High rate fingerprinting codes and the fingerprinting capacity

Abstract

Including a unique code in each copy of a distributed document is an effective way of fighting intellectual piracy. Codes designed for this purpose that are secure against collusion attacks are called fingerprinting codes.In this paper we consider fingerprinting with the marking assumption and design codes that achieve much higher rates than previous constructions. We conjecture that these codes attain the maximum possible rate (the fingerprinting capacity) for any fixed number of pirates. We prove new upper bounds for the fingerprinting capacity that are not far from the rate of our codes. On the downside the accusation algorithm of our codes are much slower than those of earlier codes.We introduce the novel model of weak fingerprinting codes where one pirate should be caught only if the identity of all other pirates are revealed. We construct fingerprinting codes in this model with improved rates but our upper bound on the rate still applies. In fact, these improved codes achieve the fingerprinting capacity of the weak model by a recent upper bound.Using analytic techniques we compare the rates of our codes in the standard model and the rates of the optimal codes in the weak model. To our surprise these rates asymptotically agree, that is, their ratio tends to 1 as t goes to infinity. Although we cannot prove that each one of our codes in the standard model achieves the fingerprinting capacity, this proves that asymptotically they do.

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

“…Under the arbitrary digit model they can put arbitrary symbols in detectable positions, while the general digit model additionally allows erasures at detectable positions. 1 …”

“…When this is the case, the statistical analysis of the code's performance can be drastically simplified; the performance is almost completely determined by a single parameter, namely the average scoreμ of the coalition. The Gaussian assumption is motivated by the Central Limit Theorem (CLT): A user accusation consists of a sum of per-segment contributions, which are independent and identically distributed 1 The proportionality m ∝ c 2 0 was already known in the context of spread-spectrum watermarking. Kilian et al [9] showed that, if the watermarks have a component-wise normal distribution, then Ω( p m/ln n) differently marked copies are required to successfully erase any mark with non-negligible probability.…”

“…In contrast, one can also use a 'joint decoder' which considers sets of users. Amiri and Tardos [1] have given a capacity-achieving joint decoder construction for the binary code. (Capacity refers to the information-theoretic treatment [15,10,7,3] of the colluder attack as a communication channel.)…”

Accusation probabilities in Tardos codes: beyond the Gaussian approximation

“…Kilian et al [13] showed that, if the watermarks have a component-wise normal distribution, then Ω( √ m/ln n) differently marked copies are required to successfully erase any mark with non-negligible probability. 2 Not to be confused with the total false positive probability (which we denote as η). The relation is η…”

“…In contrast, one can also use a 'joint decoder' which considers sets of users. 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.)…”