Abstract
Codes with the identifiable “parent” property appeared as one of solutions for the broadcast encryption problem. We propose a new, more general model of such codes, give an overview of known results, and formulate some unsolved problems.
Similar content being viewed by others
References
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.
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.
Shamir, A., How to Share a Secret, Comm. ACM, 1979, vol. 22, no. 11, pp. 612–613.
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.
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.
Collins, M.J., Upper Bounds for Parent-Identifying Set Systems, Des. Codes Cryptogr., 2009, vol. 51, no. 2, pp. 167–173.
Egorova, E.E., Generalization of IPP Codes and IPP Set Systems, Probl. Peredachi Inf., 2019, vol. 55, no. 3, pp. 46–59 [Probl. Inf. Transm. (Engl. Transl.), 2019, vol. 55, no. 3, pp. 241–253].
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].
Benaloh, J. and Leichter, J., Generalized Secret Sharing and Monotone Functions, Advances in Cryptology—CRYPTO’88 (Proc. 8th Annual Int. Cryptology Conf., Santa Barbara, CA, USA, Aug. 21–25, 1988), Goldwasser, S., Ed., Lect. Notes Comp. Sci., vol. 403, Berlin: Springer, 1990, pp. 27–35.
Ito, M., Saito, A., and Nishizeki, T., Secret Sharing Scheme Realizing General Access Structure, Electron. Comm. Japan Part III Fund. Electron. Sci., 1989, vol. 72, no. 9, pp. 56–63.
Egorova, E. and Kabatiansky, G., PatAnalysis 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.
Sagalovich, Yu.L., Separating Systems, Probl. Peredachi Inf., 1994, vol. 30, no. 2, pp. 14–35 [Probl. Inf. Transm. (Engl. Transl.), 1994, vol. 30, no. 2, pp. 105–123].
Cohen, G.D. and Schaathun, H.G., Asymptotic Overview on Separating Codes, Tech. Rep. of Dept. of Informatics, Univ. of Bergen, Bergen, Norway, 2003, no. 248.
Bassalygo, L.A., Burmester, M., Dyachkov, A., and Kabatianskii, G., Hash Codes, in Proc. 1997 IEEE Int. Sympos. on Information Theory (ISIT’97), Ulm, Germany, June 29–July 4, 1997, p. 174.
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].
Fernandez, M., Cotrina J., Soriano, M., and Domingo, N., A Note about the Identifier Parent Property in Reed–Solomon Codes, Comput. Secur., 2010, vol. 29, no. 5, pp. 628–635.
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.
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.
Vorob’ev, I.V., Probl. Peredachi Inf., 2017, vol. 53, no. 1, pp. 34–46 [Probl. Inf. Transm. (Engl. Transl.), 2017, vol. 53, no. 1, pp. 30-41].
Blackburn, S.R., Etzion, T., and Ng, S.-L., Traceability Codes, J. Combin. Theory Ser. A, 2010, vol. 117, no. 8, pp. 1049–1057.
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.
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.
Kautz, W.H. and Singleton, R.C., Nonrandom Binary Superimposed Codes, IEEE Trans. Inform. Theory, 1964, vol. 10, no. 4, pp. 363–377.
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].
Levenshtein, V.I., Upper-Bound Estimates for Fixed-Weight Codes, Probl. Peredachi Inf., 1971, vol. 7, no. 4, pp. 3–12 [Probl. Inf. Transm. (Engl. Transl.), 1971, vol. 7, no. 4, pp. 281–287].
Gu, Y. and Miao, Y., Bounds on Traceability Schemes, IEEE Trans. Inform. Theory, 2018, vol. 64, no. 5, pp. 3450–3460.
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.
Barg, A. and Kabatiansky, G., A Class of I.P.P. Codes with Efficient Identification, J. Complexity, 2004, vol. 20, no. 2–3, pp. 137–147.
Egorova, E., Fernandez, M., and Kabatiansky, G., A Construction of Traceability Set Systems with Polynomial Tracing Algorithm, to appear in Proc. 2019 IEEE Int. Sympos. on Information Theory (ISIT’2019), Paris, France, July 7–12, 2019.
Tsfasman, M.A., Vlˇadu¸t, S.G., and Nogin, D.Yu., Algebraic Geometric Codes: Basic Notions, Providence, R.I.: Amer. Math. Soc., 2007.
Guruswami, V., List Decoding of Error-Correcting Codes (Winning Thesis of the 2002 ACM Doct. Diss. Competition), Lect. Notes Comp. Sci., vol. 3282. Berlin: Springer, 2004.
Ericson, T. and Zinoviev, V.A., An Improvement of the Gilbert Bound for Constant Weight Codes, IEEE Trans. Inform. Theory, 1987, vol. 33, no. 5, pp. 721–723.
Boneh, D. and Shaw, J., Collusion-Secure Fingerprinting for Digital Data, IEEE Trans. Inform. Theory, 1998, vol. 44, no. 5, pp. 1897–1905.
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.
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.
Fernandez, M., Kabatiansky, G., and Moreira, J., Almost IPP-Codes or Provably Secure Digital Fingerprinting Codes, in Proc. 2015 IEEE Int. Sympos. on Information Theory (ISIT’2015), Hong Kong, China, June 14–19, 2015, pp. 1595–1599.
Fernandez, M., Egorova, E., and Kabatiansky, G., Binary Fingerprinting Codes — Can We Prove that Someone Is Guilty?!, in Proc. 2015 IEEE Int. Workshop on Information Forensics and Security (WIFS’2015), Rome, Italy, Nov. 16–19, 2015, pp. 1–4.
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Problemy Peredachi Informatsii, 2019, Vol. 55, No. 3, pp. 93–105.
Rights and permissions
About this article
Cite this article
Kabatiansky, G.A. Traceability Codes and Their Generalizations. Probl Inf Transm 55, 283–294 (2019). https://doi.org/10.1134/S0032946019030074
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0032946019030074