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

Dynamic Traitor Tracing Schemes, Revisited

We revisit recent results from the area of collusion-resistant traitor tracing, and show how they can be combined and improved to obtain more efficient dynamic traitor tracing schemes. In particular, we show how the dynamic Tardos scheme of Laarhoven et al. can be combined with the optimized score functions of Oosterwijk et al. to trace coalitions much faster. If the attack strategy is known, in many cases the order of the code length goes down from quadratic to linear in the number of colluders, while if the attack is not known, we show how the interleaving defense may be used to catch all colluders about twice as fast as in the dynamic Tardos scheme. Some of these results also apply to the static traitor tracing setting where the attack strategy is known in advance, and to group testing.Comment: 7 pages, 1 figure (6 subfigures), 1 tabl

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

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

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

In this work 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 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 1.44 for large numbers of defectives.Comment: 14 pages, 6 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

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

Ad Hoc (Decentralized) Broadcast, Trace, and Revoke

Traitor tracing schemes [Chor–Fiat–Naor, Crypto ’94] help content distributors fight against piracy and are defined with the content distributor as a trusted authority having access to the secret keys of all users. While the traditional model caters well to its original motivation, its centralized nature makes it unsuitable for many scenarios. For usage among mutually untrusted parties, a notion of *ad hoc* traitor tracing (naturally with the capability of broadcast and revocation) is proposed and studied in this work. Such a scheme allows users in the system to generate their own public/secret key pairs, without trusting any other entity. To encrypt, a list of public keys is used to identify the set of recipients, and decryption is possible with a secret key for any of the public keys in the list. In addition, there is a tracing algorithm that given a list of recipients’ public keys and a pirate decoder capable of decrypting ciphertexts encrypted to them, identifies at least one recipient whose secret key must have been used to construct the said decoder. Two constructions are presented. The first is based on obfuscation and has constant-size ciphertext, yet its decryption time is linear in the number of recipients. The second is a generic transformation that reduces decryption time at the cost of increased ciphertext size. A lower bound on the trade-off between ciphertext size and decryption time is shown, indicating that the two constructions achieve all possible optimal trade-offs, i.e., they fully demonstrate the Pareto front of efficiency. The lower bound also applies to broadcast encryption and is of independent interest