Tardos codes for real

Abstract

This paper deals with active fingerprinting a.k.a. traitor tracing where a collusion of dishonest users merges their individual versions of a content to yield a pirated copy. The Tardos codes are one of the most powerful tools to fight against such collusion process by identifying the colluders.Instead of studying as usual the necessary and sufficient code length in a theoretical setup, we adopt the point of view of the practitioner. We call this the operational mode, i.e. a practical setup where a Tardos code has already been deployed and a pirated copy has been found.This new paradigm shows that the known bounds on the probability of accusing an innocent in the theoretical setup are way too pessimistic. Indeed the practitioner can resort to much tighter bounds because the problem is fundamentally much simpler under the operational mode.In the end, we benchmark under the operational mode several single decoders recently proposed in the literature. We believe this is a fair comparison reflecting what matters in reality.

Tally-Based Simple Decoders for Traitor Tracing and Group Testing

“…(i) Investigate how much performance difference there is between (20) and the score that would be obtained if the finitec saddlepoint is substituted into Theorem 1; (ii) More elaborate simulations (for many combinations of q, c, c 0 , , n, and attack strategy) to study the difference between the various decoders; (iii) Get a tighter bound on the FP, e.g. using techniques from [12]; (iv) Use the method of Simone andŠkorić [32] to determine the full probability distribution of the score (48) (20) and set the accusation threshold as where the expectation is over the 'innocent' part of the matrix x. We write S j i as in (35).…”

“…Such an occurence allows for errorless decoding. Then we upper-bound the False Positive error rate using an approach similar to the 'operational mode' that was recently proposed by Furon and Desoubeaux [12]. We show that there is quite a large gap between this bound and error rates in simulations.…”

“…The original paper [36], [37] was followed by a lot of activity, e.g. improved analyses [4], [13], [14], [22], [32], [40], [41], code modifications [16], [28], [29], decoder modifications [2], [8], [12], [24], [30] and various generalizations [7], [38], [39], [42]. The advantage of bias-based versus deterministic codes is that they can achieve the asymptotically optimal relationship ∝ c 2 between the sufficient code length and the coalition size c.…”

“…We analyze this more complicated situation by considering the following sequence of experiments. This approach is similar to the 'operational mode' of Furon and Desoubeaux [12].…”

Nearest Neighbor Decoding for Tardos Fingerprinting Codes

“…scaling logarithmically in the often large number of users n, and quarticly in the number of colluders c. The milestone work of Tardos [40] later improved upon this with a code length ℓ = O(c 2 log n), and he proved that this quadratic scaling in c is optimal. Later work focused on bringing down the leading constants in Tardos' scheme [8,15,16,19,30,32,38,39], leading to an optimal code length of ℓ ∝ 1 2 π 2 c 2 ln n for the original (symmetric) Tardos score function [24,25,37], and an optimal overall code length of ℓ ∝ 2c 2 ln n when using further improved decoders [12,15,21,32,33].…”