Obtaining Asymptotic Fingerprint Codes Through a New Analysis of the Boneh-Shaw Codes

Abstract

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 ε 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 error, where n also denotes the number of authorized users. Unfortunately, the length the Boneh-Shaw codes should be of order O(n ³log(n/ε)), 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 ²log(n/ε)).

Moreover we show how to use these codes to construct binary fingerprinting codes with length L=O(c ⁶logc logn), with probability of error O(1/n)=exp(–Ω(L)), and identification algorithm of complexity poly(logn)=poly(L). These results improve in some aspects the best known schemes and with a much more simple construction.