Worst-Case Optimal Fingerprinting Codes for Non-threshold Collusion

  • Takaaki Mizuki
  • Satoshi Nounin
  • Hideaki Sone
  • Yousuke Toyota
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3919)


This paper investigates collusion-secure fingerprinting codes for digital data. Most previous works assume the threshold number of collusive users. Whereas, in order to treat a more general non-threshold collusion, we first introduce a notion of a potentially collusive family. Furthermore, we develop a novel way to measure collusion-secure codes according to combinatorial properties in a natural way. Our measurement immediately implies the definition of optimal codes. We then actually illustrate an optimal code. Finally, we give a necessary and sufficient condition for a code to be optimal by using a new notion of family-intersecting codes.


Digital Content Information Hiding Secret Sharing Scheme Optimal Code Collusion Attack 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N., Guruswami, V., Kaufman, T., Sudan, M.: Guessing secrets efficiently via list decoding. In: Proc. the thirteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 254–262 (2002)Google Scholar
  2. 2.
    Banno, K., Orihara, S., Mizuki, T., Nishizeki, T.: Best security index for digital fingerprinting. In: Barni, M., Herrera-Joancomartí, J., Katzenbeisser, S., Pérez-González, F. (eds.) IH 2005. LNCS, vol. 3727, pp. 398–412. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Blakley, G.R., Meadows, C., Purdy, G.B.: Fingerprinting long forgiving messages. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 180–189. Springer, Heidelberg (1986)Google Scholar
  4. 4.
    Boneh, D., Shaw, J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theory 44(5), 1897–1905 (1998)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Cohen, G., Encheva, S., Litsyn, S., Schaathun, H.G.: Intersecting codes and separating codes. Discrete Applied Mathematics 128, 75–83 (2003)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Cohen, G., Lempel, A.: Linear intersecting codes. Discrete Mathematics 56, 35–43 (1985)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Cohen, G., Zemor, G.: Intersecting codes and independent families. IEEE Trans. Inf. Theory 40(6), 1872–1881 (1994)CrossRefMATHGoogle Scholar
  8. 8.
    Cotrina-Navau, J., Fernandez, M., Soriano, M.: A family of collusion 2-secure codes. In: Barni, M., Herrera-Joancomartí, J., Katzenbeisser, S., Pérez-González, F. (eds.) IH 2005. LNCS, vol. 3727, pp. 387–397. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Fernandez, M., Soriano, M.: Fingerprinting concatenated codes with efficient identification. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 459–470. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Furon, T.: A survey of watermarking security. In: Barni, M., Cox, I., Kalker, T., Kim, H.J. (eds.) IWDW 2005. LNCS, vol. 3710, pp. 201–215. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Guillaume, J.-L., Latapy, M.: Bipartite structure of all complex networks. Information Processing Letters 90(5), 215–221 (2004)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Guo, H., Georganas, N.D.: A novel approach to digital image watermarking based on a generalized secret sharing scheme. Multimedia Systems 9(3), 249–260 (2003)CrossRefGoogle Scholar
  13. 13.
    Guth, H., Pfitzmann, B.: Error- and collusion-secure fingerprinting for digital data. In: Pfitzmann, A. (ed.) IH 1999. LNCS, vol. 1768, pp. 134–145. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Le, T.V., Burmester, M., Hu, J.: Short c-secure fingerprinting codes. In: Boyd, C., Mao, W. (eds.) ISC 2003. LNCS, vol. 2851, pp. 422–427. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Muratani, H.: A collusion-secure fingerprinting code reduced by Chinese remaindering and its random-error resilience. In: Moskowitz, I.S. (ed.) IH 2001. LNCS, vol. 2137, pp. 303–315. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Orihara, S., Mizuki, T., Nishizeki, T.: New security index for digital fingerprinting and its bounds. IEICE Trans. Fundamentals E86-A(5), 1156–1163 (2003)Google Scholar
  18. 18.
    Peikert, C., Shelat, A., Smith, A.: Lower bounds for collusion-secure fingerprinting. In: Proc. the fourteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 472–479 (2003)Google Scholar
  19. 19.
    Staddon, J.N., Stinson, D.R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theory 47(3), 1042–1049 (2001)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Stinson, D.R., van Trung, T., Wei, R.: Secure frameproof codes, key distribution patterns, group testing algorithms and related structures. J. Stat. Plan. Inference 86(2), 595–617 (2000)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Tardos, G.: Optimal probabilistic fingerprint codes. Journal of the ACM (to appear)Google Scholar
  22. 22.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  23. 23.
    Wu, M., Trappe, W., Wang, Z.J., Liu, K.J.R.: Collusion-resistant fingerprinting for multimedia. IEEE Signal Processing Magazine 21(2), 15–27 (2004)CrossRefGoogle Scholar
  24. 24.
    Yoshioka, K., Shikata, J., Matsumoto, T.: Collusion secure codes: systematic security definitions and their relations. IEICE Trans. Fundamentals E87-A(5), 1162–1171 (2004)MATHGoogle Scholar
  25. 25.
    Yoshioka, K., Shikata, J., Matsumoto, T.: On collusion security of random codes. IEICE Trans. Fundamentals E88-A(1), 296–304 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Takaaki Mizuki
    • 1
  • Satoshi Nounin
    • 2
  • Hideaki Sone
    • 1
  • Yousuke Toyota
    • 3
  1. 1.Information Synergy CenterTohoku UniversitySendaiJapan
  2. 2.Sone Lab., Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.KDDI R&D Laboratories Inc.SaitamaJapan

Personalised recommendations