A family of asymptotically good binary fingerprinting codes

  • Authors:
  • Josep Cotrina-Navau;Marcel Fernández

  • Affiliations:
  • Department d'Enginyeria Telemàtica, Universitat Politècnica de Catalunya, Barcelona, Spain;Department d'Enginyeria Telemàtica, Universitat Politècnica de Catalunya, Barcelona, Spain

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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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 Ζ 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 - Ζ. The Boneh-Shaw fingerprinting codes are n-secure codes with ΖB error, where n also denotes the number of authorized users. Unfortunately, the length the Boneh-Shaw codes should be of order O(n3 log(n/ΖB)), which is prohibitive for practical applications. In this paper, we prove that the Boneh-Shaw codes are (c )-secure for lengths of order O(nc2 log(n/ΖB)). Moreover, in this paper it is also shown how to use these codes to construct binary fingerprinting codes of length L = O(c6 log(c/Ζ) log n), with probability of error Ζ B 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.