Maximin optimality of the arcsine fingerprinting distribution and the interleaving attack for large coalitions

Fingerprinting codes provide a means for the digital content distributor to trace the origin of an unauthorized redistribution. The maximum achievable rate, or capacity, has recently been derived as the value of a two-person zero-sum game between the fingerprinting embedder and the pirates. Under the so-called Boneh-Shaw marking assumption, we prove rigorously that the asymptotic capacity is 1/(k² 2 ln 2), where k is the number of pirates. Furthermore, we confirm our earlier conjecture that Tardos´ choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotic behavior, numerical solutions to the game for small k are also presented.