Skip to main content
SpringerLink
Log in

Short collusion-secure fingerprint codes against three pirates

  • Regular Contribution
  • Published:
International Journal of Information Security Aims and scope Submit manuscript

Abstract

In this article, we propose a new construction of probabilistic collusion-secure fingerprint codes against up to three pirates and give a theoretical security evaluation. Our pirate tracing algorithm combines a scoring method analogous to Tardos codes (J ACM 55:1–24, 2008) with an extension of parent search techniques of some preceding 2-secure codes. Numerical examples show that our code lengths are significantly shorter than (about 30–40% of) the shortest known c-secure codes by Nuida et al. (Des Codes Cryptogr 52:339–362, 2009) with c = 3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amiri, E., Tardos, G.: High rate fingerprinting codes and the fingerprinting capacity. In: Proceedings of SODA 2009, pp. 336–345. ACM (2009)

  2. Barg A., Blakley G.R., Kabatiansky G.A.: Digital fingerprinting codes: problem statements, constructions, identification of traitors. IEEE Trans. Inf. Theory 49, 852–865 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blakley, G.R., Kabatiansky, G.A.: Random coding technique for digital fingerprinting codes. In: Proceedings of IEEE ISIT 2004, p. 202. IEEE, Los Alamitos (2004)

  4. Blayer O., Tassa T.: Improved versions of Tardos’ fingerprinting scheme. Des. Codes Cryptogr. 48, 79–103 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boneh D., Shaw J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theory 44, 1897–1905 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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)

  7. Hoeffding W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58, 13–30 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  8. Huang, Y.-W., Moulin, P.: Maximin optimality of the arcsine fingerprinting distribution and the interleaving attack for large coalitions. In: Proceedings of IEEE WIFS 2010. IEEE, Los Alamitos (2010)

  9. Huang, Y.-W., Moulin, P.: On the saddle-point solution and the large-coalition asymptotics of fingerprinting games. e-Print arXiv (cs.IT) 1011.1261v2. http://arXiv.org/abs/1011.1261v2 (2011)

  10. Kitagawa, T., Hagiwara, M., Nuida, K., Watanabe, H., Imai, H.: A group testing based deterministic tracing algorithm for a short random fingerprint code. In: Proceedings of ISITA 2008, pp. 706–710 (2008)

  11. Nuida, K.: An improvement of short 2-secure fingerprint codes strongly avoiding false-positive. In: Katzenbeisser, S., Sadeghi, A.-R. (eds.) IH 2009. LNCS, vol. 5806, pp. 161–175. Springer, Heidelberg (2009)

  12. Nuida, K.: Making collusion-secure codes (more) robust against bit erasure. IACR Cryptology ePrint Archive 2009/549. http://eprint.iacr.org/2009/549 (2009)

  13. Nuida, K.: Short collusion-secure fingerprint codes against three pirates. In: Böhme, R., Fong, P.W.L., Safavi-Naini, R. (eds.) IH 2010. LNCS, vol. 6387, pp. 86–102. Springer, Heidelberg (2010)

  14. Nuida, K., Fujitsu, S., Hagiwara, M., Imai, H., Kitagawa, T., Ogawa, K., Watanabe, H.: An efficient 2-secure and short random fingerprint code and its security evaluation. IEICE Trans. Fundam. E92-A, 197–206 (2009)

  15. Nuida K., Fujitsu S., Hagiwara M., Kitagawa T., Watanabe H., Ogawa K., Imai H.: An improvement of discrete Tardos fingerprinting codes. Des. Codes Cryptogr. 52, 339–362 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Nuida, K., Hagiwara, M., Kitagawa, T., Watanabe, H., Ogawa, K., Fujitsu, S., Imai, H.: A tracing algorithm for short 2-secure probabilistic fingerprinting codes strongly protecting innocent users. In: Proceedings of IEEE CCNC 2007, pp. 1068–1072. IEEE, Los Alamitos (2007)

  17. Schaathun, H.G.: Fighting three pirates with scattering codes. In: Proceedings of IEEE ISIT 2004. IEEE, Los Alamitos (2004)

  18. Schaathun, H.G.: Fighting three pirates with scattering codes. Reports in informatics 263, Department of Informatics, University of Bergen. http://www.ii.uib.no/publikasjoner/texrap/pdf/2004-263.pdf (2004)

  19. Schaathun H.G.: On the assumption of equal contributions in fingerprinting. IEEE Trans. Inf. Forensics Secur. 3, 569–572 (2008)

    Article  Google Scholar 

  20. Sebé, F., Domingo-Ferrer, J.: Short 3-secure fingerprinting codes for copyright protection. In: Batten, L., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 316–327. Springer, Heidelberg (2002)

  21. Škorić B., Katzenbeisser S., Celik M.U.: Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes. Des. Codes Cryptogr. 46, 137–166 (2008)

    Article  MathSciNet  Google Scholar 

  22. Škorić, B., Katzenbeisser, S., Schaathun, H.G., Celik, M.U.: Tardos fingerprinting codes in the combined digit model. In: Proceedings of IEEE WIFS 2009. IEEE, Los Alamitos (2009)

  23. Škorić B., Vladimirova T.U., Celik M.U., Talstra J.C.: Tardos fingerprinting is better than we thought. IEEE Trans. Inf. Theory 54, 3663–3676 (2008)

    Article  Google Scholar 

  24. Tardos G.: Optimal probabilistic fingerprint codes. J. ACM 55, 1–24 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan

    Koji Nuida

Authors
  1. Koji Nuida
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Koji Nuida.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nuida, K. Short collusion-secure fingerprint codes against three pirates. Int. J. Inf. Secur. 11, 85–102 (2012). https://doi.org/10.1007/s10207-012-0155-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10207-012-0155-8

Keywords

Search

Navigation