Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure

Enhanced blind decoding of Tardos codes with new map-based functions

This paper presents a new decoder for probabilistic binary traitor tracing codes under the marking assumption. It is based on a binary hypothesis testing rule which integrates a collusion channel relaxation so as to obtain numerical and simple accusation functions. This decoder is blind as no estimation of the collusion channel prior to the accusation is required. Experimentations show that using the proposed decoder gives better performance than the well-known symmetric version of the Tardos decoder for common attack channels

Optimal symmetric Tardos traitor tracing schemes

For the Tardos traitor tracing scheme, we show that by combining the symbol-symmetric accusation function of Skoric et al. with the improved analysis of Blayer and Tassa we get further improvements. Our construction gives codes that are up to 4 times shorter than Blayer and Tassa's, and up to 2 times shorter than the codes from Skoric et al. Asymptotically, we achieve the theoretical optimal codelength for Tardos' distribution function and the symmetric score function. For large coalitions, our codelengths are asymptotically about 4.93% of Tardos' original codelengths, which also improves upon results from Nuida et al.Comment: 16 pages, 1 figur

Discrete Distributions in the Tardos Scheme, Revisited

The Tardos scheme is a well-known traitor tracing scheme to protect copyrighted content against collusion attacks. The original scheme contained some suboptimal design choices, such as the score function and the distribution function used for generating the biases. Skoric et al. previously showed that a symbol-symmetric score function leads to shorter codes, while Nuida et al. obtained the optimal distribution functions for arbitrary coalition sizes. Later, Nuida et al. showed that combining these results leads to even shorter codes when the coalition size is small. We extend their analysis to the case of large coalitions and prove that these optimal distributions converge to the arcsine distribution, thus showing that the arcsine distribution is asymptotically optimal in the symmetric Tardos scheme. We also present a new, practical alternative to the discrete distributions of Nuida et al. and give a comparison of the estimated lengths of the fingerprinting codes for each of these distributions.Comment: 5 pages, 2 figure

Worst case attacks against binary probabilistic traitor tracing codes

An insightful view into the design of traitor tracing codes should necessarily consider the worst case attacks that the colluders can lead. This paper takes an information-theoretic point of view where the worst case attack is defined as the collusion strategy minimizing the achievable rate of the traitor tracing code. Two different decoders are envisaged, the joint decoder and the simple decoder, as recently defined by P. Moulin \cite{Moulin08universal}. Several classes of colluders are defined with increasing power. The worst case attack is derived for each class and each decoder when applied to Tardos' codes and a probabilistic version of the Boneh-Shaw construction. This contextual study gives the real rates achievable by the binary probabilistic traitor tracing codes. Attacks usually considered in literature, such as majority or minority votes, are indeed largely suboptimal. This article also shows the utmost importance of the time-sharing concept in a probabilistic codes.Comment: submitted to IEEE Trans. on Information Forensics and Securit

Towards joint decoding of binary Tardos fingerprinting codes

The class of joint decoder of probabilistic fingerprinting codes is of utmost importance in theoretical papers to establish the concept of fingerprint capacity. However, no implementation supporting a large user base is known to date. This article presents an iterative decoder which is, as far as we are aware of, the first practical attempt towards joint decoding. The discriminative feature of the scores benefits on one hand from the side-information of previously accused users, and on the other hand, from recently introduced universal linear decoders for compound channels. Neither the code construction nor the decoder make precise assumptions about the collusion (size or strategy). The extension to incorporate soft outputs from the watermarking layer is straightforward. An extensive experimental work benchmarks the very good performance and offers a clear comparison with previous state-of-the-art decoders.Comment: submitted to IEEE Trans. on Information Forensics and Security. - typos corrected, one new plot, references added about ECC based fingerprinting code

Asymptotically false-positive-maximizing attack on non-binary Tardos codes

We use a method recently introduced by Simone and Skoric to study accusation probabilities for non-binary Tardos fingerprinting codes. We generalize the pre-computation steps in this approach to include a broad class of collusion attack strategies. We analytically derive properties of a special attack that asymptotically maximizes false accusation probabilities. We present numerical results on sufficient code lengths for this attack, and explain the abrupt transitions that occur in these results

Asymptotics of Fingerprinting and Group Testing: Capacity-Achieving Log-Likelihood Decoders

We study the large-coalition asymptotics of fingerprinting and group testing, and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (fast but suboptimal) and for joint decoders (slow but optimal), and both for informed and uninformed settings. For fingerprinting, we show that if the pirate strategy is known, the Neyman-Pearson-based log-likelihood decoders provably achieve capacity, regardless of the strategy. The decoder built against the interleaving attack is further shown to be a universal decoder, able to deal with arbitrary attacks and achieving the uninformed capacity. This universal decoder is shown to be closely related to the Lagrange-optimized decoder of Oosterwijk et al. and the empirical mutual information decoder of Moulin. Joint decoders are also proposed, and we conjecture that these also achieve the corresponding joint capacities. For group testing, the simple decoder for the classical model is shown to be more efficient than the one of Chan et al. and it provably achieves the simple group testing capacity. For generalizations of this model such as noisy group testing, the resulting simple decoders also achieve the corresponding simple capacities.Comment: 14 pages, 2 figure

Tardos fingerprinting is better than we thought

We review the fingerprinting scheme by Tardos and show that it has a much better performance than suggested by the proofs in Tardos' original paper. In particular, the length of the codewords can be significantly reduced. First we generalize the proofs of the false positive and false negative error probabilities with the following modifications: (1) we replace Tardos' hard-coded numbers by variables and (2) we allow for independently chosen false positive and false negative error rates. It turns out that all the collusion-resistance properties can still be proven when the code length is reduced by a factor of more than 2. Second, we study the statistical properties of the fingerprinting scheme, in particular the average and variance of the accusations. We identify which colluder strategy forces the content owner to employ the longest code. Using a gaussian approximation for the probability density functions of the accusations, we show that the required false negative and false positive error rate can be achieved with codes that are a factor 2 shorter than required for rigid proofs. Combining the results of these two approaches, we show that the Tardos scheme can be used with a code length approximately 5 times shorter than in the original construction.Comment: Modified presentation of result