Discrete Distributions in the Tardos Scheme, Revisited

The Tardos scheme is a well-known traitor tracing scheme to protect copyrighted content against collusion attacks. The original scheme contained some suboptimal design choices, such as the score function and the distribution function used for generating the biases. Škoric ́ et al. previously showed that a symbol-symmetric score function leads to shorter codes, while Nuida et al. obtained the optimal distribution functions for arbitrary coalition sizes. Later, Nuida et al. showed that combining these results leads to even shorter codes when the coalition size is small. We extend their anal-ysis to the case of large coalitions and prove that these opti-mal distributions converge to the arcsine distribution, thus showing that the arcsine distribution is asymptotically op-timal in the symmetric Tardos scheme. We also present a new, practical alternative to the optimal discrete distribu-tions of Nuida et al. and give a comparison of the estimated codelengths for each of these distributions