Analysis of Two Tracing Traitor Schemes via Coding Theory

  • Elena Egorova
  • Grigory Kabatiansky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10495)


We compare two popular tracing traitor schemes (1) using non-binary codes with identifiable parent property (IPP-codes) and (2) using family of sets with identifiable parent property. We establish a natural basis for comparing and show that the second approach is stronger than IPP-codes. We also establish a new lower bound on the cardinality of the family of sets with identifiable parent property.


  1. 1.
    Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994). doi: 10.1007/3-540-48658-5_25 Google Scholar
  2. 2.
    Hollmann, H.D., van Lint, J.H., Linnartz, J.P., Tolhuizen, L.M.: On codes with the identifiable parent property. J. Comb. Theor. Ser. A 82(2), 121–133 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Barg, A., Cohen, G., Encheva, S., Kabatiansky, G., Zémor, G.: A hypergraph approach to the identifying parent property: the case of multiple parents. SIAM J. Discrete Math. 14(3), 423–431 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Alon, N., Cohen, G., Krivelevich, M., Litsyn, S.: Generalized hashing and parent-identifying codes. J. Comb. Theor. Ser. A 10(1), 207–215 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theor. 47, 1042–1049 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Blackburn, S.R.: Combinatorial schemes for protecting digital content. Surv. Comb. 307, 43–78 (2003)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Blakley, G.R.: Safeguarding cryptographic keys. Proc. Natl. Comput. Conf. 48, 313–317 (1979)Google Scholar
  9. 9.
    Stinson, D.R., Wei, R.: Combinatorial properties and constructions of traceability schemes and frameproof codes. SIAM J. Discrete Math. 11(1), 41–53 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Collins, M.J.: Upper bounds for parent-identifying set systems. Des. Codes Cryptogr. 51(2), 167–173 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gu, Y., Miao, Y.: Bounds on traceability schemes. arXiv preprint arXiv:1609.08336 (2016)
  12. 12.
    Boneh, D., Shaw, J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theor. 44, 1897–1905 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Erdos, P., Frankl, P., Furedi, Z.: Families of finite sets in which no set is covered by the union of two others. J. Comb. Theor. Ser. A 33(2), 158–166 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Furedi, Z., Erdos, P., Frankl, P.: Families of finite sets in which no set is covered by the union ofr others. Isr. J. Math. 51(1), 79–89 (1985)zbMATHGoogle Scholar
  15. 15.
    Kautz, W., Singleton, R.: Nonrandom binary superimposed codes. IEEE Trans. Inf. Theor. 10(4), 363–377 (1964)CrossRefzbMATHGoogle Scholar
  16. 16.
    Dyachkov, A.G., Rykov, V.V.: Bounds on the length of disjunctive codes. Probl. Inf. Transm. 18(2), 166–171 (1982)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Quang, A.N., Zeisel, T.: Bounds on constant weight binary superimposed codes. Probl. Control Inf. Theor. 17, 223–230 (1988)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Zinov’ev, V.A., Ericson, T.: On concatenated constant-weight codes beyond the Varshamov-Gilbert bound. Probl. Inf. Transm. 23(1), 110–111 (1987)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Skolkovo Institute of Science and Technology (Skoltech)Moscow RegionRussia

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