[Tar08] Optimal probabilistic fingerprint codes

Authors: Gábor Tardos | Venue: Journal of the ACM 2008 | Source

Abstract

We construct binary codes for fingerprinting digital documents. Our codes for $n$ users that are $ϵ$-secure against $c$ pirates have length $O(c^2\log (n/ϵ))$. This improves the codes proposed by Boneh and Shaw BS98 whose length is approximately the square of this length. The improvement carries over to works using the Boneh—Shaw code as a primitive, for example, to the dynamic traitor tracing scheme of Tassa [2005]. By proving matching lower bounds we establish that the length of our codes is best within a constant factor for reasonable error probabilities. This lower bound generalizes the bound found independently by Peikert et al. [2003] that applies to a limited class of codes. Our results also imply that randomized fingerprint codes over a binary alphabet are as powerful as over an arbitrary alphabet and the equal strength of two distinct models for fingerprinting.