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Generalization of IPP Codes and IPP Set Systems

  • Coding Theory
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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.

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References

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  4. Collins, M.J., Upper Bounds for Parent-Identifying Set Systems, Des. Codes Cryptogr., 2009, vol. 51, no. 2, pp. 167–173.

    Article  MathSciNet  Google Scholar 

  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. Shamir, A., How to Share a Secret, Comm. ACM, 1979, vol. 22, no. 11, pp. 612–613.

    Article  MathSciNet  Google Scholar 

  7. Kabatiansky, G.A., Mathematics of Secret Sharing, Mat. Pros., Ser. 3, 1998, Issue 2, Moscow: MCCME, pp. 115–126.

    Google Scholar 

  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].

    MathSciNet  MATH  Google Scholar 

  9. Kautz, W.H. and Singleton, R.C., Nonrandom Binary Superimposed Codes, IEEE Trans. Inform. Theory, 1964, vol. 10, no. 4, pp. 363–377.

    Article  Google Scholar 

  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].

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  14. Küorner, J., On the Extremal Combinatorics of the Hamming Space, J. Combin. Theory Ser. A, 1995, vol. 71, no. 1, pp. 112–126.

    Article  MathSciNet  Google Scholar 

  15. Boneh, D. and Shaw, J., Collusion-Secure Fingerprinting for Digital Data, IEEE Trans. Inform. Theory, 1998, vol. 44, no. 5, pp. 1897–1905.

    Article  MathSciNet  Google Scholar 

  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.

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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. 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].

    MathSciNet  Google Scholar 

  21. Gu, Y. and Miao, Y., Bounds on Traceability Schemes, IEEE Trans. Inform. Theory, 2018, vol. 64, no. 5, pp. 3450–3460.

    Article  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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].

    MATH  Google Scholar 

  24. Hoeffding, W., Probability Inequalities for Sums of Bounded Random Variables, J. Amer. Statist. Assoc., 1963, vol. 58, no. 301, pp. 13–30.

    Article  MathSciNet  Google Scholar 

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  1. Skolkovo Institute of Science and Technology, Moscow, Russia

    E. E. Egorova

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Russian Text © The Author(s), 2019, published in Problemy Peredachi Informatsii, 2019, Vol. 55, No. 3, pp. 46–59.

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Egorova, E.E. Generalization of IPP Codes and IPP Set Systems. Probl Inf Transm 55, 241–253 (2019). https://doi.org/10.1134/S0032946019030049

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