Dynamic Traitor Tracing for Arbitrary Alphabets: Divide and Conquer

We give a generic divide-and-conquer approach for constructing collusion-resistant probabilistic dynamic traitor tracing schemes with larger alphabets from schemes with smaller alphabets. This construction offers a linear tradeoff between the alphabet size and the codelength. In particular, we show that applying our results to the binary dynamic Tardos scheme of Laarhoven et al. leads to schemes that are shorter by a factor equal to half the alphabet size. Asymptotically, these codelengths correspond, up to a constant factor, to the fingerprinting capacity for static probabilistic schemes. This gives a hierarchy of probabilistic dynamic traitor tracing schemes, and bridges the gap between the low bandwidth, high codelength scheme of Laarhoven et al. and the high bandwidth, low codelength scheme of Fiat and Tassa.Comment: 6 pages, 1 figur

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 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

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 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

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 c_0 is the number of colluders. In this paper we give alternative security proofs for the Tardos code, working with the assumption that the strongest coalition strategy is position-independent. We employ the Bernstein inequality and Bennett inequality instead of the typically used Markov inequality. This proof technique requires fewer steps and 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. Keywords: Traitor tracing; Tardos fingerprinting; Collusio

Riding the saddle point: asymptotics of the capacity-achieving simple decoder for bias-based traitor tracing

We study the asymptotic-capacity-achieving score function that was recently proposed by Oosterwijk et al. for bias-based traitor tracing codes. For the bias function, we choose the Dirichlet distribution with a cutoff. Using Bernstein’s inequality and Bennett’s inequality, we upper bound the false-positive and false-negative error probabilities. From these bounds we derive sufficient conditions for the scheme parameters. We solve these conditions in the limit of large coalition size c0 and obtain asymptotic solutions for the cutoff, the sufficient code length, and the corresponding accusation threshold. We find that the code length converges to its asymptote approximately as c0 −1/2, which is faster than the c0 −1/3 of Tardos’ score function. MSC:94B6

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 $m\propto c_0^2$, where $c_0$ 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. Keywords: collusion, watermarking, fingerprintin

Tuple decoders for traitor tracing schemes

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

Riding the Saddle Point : asymptotics of the capacity-achieving simple decoder for bias-based traitor tracing

We study the asymptotic-capacity-achieving score function that was recently proposed by Oosterwijk et al. for bias-based traitor tracing codes. For the bias function we choose the Dirichlet distribution with a cutoff. Using Bernstein's inequality and Bennett's inequality, we upper bound the false positive and false negative error probabilities. From these bounds we derive sufficient conditions for the scheme parameters. We solve these conditions in the limit of large coalition size $c_0$ and obtain asymptotic solutions for the cutoff, the sufficient code length and the corresponding accusation threshold. The code length converges to its asymptote approximately as $c_0^{-1/2}$, which is faster than the $c_0^{-1/3}$ of Tardos' score function. Keywords: traitor tracin