Riding the Saddle Point: asymptotics of the capacity-achieving simple decoder for bias-based traitor tracing

We study the asymptotic-capacity-achieving score function that was recently proposed by Oosterwijk et al. for bias-based traitor tracing codes. For the bias function we choose the Dirichlet distribution with a cutoff. Using Bernstein’s inequality and Bennett’s inequality, we upper bound the false positive and false negative error probabilities. From these bounds we derive sufficient conditions for the scheme parameters. We solve these conditions in the limit of large coalition size c0 and obtain asymptotic solutions for the cutoff, the sufficient code length and the corresponding accusation threshold. The code length converges to its asymptote approximately as c −1/2 0 , which is faster than the c −1/3 0 of Tardos’ score function.