Fighting Two Pirates

A pirate is a person who buys a legal copy of a copyrighted work and who reproduces it to sell illegal copies. Artists and authors are worried as they do not get the income which is legally theirs. It has been suggested to mark every copy sold with a unique fingerprint, so that any unauthorised copy may be traced back to the source and the pirate who bought it. The fingerprint must be embedded in such a way that it cannot be destroyed. Two pirates who cooperate, can compare their copies and they will find some bits which differ. These bits must be part of the fingerprint, and when the pirates can see and change these bits, they get an illegal copy with neither of their fingerprints. Collusion-secure fingerprinting schemes are designed to trace at least one of the pirates in such a collusion. In this paper we prove that socalled (2,2)-separating codes often are collusionsecure against two pirates. In particular, we consider the best known explicit asymptotic construction of such codes, and prove that it is collusion-secure with better rate than any previously known schemes.