Obtaining asymptotic fingerprint codes through a new analysis of the boneh-shaw codes

  • Authors:
  • Marcel Fernandez;Josep Cotrina

  • Affiliations:
  • Departament of Telematics Engineering., Universitat Politècnica de Catalunya, Barcelona, Spain;Departament of Telematics Engineering., Universitat Politècnica de Catalunya, Barcelona, Spain

  • Venue:
  • Inscrypt'06 Proceedings of the Second SKLOIS conference on Information Security and Cryptology
  • Year:
  • 2006

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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 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(n3log(n/ε)), which is prohibitive for practical applications. In this paper, we prove that the Boneh-Shaw codes are (cn)-secure for lengths of order O(nc2log(n/ε)). Moreover we show how to use these codes to construct binary fingerprinting codes with length L=O(c6logc 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.