  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. Skoric 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 analysis to the case of
large coalitions and prove that these optimal distributions converge to the
arcsine distribution, thus showing that the arcsine distribution is
asymptotically optimal in the symmetric Tardos scheme. We also present a new,
practical alternative to the discrete distributions of Nuida et al. and give a
comparison of the estimated lengths of the fingerprinting codes for each of
these distributions.
