EM decoding of tardos traitor tracing codes

Abstract

This paper proposes a major shift in the decoding of probabilistic Tardos traitor tracing code. The goal of the decoder is to accuse colluders but it ignores how they have been mixing their copies in order to forge the pirated content. As originally proposed by Tardos, so far proposed decoders are agnostic and their performances are stable with respect to this unknown collusion attack. However, this stability automatically leads to non-optimality from a detection theory perspective. This is the reason why this paper proposes to estimate the collusion attack in order to approximate the optimal matched decoder. This is done iteratively thanks to the application of the well-known Expectation-Maximization algorithm. We have dropped the stability: the power of our decoding algorithm deeply depends on the collusion attack. Some attacks are worse than others. However, even for the worst collusion channel, our decoder performs better than the original Tardos decoding.

Probabilistic fingerprinting codes used to detect traitor zero-bit watermark

“…However the method used to select suspicious users in this paper is suboptimal from a hypothesis testing view-point, our future works will be concerned in integrating more efficient tracing decoders. 5 …”

“…We used the mathematical model presented in Ref. 5. In this model four assumptions must be respected about the collusion channel :…”

Universal Threshold Calculation for Fingerprinting Decoders using Mixture Models

“…The seminal work of probabilistic or bias-based fingerprinting codes is the well known Tardos Codes introduced by Tardos [19] proving that a fingerprinting scheme must satisfy l ∝ c 2 ln nε −1 1 for a large number of fingerprints n, with code length l, number of colluders c and upper bound on the probability of accusing a specific innocent ε1. It followed a long list of descendants, that proposed optimizations by sharpening the bounds ( [22], [15], [16], [9]), improving the distribution function ( [5], [1], 1 For binary fingerprints, both models are equal [7]) or introducing a more discriminative or practical accusation score function ( [20], [10], [6], [17]). …”

“…We follow the idea of Furon and Pérez-Freire [6] who made use of the Expectation-Maximization (EM) algorithm inside the decoder. Whereas [6] used the EM in order to gain knowledge of the collusion attack strategy, we focus on the accusation scores.…”

“…We follow the idea of Furon and Pérez-Freire [6] who made use of the Expectation-Maximization (EM) algorithm inside the decoder. Whereas [6] used the EM in order to gain knowledge of the collusion attack strategy, we focus on the accusation scores. Applying mixture models, we estimate the actual distribution of the accusation scores for a given model and thereby we are able to calculate feasible thresholds for every type of decoder.…”