Short collusion-secure fingerprint codes against three pirates

TL;DR

This paper introduces a new probabilistic fingerprint code construction secure against three pirates, combining scoring and parent search techniques, resulting in significantly shorter codes than previous methods.

Contribution

The paper presents a novel probabilistic collusion-secure fingerprint code for three pirates, with a combined tracing algorithm and improved efficiency over existing codes.

Findings

Code lengths are 30-40% shorter than previous secure codes.

The proposed tracing algorithm shows promising efficiency improvements.

Theoretical security evaluation confirms robustness against three pirates.

Abstract

In this article, we propose a new construction of probabilistic collusion-secure fingerprint codes against up to three pirates and give a theoretical security evaluation. Our pirate tracing algorithm combines a scoring method analogous to Tardos codes (J. ACM, 2008) with an extension of parent search techniques of some preceding 2-secure codes. Numerical examples show that our code lengths are significantly shorter than (about 30% to 40% of) the shortest known c-secure codes by Nuida et al. (Des. Codes Cryptogr., 2009) with c = 3. Some preliminary proposal for improving efficiency of our tracing algorithm is also given.