Discrete Distributions in the Tardos Scheme, Revisited

TL;DR

This paper analyzes and extends the optimal bias distributions in the Tardos traitor tracing scheme, demonstrating asymptotic optimality of the arcsine distribution for large coalitions and proposing practical alternatives.

Contribution

It proves the asymptotic optimality of the arcsine distribution in the symmetric Tardos scheme and introduces a new practical distribution alternative.

Findings

Optimal distributions converge to the arcsine distribution for large coalitions.

The arcsine distribution is asymptotically optimal in the symmetric Tardos scheme.

A new practical alternative to existing discrete distributions is proposed.

Abstract

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.