A Family of Asymptotically Good Binary Fingerprinting Codes

A fingerprinting code is a set of codewords that are embedded in each copy of a digital object with the purpose of making each copy unique. If the fingerprinting code is c-secure with error, then the decoding of a pirate word created by a coalition of at most c dishonest users, will expose at least one of the guilty parties with probability 1-ϵ. The Boneh-Shaw fingerprinting codes are n-secure codes with ϵ<sub>B</sub> error, where n also denotes the number of authorized users. Unfortunately, the length the Boneh-Shaw codes should be of order O(n<sup>3</sup> log(n/ϵ<sub>B</sub>)), which is prohibitive for practical applications. In this paper, we prove that the Boneh-Shaw codes are (c<; n)-secure for lengths of order O(nc<sup>2</sup> log(n/ϵ<sub>B</sub>)). Moreover, in this paper it is also shown how to use these codes to construct binary fingerprinting codes of length L=O(c<sup>6</sup> log(c/ϵ) log n), with probability of error ϵ<;ϵ<sub>B</sub> and an identification algorithm of complexity poly(log n)=poly(L). These results improve in some aspects the best known schemes and with a much more simple construction.