Impacts of Watermarking Security on Tardos-Based Fingerprinting

Abstract

<?Pub Dtl=""?> This paper presents a study of the embedding of Tardos binary fingerprinting codes with watermarking techniques. By taking into account the security of the embedding scheme, we present a new approach for colluding strategies which relies on the possible estimation error rate of the code symbols (denoted <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\epsilon$</tex> </formula> ). We derive a new attack strategy called “ <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\epsilon$</tex></formula> -Worst Case Attack” and show its efficiency using the computation of achievable rates for simple decoding. Then we consider the interplay between security and robustness regarding the accusation performances of the fingerprinting scheme and show that 1) for the same accusation rate secure schemes can afford to be less robust than insecure ones, and 2) that secure schemes enable to cast the Worst Case Attack into an interleaving attack. Additionally, we use the security analysis of the watermarking scheme to derive from <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\epsilon$</tex></formula> a security attack for a fingerprinting scheme based on Tardos codes and a new scheme called stochastic spread-spectrum watermarking. We compare a removal attack against an AWGN robustness attack and we show that for the same distortion, the combination of a fingerprinting attack and a security attack easily outperform classical attacks even with a small number of observations.