Saddle-point solution of the fingerprinting capacity game under the marking assumption

2014

Des. Codes Cryptogr.

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 orμ-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.

mentioning

confidence: 99%

False positive probabilities in q-ary Tardos codes: comparison of attacks

Simone

2014

Des. Codes Cryptogr.

“…For q = 2 it was conjectured that the capacity is asymptotically 1/(c 2 2 ln 2). The conjecture was proved in [1,6]. Amiri and Tardos [1] developed a joint decoder scheme (for the binary case) where candidate coalitions get a score related to the mutual information between their symbols and y.…”

Section: Asymptotic Channel Capacitymentioning

confidence: 98%

“…The analysis of achievable performance was greatly helped by the onset of an information-theoretic treatment of anti-collusion codes. The whole class of bias-based codes can be treated as a maximin game between the watermarker and the colluders [2,6,12], independently played for each segment, where the payoff function is the mutual information between the symbols x 1 , . .…”

Section: Asymptotic Channel Capacitymentioning

confidence: 99%

Asymptotic Fingerprinting Capacity in the Combined Digit Model

Boesten

2013

Information Hiding

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.

“…Amiri and Tardos [2] have given a capacity-achieving joint decoder construction for the binary code. (Capacity refers to the informationtheoretic treatment [11,16,22] of the colluder attack as a communication channel.) However, the construction is rather impractical, requiring computations for many candidate coalitions.…”

Section: Tardos Codesmentioning

confidence: 99%

“…This guarantees convergence to the normal distribution. -The 'interleaving' colluder strategy, which is known to be information-theoretically optimal [10,12] for c 0 → ∞ and binary alphabet, turns out to have special properties: the pdf andμ do not depend on the coalition size; the left and right tail are maximally heavy. -We compute the Fourier transformφ (characteristic function) of ϕ.…”

Section: Contributions and Outlinementioning

confidence: 99%

Accusation probabilities in Tardos codes: beyond the Gaussian approximation

Simone

2011

Des. Codes Cryptogr.

We study the probability distribution of user accusations in the q-ary Tardos fingerprinting system under the Marking Assumption, in the restricted digit model. In particular, we look at the applicability of the so-called Gaussian approximation, which states that accusation probabilities tend to the normal distribution when the fingerprinting code is long. We introduce a novel parametrization of the attack strategy which enables a significant speedup of numerical evaluations. We set up a method, based on power series expansions, to systematically compute the probability of accusing innocent users. The 'small parameter' in the power series is 1/m, where m is the code length. We use our method to semi-analytically study the performance of the Tardos code against majority voting and interleaving attacks. The bias function 'shape' parameter κ strongly influences the distance between the actual probabilities and the asymptotic Gaussian curve. The impact on the collusion-resilience of the code is shown. For some realistic parameter values, the false accusation probability is even lower than the Gaussian approximation predicts. Keywords