Optimal symmetric Tardos traitor tracing schemes

For the Tardos traitor tracing scheme, we show that by combining the symbol-symmetric accusation function of Skoric et al. with the improved analysis of Blayer and Tassa we get further improvements. Our construction gives codes that are up to 4 times shorter than Blayer and Tassa's, and up to 2 times shorter than the codes from Skoric et al. Asymptotically, we achieve the theoretical optimal codelength for Tardos' distribution function and the symmetric score function. For large coalitions, our codelengths are asymptotically about 4.93% of Tardos' original codelengths, which also improves upon results from Nuida et al.Comment: 16 pages, 1 figur

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

Asymptotic fingerprinting capacity for non-binary alphabets

We compute the channel capacity of non-binary fingerprinting under the Marking Assumption, in the limit of large coalition size c. The solution for the binary case was found by Huang and Moulin. They showed that asymptotically, the capacity is $1/(c^2 2\ln 2)$, the interleaving attack is optimal and the arcsine distribution is the optimal bias distribution. In this paper we prove that the asymptotic capacity for general alphabet size q is $(q-1)/(c^2 2\ln q)$. Our proof technique does not reveal the optimal attack or bias distribution. The fact that the capacity is an increasing function of q shows that there is a real gain in going to non-binary alphabets

Estimating the minimal length of tardos code

Abstract. This paper estimates the minimal length of a binary probabilistic traitor tracing code. We consider the code construction proposed by G. Tardos in 2003, with the symmetric accusation function as improved by B. Skoric et al. The length estimation is based on two pillars. First, we consider the Worst Case Attack that a group of c colluders can lead. This attack minimizes the mutual information between the code sequence of a colluder and the pirated sequence. Second, an algorithm pertaining to the field of rare event analysis is presented in order to estimate the probabilities of error: the probability that an innocent user is framed, and the probabilities that all colluders are missed. Therefore, for a given collusion size, we are able to estimate the minimal length of the code satisfying some error probabilities constraints. This estimation is far lower than the known lower bounds

Asymptotic fingerprinting capacity in the Combined Digit Model

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.

Message-Based Traitor Tracing with Optimal Ciphertext Rate

International audienceTraitor tracing is an important tool to discourage defrauders from illegally broadcasting multimedia content. However, the main techniques consist in tracing the traitors from the pirate decoders they built from the secret keys of dishonest registered users: with either a black-box or a white-box tracing procedure on the pirate decoder, one hopes to trace back one of the traitors who registered in the system. But new techniques for pirates consist either in sending the ephemeral decryption keys to the decoders for real-time decryption, or in making the full content available on the web for later viewing. This way, the pirate does not send any personal information. In order to be able to trace the traitors, one should embed some information, or watermarks, in the multimedia content itself to make it specific to the registered users. This paper addresses this problem of tracing traitors from the decoded multimedia content or rebroadcasted keys, without increasing too much the bandwidth requirements. More precisely, we construct a message-traceable encryption scheme that has an optimal ciphertext rate, i.e. the ratio of global ciphertext length over message length is arbitrarily close to one