False Negative probabilities in Tardos codes

Abstract

Forensic watermarking is the application of digital watermarks for the purpose of tracing unauthorized redistribution of content. The most powerful type of attack on watermarks is the collusion attack, in which multiple users compare their differently watermarked versions of the same content. Collusionresistant codes have been developed against these attacks. One of the most famous such codes is the Tardos code. It has the asymptotically optimal property that it can resist c attackers with a code of length proportional to c 2 .Determining error rates for the Tardos code and its various extensions and generalizations turns out to be a nontrivial problem. In recent work we developed an approach called the Convolution and Series Expansion (CSE) method to accurately compute false positive accusation probabilities. In this paper we extend the CSE method in order to make it possible to compute false negative accusation probabilities as well.

Tardos codes for real

“…Yet, it is not easy to find tight bounds because U i is a continuous random variable with a complex law due to its dependency on X i , P i , and Y i . The Ph.D. thesis of A. Simone [13] is indeed devoted to the study of the distribution of U i . 1) Tardos' inequality: In his seminal paper [16], Tardos uses this bound:…”