Advertisement

Problems of Information Transmission

, Volume 55, Issue 3, pp 241–253 | Cite as

Generalization of IPP Codes and IPP Set Systems

  • E. E. EgorovaEmail author
Coding Theory
  • 10 Downloads

Abstract

A quarter century ago Chor, Fiat, and Naor proposed mathematical models for revealing a source of illegal redistribution of digital content (tracing traitors) in the broadcast encryption framework, including the following two combinatorial models: nonbinary IPP codes, based on an (n, n)-threshold secret sharing scheme, and IPP set systems, based on the general (w, n)-threshold secret sharing scheme. We propose a new scheme combining the main ideas of nonbinary IPP codes and IPP set systems, which can also be considered as a generalization of nonbinary IPP codes to the case of constant-weight codes. In the simplest case of a coalition of size two, we compare the new scheme with previously known ones.

Key words

IPP codes IPP set systems secret sharing schemes broadcast encryption constant-weight codes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chor, B., Fiat, A., and Naor, M., Tracing Traitors, Advances in Cryptology—CRYPTO’94 (Proc. 14th Annual Int. Cryptology Conf., Santa Barbara, CA, USA, Aug. 21–25, 1994), Desmedt, Y.G., Ed., Lect. Notes Comp. Sci., vol. 839, Berlin: Springer, 1994, pp. 257–270.CrossRefGoogle Scholar
  2. 2.
    Hollmann, H.D.L., van Lint, J.H., Linnartz, J.-P., and Tolhuizen, L.M.G.M., On Codes with the Identifiable Parent Property, J. Combin. Theory Ser. A, 1998, vol. 82, no. 2, pp. 121–133.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Stinson, D.R. and Wei, R., Combinatorial Properties and Constructions of Traceability Schemes and Frameproof Codes, SIAM J. Discrete Math., 1998, vol. 11, no. 1, pp. 41–53.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Collins, M.J., Upper Bounds for Parent-Identifying Set Systems, Des. Codes Cryptogr., 2009, vol. 51, no. 2, pp. 167–173.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Blakley, G.R., Safeguarding Cryptographic Keys, Proc. 1979 National Computer Conf.: Int. Workshop on Managing Requirements Knowledge, New York, June 4–7, 1979, Merwin, R.E., Zanca, J.T., and Smith, M., Eds., AFIPS Conf. Proceedings, V. 48, Montvale, NJ: AFIPS Press, 1979, pp. 313–317.Google Scholar
  6. 6.
    Shamir, A., How to Share a Secret, Comm. ACM, 1979, vol. 22, no. 11, pp. 612–613.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kabatiansky, G.A., Mathematics of Secret Sharing, Mat. Pros., Ser. 3, 1998, Issue 2, Moscow: MCCME, pp. 115–126.Google Scholar
  8. 8.
    Blakley, G.R. and Kabatianski, G.A., Generalized Ideal Secret-Sharing Schemes and Matroids, Probl. Peredachi Inf., 1997, vol. 33, no. 3, pp. 102–110 [Probl. Inf. Transm. (Engl. Transl.), 1997, vol. 33, no. 3, pp. 277–284].MathSciNetzbMATHGoogle Scholar
  9. 9.
    Kautz, W.H. and Singleton, R.C., Nonrandom Binary Superimposed Codes, IEEE Trans. Inform. Theory, 1964, vol. 10, no. 4, pp. 363–377.CrossRefGoogle Scholar
  10. 10.
    D’yachkov, A.G. and Rykov, V.V., Bounds on the Length of Disjunctive Codes, Probl. Peredachi Inf., 1982, vol. 18, no. 3, pp. 7–13 [Probl. Inf. Transm. (Engl. Transl.), 1982, vol. 18, no. 3, pp. 166–171].MathSciNetzbMATHGoogle Scholar
  11. 11.
    Erdős, P., Frankl, P., and Füredi, Z., Families of Finite Sets in Which No Set Is Covered by the Union of Two Others, J. Combin. Theory Ser. A, 1982, vol. 33, no. 2, pp. 158–166.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Erdős, P., Frankl, P., and Füredi, Z., Families of Finite Sets in Which No Set Is Covered by the Union of r Others, Israel J. Math., 1985, vol. 51, no. 1–2, pp. 79–89.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Barg, A., Blakley, G.R., and Kabatiansky, G.A., Digital Fingerprinting Codes: Problem Statements, Constructions, Identification of Traitors, IEEE Trans. Inform. Theory, 2003, vol. 49, no. 4, pp. 852–865.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Küorner, J., On the Extremal Combinatorics of the Hamming Space, J. Combin. Theory Ser. A, 1995, vol. 71, no. 1, pp. 112–126.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Boneh, D. and Shaw, J., Collusion-Secure Fingerprinting for Digital Data, IEEE Trans. Inform. Theory, 1998, vol. 44, no. 5, pp. 1897–1905.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tardos, G., Optimal Probabilistic Fingerprint Codes, in Proc. 35th Annual ACM Sympos. on Theory of Computing (STOC’03), San Diego, CA, USA, June 9–11, 2003, pp. 116–125.Google Scholar
  17. 17.
    Barg, A., Cohen, G., Encheva, S., Kabatiansky, G., and Z´emor, G., A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents, SIAM J. Discrete Math., 2001, vol. 14, no. 3, pp. 423–431.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Alon, N., Cohen, G., Krivelevich, M., and Litsyn, S., Generalized Hashing and Parent-Identifying Codes, J. Combin. Theory Ser. A, 2003, vol. 104, no. 1, pp. 207–215.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Blackburn, S.R., Combinatorial Schemes for Protecting Digital Content, Surveys in Combinatorics, 2003 (Proc. 19th British Combinatorial Conf., Univ. of Wales, Bangor, UK, June 29–July 4, 2003), Wensley, C.D., Ed., Lond. Math. Soc. Lect. Note Ser., vol. 307, Cambridge, UK: Cambridge Univ. Press, 2003, pp. 43–78.Google Scholar
  20. 20.
    Kabatiansky, G.A., Codes for Copyright Protection: The Case of Two Pirates, Probl. Peredachi Inf., 2005, vol. 41, no. 2, pp. 123–127 [Probl. Inf. Transm. (Engl. Transl.), 2005, vol. 41, no. 2, pp. 182–186].MathSciNetGoogle Scholar
  21. 21.
    Gu, Y. and Miao, Y., Bounds on Traceability Schemes, IEEE Trans. Inform. Theory, 2018, vol. 64, no. 5, pp. 3450–3460.MathSciNetCrossRefGoogle Scholar
  22. 22.
    Egorova, E. and Kabatiansky, G., Analysis of Two Tracing Traitor Schemes via Coding Theory, Coding Theory and Applications (Proc. 5th Int. Castle Meeting, ICMCTA 2017, Vihula, Estonia, Aug. 28–31, 2017), Barbero, A.I., Skachek, V., and Ytrehus, Ø, Eds., Lect. Notes Comp. Sci., vol. 10495, Cham: Springer, 2017, pp. 84–92.CrossRefGoogle Scholar
  23. 23.
    Bassalygo, L.A., Gelfand, S.I., and Pinsker, M.S., Simple Methods for Deriving Lower Bounds in Coding Theory, Probl. Peredachi Inf., 1991, vol. 27, no. 4, pp. 3–8 [Probl. Inf. Transm. (Engl. Transl.), 1991, vol. 27, no. 4, pp. 277–281].zbMATHGoogle Scholar
  24. 24.
    Hoeffding, W., Probability Inequalities for Sums of Bounded Random Variables, J. Amer. Statist. Assoc., 1963, vol. 58, no. 301, pp. 13–30.MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Skolkovo Institute of Science and TechnologyMoscowRussia

Personalised recommendations