraceable, illegal copy. Some theoretical bounds on the performance of such codes are presented. A general method to statistically test whether certain users have taken part in the creation of a particular illegal copy is presented, and pirate strategies that prevent this kind of testing are derived. A simple testing method is presented that tests whether a certain, proposed group of users should be considered guilty of having created a specific illegal fingerprint. The set of possible pirate strategies

is derived and a compact representation is presented. It is shown that the fingerprinting problem is fundamentally a game theoretical problem. Finally, a combinatorial performance measure for binary fingerprinting codes is presented, and several code constructions are analyzed using this measure.