On fingerprinting capacity games for arbitrary alphabets and their asymptotics

Huang, Yen-Wei; Moulin, Pierre

doi:10.1109/isit.2012.6283982

Cited by 18 publications

(24 citation statements)

References 8 publications

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“…• The gap between the simple and joint capacities of the interleaving attack contradicts previous results of Huang and Moulin [24], [25]. As a result, finding the fingerprinting capacity is again an open problem.…”

Section: E Contributions and Outlinementioning

confidence: 83%

Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities

Laarhoven

2015

IEEE Trans.Inform.Forensic Secur.

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In this paper, we consider the large-coalition asymptotics of various fingerprinting and group testing games, and derive explicit expressions for the capacities for each of these models. We do this both for simple (fast but suboptimal) and arbitrary, joint decoders (slow but optimal). For fingerprinting, we show that if the pirate strategy is known, the capacity often decreases linearly with the number of colluders, instead of quadratically as in the uninformed fingerprinting game. For all considered attacks, the joint capacity is shown to be strictly higher than the simple capacity, including the interleaving attack. This last result contradicts the results of Huang and Moulin regarding the joint fingerprinting capacity, which implies that finding the fingerprinting capacity without restrictions on the tracer's capabilities remains an open problem. For group testing, we improve upon the previous work about the joint capacities, and derive new explicit asymptotics for the simple capacities of various models. These show that the existing simple group testing algorithms of Chan et al. are suboptimal, and that simple decoders cannot asymptotically be as efficient as joint decoders. For the traditional group testing model, we show that the gap between the simple and joint capacities is a factor log 2 (e) ≈ 1.44 for large numbers of defectives.

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Section: E Contributions and Outlinementioning

confidence: 83%

Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities

Laarhoven

2015

IEEE Trans.Inform.Forensic Secur.

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“…As they further prove the interleaving attack to be the asymptotic optimal attack [8], and as Oosterwijk et al prove the score function in [17] to be the best defense against this attack, the game seemed solved 2 . In [16], they prove that this score function achieves capacity, which means with this choice of encoder [19] and decoder [17], they achieve asymptotic optimal code lengths for binary fingerprints of l ∼ 2c 2 ln nε −1 1 .…”

Section: Related Workmentioning

confidence: 98%

Universal Threshold Calculation for Fingerprinting Decoders using Mixture Models

Schäfer

Mair

Berchtold

et al. 2015

Proceedings of the 3rd ACM Workshop on Information Hiding and Multimedia Security

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Collusion attacks on watermarked media copies are commonly countered by probabilistically generated fingerprinting codes and appropriate tracing algorithms. The latter calculates accusation scores representing the suspiciousness of the fingerprints. In a 'detect many' scenario a threshold decides which scores are associated to the colluders. This work proposes a universal method to calculate thresholds for different decoders solely with knowledge of the accusation scores from the actual attack. Applying mixture models on the scores, the threshold is set up satisfying the selected error probabilities. It is independent from the fingerprint generation and can be applied at any decoder. Also no knowledge about the number of attackers or their strategy is needed.

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“…One of the main advances in recent years was finding [16], [18] the saddlepoint of the information-theoretic max-min game (see Section II-E) in the case of joint decoding. Knowing the location of the saddlepoint makes it easier for the tracer to build a decoder that works optimally against the worst-case attack and that works well against all other attacks too.…”

Section: A Collusion Attacks On Watermarkingmentioning

confidence: 99%

“…Asymptotically the symmetry is restored (due to → ∞); the attack strategy can then be parametrized more compactly as a set of probabilities θ ψ|m applied in each position independently. In the RDM the asymptotically optimal attack [17], [18] is the Interleaving attack: a colluder is selected uniformly at random and his symbol is output.…”

Section: Collusion Attackmentioning

confidence: 99%

“…The asymptotic (large c) capacity in the RDM was found [2], [5], [17] to be C RDM,asym joint = (q − 1)/(2c 2 ln q), leading to a sufficient code length RDM,asym suff = 2 q−1 c 2 0 ln(n/P FP ). In the asymptotic saddlepoint [18] the bias distribution is the Dirichlet distribution as specified in Section II-B, and the attack strategy is the Interleaving attack applied independently in each content position. For non-asymptotic c 0 only numerical results are available (except at c 0 = 2).…”

Section: E Joint Decoder Saddlepointmentioning

confidence: 99%

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Tally-Based Simple Decoders for Traitor Tracing and Group Testing

Škorić

2015

IEEE Trans.Inform.Forensic Secur.

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The topic of this paper is collusion resistant watermarking, also known as traitor tracing, in particular bias-based traitor tracing codes as introduced by Tardos. The past years have seen an ongoing effort to construct efficient highperformance decoders for these codes. In this paper we construct a score system from the Neyman-Pearson hypothesis test (which is known to be the most powerful test possible) into which we feed more evidence than in previous work, in particular the symbol tallies for all columns of the code matrix. As far as we know, until now simple decoders using Neyman-Pearson have taken into consideration only the codeword of a single user, namely the user under scrutiny. The Neyman-Pearson score needs as input the attack strategy of the colluders, which typically is not known to the tracer. We insert the interleaving attack, which plays a very special role in the theory of bias-based traitor tracing by virtue of being part of the asymptotic (i.e., large coalition size) saddle-point solution. The score system obtained in this way is universal: effective not only against the interleaving attack, but against all other attack strategies as well. Our score function for one user depends on the other users' codewords in a very simple way through the symbol tallies, which are easily computed. We present bounds on the false positive probability and show receiver operating characteristic curves obtained from simulations. We investigate the probability distribution of the score. Finally, we apply our construction to the area of (medical) group testing, which is related to traitor tracing.

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On fingerprinting capacity games for arbitrary alphabets and their asymptotics

Cited by 18 publications

References 8 publications

Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities

Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities

Universal Threshold Calculation for Fingerprinting Decoders using Mixture Models

Tally-Based Simple Decoders for Traitor Tracing and Group Testing

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