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

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

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 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

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

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

Capacities and Capacity-Achieving Decoders for Various Fingerprinting Games

Combining an information-theoretic approach to fingerprinting with a more constructive, statistical approach, we derive new results on the fingerprinting capacities for various informed settings, as well as new log-likelihood decoders with provable code lengths that asymptotically match these capacities. The simple decoder built against the interleaving attack is further shown to achieve the simple capacity for unknown attacks, and is argued to be an improved version of the recently proposed decoder of Oosterwijk et al. With this new universal decoder, cut-offs on the bias distribution function can finally be dismissed. Besides the application of these results to fingerprinting, a direct consequence of our results to group testing is that (i) a simple decoder asymptotically requires a factor 1.44 more tests to find defectives than a joint decoder, and (ii) the simple decoder presented in this paper provably achieves this bound.Comment: 13 pages, 2 figure

Efficient Probabilistic Group Testing Based on Traitor Tracing

Inspired by recent results from collusion-resistant traitor tracing, we provide a framework for constructing efficient probabilistic group testing schemes. In the traditional group testing model, our scheme asymptotically requires T ~ 2 K ln N tests to find (with high probability) the correct set of K defectives out of N items. The framework is also applied to several noisy group testing and threshold group testing models, often leading to improvements over previously known results, but we emphasize that this framework can be applied to other variants of the classical model as well, both in adaptive and in non-adaptive settings.Comment: 8 pages, 3 figures, 1 tabl

On the Saddle-point Solution and the Large-Coalition Asymptotics of Fingerprinting Games

We study a fingerprinting game in which the number of colluders and the collusion channel are unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is k and the fingerprinting alphabet is binary, we show that capacity decays quadratically with k. Furthermore, we prove rigorously that the asymptotic capacity is 1/(k^2 2ln2) and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotic behavior, numerical solutions to the game for small k are also presented.Comment: submitted to IEEE Trans. on Information Forensics and Securit