Breaking Two k-Resilient Traitor Tracing Schemes with Sublinear Ciphertext Size

  • MoonShik Lee
  • Daegun Ma
  • MinJae Seo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5536)


In 2004, Matsushita and Imai proposed a k-resilient public-key traitor tracing scheme which has sublinear ciphertext size 4k + 2 + (n/2k) with efficient black-box tracing against self-defensive pirates, where n, k are the total number of subscribers and the maximum number of colluders. After that, in 2006, they presented a hierarchical key assignment method to reduce the ciphertext size into 4k + 5 + log(n/2k) by combining a complete binary tree with the former scheme.

In this paper, we show that the proposed schemes are vulnerable to our attack which makes pirate keys able to avoid the black-box tracing. Their schemes are based on multiple polynomials and our attack use a combination between different polynomials. The latter scheme can be broken by other attacks which use secret values of the key generation polynomial or use partial keys.


cryptanalysis public-key traitor tracing black-box tracing self-defensive pirates linear attack 


  1. 1.
    Boneh, D., Franklin, M.: An Efficient Public Key Traitor Tracing Scheme. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 338–353. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Boneh, D., Sahai, A., Waters, B.: Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 573–592. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    Kiayias, A., Yung, M.: On Crafty Pirates and Foxy Tracers. In: Sander, T. (ed.) DRM 2001. LNCS, vol. 2320, pp. 450–465. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Kurosawa, K., Desmedt, Y.: Optimum Traitor Tracing and Asymmetric Scheme. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 145–157. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Matsushita, T., Imai, H.: A Public-Key Black-Box Traitor Tracing Scheme with Sublinear Ciphertext Size against Self-Defensive Pirates. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 260–275. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Matsushita, T., Imai, H.: Hierarchical Key Assignment for Black-Box Tracing with Efficient Ciphertext Size. In: Ning, P., Qing, S., Li, N. (eds.) ICICS 2006. LNCS, vol. 4307, pp. 92–111. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Naor, D., Naor, M., Lotspiech, J.: Revocation and Tracing Schemes for Stateless Receivers. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 41–62. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Stinson, D., Wei, R.: Key Preassigned Traceability Schemes for Broadcast Encryption. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 144–156. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • MoonShik Lee
    • 1
  • Daegun Ma
    • 1
  • MinJae Seo
    • 1
  1. 1.Department of Mathematical Sciences and ISaC-RIMSeoul National UniversitySeoulKorea

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