Random Binary Fingerprinting Codes for Arbitrarily Sized Coalitions

New lower bounds are established on the rate of fingerprinting codes secure against coalitions of an arbitrary constant size t. In particular, it is proved that there exist sequences of binary fingerprinting codes with vanishing probability of misidentification and rate approximately 1/(t 2t). In the case of t = 3 it is shown that there exist codes of rate 0.064 which is better by an order of magnitude than previously known results.