Analysis of properties of \(q\)-ary Reed-Muller error-correcting codes viewed as codes for copyright protection. (English. Russian original) Zbl 1396.94108

Probl. Inf. Transm. 51, No. 4, 398-408 (2015); translation from Probl. Peredachi Inf. 51, No. 4, 99-111 (2015).
Summary: We consider a data protection scheme where error-correcting codes can be used for efficient protection against unauthorized copying organized by coalitions of cardinality \(c \in \mathbb{N}\) of malicious users. We find limits of range of the parameters of prospective \(q\)-ary Reed-Muller codes for which these codes are \(c\)-TA and \(c\)-FP codes for copyright protection.


94B05 Linear codes (general theory)
Full Text: DOI


[1] 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. Trans. (Engl. Transl.), 2005, vol. 41, no. 2, pp. 182-186]. · Zbl 1130.94018
[2] Silverberg, A., Staddon, J., and Walker, J.L., Efficient Traitor Tracing Algorithms Using List Decoding, Advances in Cryptology¡ªASIACRYPT’2001 (Proc. 7th Int. Conf. on the Theory and Application of Cryptology and Information Security, Gold Coast, Australia, Dec. 9-13, 2001), Boyd, C., Ed., Lect. Notes Comp. Sci., vol. 2248, Berlin: Springer, 2001, pp. 175-192. · Zbl 1062.94552 · doi:10.1007/3-540-45682-1_11
[3] Staddon, J.N., Stinson, D.R., and Wei, R., Combinatorial Properties of Frameproof and Traceability Codes, IEEE Trans. Inform. Theory, 2001, vol. 47, no. 3, pp. 042-1049. · Zbl 1001.94032 · doi:10.1109/18.915661
[4] Deundyak, V.M. and Mkrtichyan, V.V., Investigation of the Limits of Applicability of an Information Protection Scheme Based on Reed-Solomon Codes, Diskretn. Anal. Issled. Oper., 2011, vol. 18, no. 3, pp. 21-38. · Zbl 1249.94027
[5] Deundyak, V.M. and Mkrtichyan, V.V., Mathematical Model of an Efficient Scheme of Special Broadcast Encrypion and Investigation of Its Applicability Limits, Izv. Vyssh. Uchebn. Zaved. Sev.-Kavk. Reg. Estestv. Nauki, 2009, no. 1, pp. 5-8. · Zbl 1224.94034
[6] 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. · Zbl 1063.94079 · doi:10.1109/TIT.2003.809570
[7] 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. · Zbl 1069.68045 · doi:10.1016/j.jco.2003.08.012
[8] Blackburn, S.R., Etzion, T., and Ng, S.-L., Traceability Codes, J. Combin. Theory Ser. A, 2010, vol. 117, no. 8, pp. 049-1057. · Zbl 1230.94004 · doi:10.1016/j.jcta.2010.02.009
[9] Fernández, M., Cotrina, J., Soriano, M., and Domingo, N., A Note about the Traceability Properties of Linear Codes, Proc. 10th Int. Conf. on Information Security and Cryptology (ICISC’2007), Seoul, Korea, Nov. 29-30, 2007, Nam, K.-H. and Rhee, G., Eds., Lect. Notes Comp. Sci., vol. 4817, Berlin: Springer, 2007, pp. 251-258. · Zbl 1337.94104 · doi:10.1007/978-3-540-76788-6_20
[10] 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. 21-133. · Zbl 0910.05070 · doi:10.1006/jcta.1997.2851
[11] Jin, H. and Blaum, M., Combinatorial Properties for Traceability Codes Using Error Correcting Codes, IEEE Trans. Inform. Theory, 2007, vol. 53, no. 2, pp. 804-808. · Zbl 1310.94237 · doi:10.1109/TIT.2006.889730
[12] Van Trung, T. and Martirosyan, S., On a Class of Traceability Codes, Des. Codes Cryptogr., 2004, vol. 31, no. 2, pp. 25-132. · Zbl 1042.94019
[13] Yevpak, S.A. and Mkrtichyan, V.V., Investigating the Possibility of Applying q-ary Reed-Muller Codes in Special Broadcast Encrypion Schemes, Izv. Vyssh. Uchebn. Zaved. Sev.-Kavk. Reg. Estestv. Nauki, 2011, no. 5, pp. 11-15.
[14] Yevpak, S.A. and Mkrtichyan, V.V., Application of q-ary Reed-Muller Codes in Special Broadcast Encrypion Schemes, in Trudy nauchnoi shkoly I.B. Simonenko (Studies of I.B. Simonenko Scientific School), Rostov-on-Don: Yuzhn. Federal. Univ., 2010, pp. 93-99.
[15] Delsarte, P., Goethals, J.-M., and MacWilliams, F.J., On Generalized Reed-Muller Codes and Their Relatives, Inform. Control, 1970, vol. 16, pp. 403-442. · Zbl 0267.94014 · doi:10.1016/S0019-9958(70)90214-7
[16] Chor, B., Fiat, A., and Naor, M., Tracing Traitors, Advances in Cryptology¡ªCRYPTO’94 (Proc. 14th Ann. Int. Cryptology Conf., Santa Barbara, CA,USA, Aug. 21-25, 1994), Desmedt, Y., Ed., Lect. Notes Comp. Sci., vol. 839, Berlin: Springer, 1994, pp. 257-270. · Zbl 0939.94555 · doi:10.1007/3-540-48658-5_25
[17] Moreira, J., Ferná ndez, M., and Soriano, M., On the Relationship between the Traceability Properties of Reed-Solomon Codes, Adv. Math. Commun., 2012, vol. 6, no. 4, pp. 467-478. · Zbl 1350.94070 · doi:10.3934/amc.2012.6.467
[18] Yevpak, S.A. and Mkrtichan, V.V., Applicability Conditions for q-ary Reed-Muller Codes in Traitor Tracing, Vladikavkaz. Mat. Zh., 2014, vol. 16, no. 2, pp. 38-45. · Zbl 1361.94057
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