Dynamic Traitor Tracing for Arbitrary Alphabets: Divide and Conquer

TL;DR

This paper introduces a divide-and-conquer method to construct dynamic traitor tracing schemes with larger alphabets, balancing alphabet size and codelength, and bridging existing schemes with different bandwidth and length tradeoffs.

Contribution

It presents a generic approach to extend small-alphabet schemes to larger alphabets, achieving shorter codelengths and connecting different existing schemes.

Findings

Achieves linear tradeoff between alphabet size and codelength.

Shortens schemes by a factor proportional to half the alphabet size.

Approaches fingerprinting capacity asymptotically.

Abstract

We give a generic divide-and-conquer approach for constructing collusion-resistant probabilistic dynamic traitor tracing schemes with larger alphabets from schemes with smaller alphabets. This construction offers a linear tradeoff between the alphabet size and the codelength. In particular, we show that applying our results to the binary dynamic Tardos scheme of Laarhoven et al. leads to schemes that are shorter by a factor equal to half the alphabet size. Asymptotically, these codelengths correspond, up to a constant factor, to the fingerprinting capacity for static probabilistic schemes. This gives a hierarchy of probabilistic dynamic traitor tracing schemes, and bridges the gap between the low bandwidth, high codelength scheme of Laarhoven et al. and the high bandwidth, low codelength scheme of Fiat and Tassa.