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13
Dynamic traitor tracing for arbitrary alphabets: divide and conquer
- In IEEE Workshop on Information Forensics and Security (WIFS
, 2012
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Optimal Suspicion Functions for Tardos Traitor Tracing Schemes
"... We investigate alternative suspicion functions for Tardos traitor tracing schemes. In the simple decoder approach (computation of a score for every user independently) we derive suspicion functions that optimize a performance indicator related to the sufficient code length ℓ in the limit of large co ..."
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We investigate alternative suspicion functions for Tardos traitor tracing schemes. In the simple decoder approach (computation of a score for every user independently) we derive suspicion functions that optimize a performance indicator related to the sufficient code length ℓ in the limit of large coalition size c. Our results hold for the Restricted-Digit Model as well as the Combined-Digit Model. The scores depend on information that is usually not available to the tracer – the attack strategy or the tallies of the symbols received by the colluders. We discuss how such results can be used in realistic contexts. We study several combinations of coalition attack strategy vs. suspicion function optimized against some attack (another attack or the same). In many of these combinations the usual scaling ℓ ∝ c 2 is replaced by a lower power of c, e.g. c 3/2. We find that the interleaving strategy is an especially powerful attack, and the suspicion function tailored against interleaving is effective against all considered attacks.
Tuple decoders for traitor tracing schemes
, 2014
"... In the field of collusion-resistant traitor tracing, Oosterwijk et al. recently determined the optimal suspicion function for simple decoders. Earlier, Moulin also considered another type of decoder: the generic joint decoder that compares all possible coalitions, and showed that usually the generic ..."
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In the field of collusion-resistant traitor tracing, Oosterwijk et al. recently determined the optimal suspicion function for simple decoders. Earlier, Moulin also considered another type of decoder: the generic joint decoder that compares all possible coalitions, and showed that usually the generic joint decoder outperforms the simple decoder. Both Amiri and Tardos, and Meerwald and Furon described constructions that assign suspicion levels to c-tuples, where c is the number of colluders. We investigate a novel idea: the tuple decoder, assigning a suspicion level to tuples of a fixed size. In contrast to earlier work, we use this in a novel accusation algorithm to decide for each distinct user whether or not to accuse him. We expect such a scheme to outperform simple decoders while not being as computationally intensive as the generic joint decoder. In this paper we generalize the optimal suspicion functions to tuples, and describe a family of accusation algorithms in this setting that accuses individual users using this tuple-based information.
Discrete distributions in the Tardos scheme, revisited
- In 1st ACM Workshop on Information Hiding and Multimedia Security (IH&MMSec
, 2013
"... ABSTRACT 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.Škorić et al. previously ..."
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ABSTRACT 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.Škorić 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.
Binary and q-ary Tardos codes, revisited
"... The Tardos code is a much studied collusion-resistant fingerprinting code, with the special property that it has asymptotically optimal length m ∝ c 2 0, where c0 is the number of colluders. In this paper we simplify the security proofs for this code, making use of the Bernstein inequality and Benne ..."
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The Tardos code is a much studied collusion-resistant fingerprinting code, with the special property that it has asymptotically optimal length m ∝ c 2 0, where c0 is the number of colluders. In this paper we simplify the security proofs for this code, making use of the Bernstein inequality and Bennett inequality instead of the typically used Markov inequality. This simplified proof technique also slightly improves the tightness of the bound on the false negative error probability. We present new results on code length optimization, for both small and asymptotically large coalition sizes.
Asymptotic fingerprinting capacity in the Combined Digit Model
, 2012
"... We study the channel capacity of q-ary fingerprinting in the limit of large attacker coalitions. We extend known results by considering the Combined Digit Model, an attacker model that captures signal processing attacks such as averaging and noise addition. For q = 2 we give results for various atta ..."
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We study the channel capacity of q-ary fingerprinting in the limit of large attacker coalitions. We extend known results by considering the Combined Digit Model, an attacker model that captures signal processing attacks such as averaging and noise addition. For q = 2 we give results for various attack parameter settings. For q ≥ 3 we present the relevant equations without providing a solution. We show how the channel capacity in the Restricted Digit Model is obtained as a limiting case of the Combined Digit Model.
False Positive probabilities in q-ary Tardos codes: comparison of attacks
, 2012
"... We investigate False Positive (FP) accusation probabilities for q-ary Tardos codes in the Restricted Digit Model. We employ a computation method recently introduced by us, to which we refer as Convolution and Series Expansion (CSE). We present a comparison of several collusion attacks on q-ary codes ..."
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We investigate False Positive (FP) accusation probabilities for q-ary Tardos codes in the Restricted Digit Model. We employ a computation method recently introduced by us, to which we refer as Convolution and Series Expansion (CSE). We present a comparison of several collusion attacks on q-ary codes: majority voting, minority voting, Interleaving, ˜µ-minimizing and Random Symbol (the q-ary equivalent of the Coin Flip strategy). The comparison is made by looking at the FP rate at approximately fixed False Negative rate. In nearly all cases we find that the strongest attack is either minority voting or ˜µ-minimizing, depending on the exact setting of parameters such as alphabet size, code length, and coalition size. Furthermore, we present results on the convergence speed of the CSE method, and we show how FP rate computations for the Random Symbol strategy can be sped up by a precomputation step.
Asymptotics of Fingerprinting and Group Testing: Tight Bounds from Channel Capacities
, 2014
"... In this work we consider the large-coalition asymp-totics 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 decoders (fast but suboptimal) and for joint decoders (slow but optimal). For fingerpri ..."
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In this work we consider the large-coalition asymp-totics 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 decoders (fast but suboptimal) and for 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 many attacks the joint capacity is further shown to be strictly higher than the simple capacity. For group testing, we improve upon known results about the joint capacities, and derive new explicit asymptotics for the simple capacities. These show that existing simple group testing algorithms 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 log2(e) ≈ 1.44 for large numbers of defectives.
Capacities and Capacity-Achieving Decoders for Various Fingerprinting Games
- ACM Workshop on Information Hiding and Multimedia Security (IH&MMSec
, 2014
"... Combining an information-theoretic approach to finger-printing 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 capac ..."
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Combining an information-theoretic approach to finger-printing 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 sim-ple capacity for unknown attacks, and is argued to be an improved version of the recently proposed decoder of Oost-erwijk 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. 1
