Tuple decoders for traitor tracing schemes

Abstract

In the field of collusion-resistant traitor tracing, Oosterwijk et al. recently determined the optimal suspicion function for simple decoders. Earlier, Moulin also considered another type of decoder: the generic joint decoder that compares all possible coalitions, and showed that usually the generic joint decoder outperforms the simple decoder. Both Amiri and Tardos, and Meerwald and Furon described constructions that assign suspicion levels to c-tuples, where c is the number of colluders. We investigate a novel idea: the tuple decoder, assigning a suspicion level to tuples of a fixed size. In contrast to earlier work, we use this in a novel accusation algorithm to decide for each distinct user whether or not to accuse him. We expect such a scheme to outperform simple decoders while not being as computationally intensive as the generic joint decoder. In this paper we generalize the optimal suspicion functions to tuples, and describe a family of accusation algorithms in this setting that accuses individual users using this tuple-based information.

Asymptotics of fingerprinting and group testing: capacity-achieving log-likelihood decoders

“…Finally, although it is hard to estimate the scores of mixed tuples with this decoder, just like in [34] we expect that the joint decoder score for a tuple is roughly equal to the sum of the c individual simple decoder scores. So a tuple of c users consisting of k colluders and c − k innocent users is expected to have a score roughly a factor k/c smaller than the expected score for the all-guilty tuple.…”

“…This generalization to q-ary alphabets was considered in e.g. [5], [18], [33], [34], [38]. For the results in this paper we did not really use that we were working with a binary alphabet, so it seems a straightforward exercise to prove that the q-ary versions of the log-likelihood decoders also achieve the q-ary capacities.…”

Optimal Sequential Fingerprinting

“…Finally, another topic often considered in the fingerprinting literature is joint decoding [2,4,9,23,33,35,36,42,51]: using the entire code X , rather than only the user's code word x j , to decide whether user j should be accused. Assigning scores to tuples of users was considered before in e.g.…”

“…Assigning scores to tuples of users was considered before in e.g. [42], but no explicit decision criterion with provable results was provided, and it was left as an open problem. 4 Wald's scheme 4…”

“…Recall that in joint decoding the entire code X is taken into account to decide whether users should be accused. In [42] it was considered to assign scores to tuples T of t ≤ c users, after which one would like to distinguish between the following t + 1 hypotheses:…”