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. We find that the code length converges to its asymptote approximately as c₀ ^−1/2, which is faster than the c₀ ^−1/3 of Tardos’ score function. MSC:94B60