text: We study the large-coalition asymptotics of fingerprinting and group testing and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (which are fast but commonly require larger code lengths) and for joint decoders (which may be slower but achieve the best code lengths). We further make the distinction between informed decoding, where the pirate strategy is exactly known, and uninformed decoding, and we design decoding schemes for both settings. For fingerprinting, we show that if the pirate strategy is known, the Neyman-Pearson-based log-likelihood decoders provably achieve capacity, regardless of the strategy. The decoder built against the interleaving attack is further shown to be a universal decoder, able to deal with arbitrary attacks and achieving the uninformed capacity. This universal decoder is shown to be closely related to the Lagrange-optimized decoder of and the empirical mutual information decoder of Moulin. Joint decoders are also proposed, and we conjecture that these also achieve the corresponding joint capacities. For group testing, the simple decoder for the classical model is shown to be more efficient than the one of and it provably achieves the simple group testing capacity. For generalizations of this model such as noisy group testing, the resulting simple decoders also achieve the corresponding simple capacities.
  @cite_25: This paper discusses methods for assigning code-words for the purpose of fingerprinting digital data, e.g., software, documents, music, and video. Fingerprinting consists of uniquely marking and registering each copy of the data. This marking allows a distributor to detect any unauthorized copy and trace it back to the user. This threat of detection will deter users from releasing unauthorized copies. A problem arises when users collude: for digital data, two different fingerprinted objects can be compared and the differences between them detected. Hence, a set of users can collude to detect the location of the fingerprint. They can then alter the fingerprint to mask their identities. We present a general fingerprinting solution which is secure in the context of collusion. In addition, we discuss methods for distributing fingerprinted data.
  @cite_8: We construct binary codes for fingerprinting digital documents. Our codes for n users that are e-secure against c pirates have length O(c2log(n e)). This improves the codes proposed by Boneh and Shaw l1998r whose length is approximately the square of this length. The improvement carries over to works using the Boneh--Shaw code as a primitive, for example, to the dynamic traitor tracing scheme of Tassa l2005r. By proving matching lower bounds we establish that the length of our codes is best within a constant factor for reasonable error probabilities. This lower bound generalizes the bound found independently by l2003r that applies to a limited class of codes. Our results also imply that randomized fingerprint codes over a binary alphabet are as powerful as over an arbitrary alphabet and the equal strength of two distinct models for fingerprinting.
summary: Work on the fingerprinting game described above started in the late 90s, and lower bounds on the code length were established of the order @math @cite_25 , until in 2003 Tardos @cite_8 proved a lower bound of the order @math and described a scheme with @math , showing this bound is tight. Since the leading constants of the upper and lower bounds did not match, later work on fingerprinting focused on finding the optimal leading constant.