Asymptotically False-Positive-Maximizing Attack on Non-binary Tardos Codes

Abstract

We use a method recently introduced by Simone andŠkorić 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.

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

“…The analysis of the RS strategy is different from other strategies because the RS strategy does not depend on the actual σ α values (other than their being zero or nonzero). We obtain a result that looks similar to the formula for MajV in [14] and the more general 'class 2' strategies in [13], even though RS does not fit in the classification scheme introduced in [13].…”

“…However, these arguments are not very precise. In [14] and [13] an in-depth analytical and numerical investigation of the Gaussian approximation was given in the RDM case. The approach is based on the convolution rule for characteristic functions, and a way to express the false accusation probability as a power series expansion in the small parameter 1/m.…”

“…For instance, if the false positive rate is around 10 −10 , then a number of simulations of order at least 10 10 is required to measure this rate; in contrast, the computational effort in the CSE method does not depend on the error rate. The work of [14,13] showed, for various parameter settings and attack strategies, how the false positive probability has a transition from Gaussian behaviour in the central region to worse-thanGaussian behaviour outside the center. However, a number of questions were left unanswered.…”

“…The pre-computation is a weighted sum over the attack parameters, and the result is referred to as 'K b ' in [14,13]. The K b was pre-computed for the following attacks: majority voting, minority voting, interleaving, and the attack that minimizes the coalition score.…”

“…Theμ-min strategy is more difficult to analyze. As shown in [13], it behaves in a rather complicated way, sometimes being equivalent to MinV, sometimes MajV, or something inbetween, depending on many parameters, mostly κ and q. …”