Practical Construction Against Theoretical Approach in Fingerprinting

We consider fingerprinting under collusion attacks in the Hamming space. To model the attacks we use the framework of Somekh-Baruch and Merhav, IEEE Trans, on Inf. Th.9 vol. 51(3), 2005. We construct a family of fingerprinting codes efficient against coalition of arbitrary size. Using this family, tracing dishonest users can be done without error and in polynomial time. The number of users is exponential in the length. The proposed construction relies on centered error correcting codes. Our results have an amazing relation with an upper bound on the number of users derived by Somekh-Baruch and Merhav: dropping two assumptions that they used we construct codes beating their bound

[1]  Dan Boneh,et al.  Collusion-Secure Fingerprinting for Digital Data , 1998, IEEE Trans. Inf. Theory.

[2]  Alexander Barg,et al.  Digital fingerprinting codes: problem statements, constructions, identification of traitors , 2003, IEEE Trans. Inf. Theory.

[3]  A. McLoughlin,et al.  The complexity of computing the covering radius of a code , 1984, IEEE Trans. Inf. Theory.

[4]  Catherine A. Meadows,et al.  Fingerprinting Long Forgiving Messages , 1985, CRYPTO.

[5]  Dan.  Collusion-Secure Fingerprinting for Digital Data , 2002 .

[6]  Gérard D. Cohen,et al.  Error-correcting WOM-codes , 1991, IEEE Trans. Inf. Theory.

[7]  Gérard D. Cohen,et al.  Covering Codes , 2005, North-Holland mathematical library.

[8]  M. S. Pinsker,et al.  CENTERED ERROR-CORRECTING CODES , 1999 .

[9]  H. Stichtenoth,et al.  A low complexity algorithm for the construction of algebraic geometric codes better than the Gilbert-Varshamov bound , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[10]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[11]  S. Yau.  Mathematics and its applications , 2002 .

[12]  Neri Merhav,et al.  On the capacity game of private fingerprinting systems under collusion attacks , 2003, IEEE Transactions on Information Theory.

[13]  M. Tsfasman,et al.  Modular curves, Shimura curves, and Goppa codes, better than Varshamov‐Gilbert bound , 1982 .

[14]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[15]  Toby Berger,et al.  Complete decoding of triple-error-correcting binary BCH codes , 1976, IEEE Trans. Inf. Theory.

[16]  Amos Fiat,et al.  Tracing traitors , 2000, IEEE Trans. Inf. Theory.

[17]  Alexander Vardy,et al.  The intractability of computing the minimum distance of a code , 1997, IEEE Trans. Inf. Theory.

[18]  Philippe Piret,et al.  Do most binary linear codes achieve the Goblick bound on the covering radius? , 1986, IEEE Trans. Inf. Theory.