Near-Optimal Collusion-Secure Fingerprinting Codes for Efficiently Tracing Illegal Re-distribution

Abstract

Digital fingerprinting provides a means of tracing unauthorized re-distribution of digital objects. With an unique fingerprint being imperceptibly embedded in each authorized copy of the object, in case a pirate copy is found, by analysing the fingerprint in the observed pirate copy, the distributer can identify the users who produced the pirate copy. Collusion-secure fingerprinting schemes address the problem of collusion, where a group of users (a coalition) detect and change the fingerprint symbols in their copies before producing pirate copies. It has been proved that there exist collusion-secure fingerprinting schemes that can identify at least one member of the coalition for any reasonably sized coalition. In order to guarantee the quality of the object, short fingerprinting codes are preferred in practical applications. A lower bound on the code length has been derived by Peikert et al, that is, any collusion-secure fingerprinting codes must have length at least o(s2log(1/se)), where s is the size of coalition. Codes which achieve the lower bound are called optimal codes. However, currently known optimal codes do not have any efficient (polynomial time-complexity) tracing procedure to identify the coalition. The best known codes with efficient tracing algorithms, which were constructed by Cortrina-Navau and Ferna 䠠ndez in 2010, have length O(s^elog(s/e)log(N)), where N is the total number of authorized users. In this paper, we construct a class of codes which have an efficient tracing algorithm and have length O(s^2log(1/e)log(N)). Our codes are much shorter than those by Cortrina-Navau and Fernandez.