Abstract
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 ∈ 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.
Similar content being viewed by others
References
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].
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.
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.
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.
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.
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.
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.
Blackburn, S.R., Etzion, T., and Ng, S.-L., Traceability Codes, J. Combin. Theory Ser. A, 2010, vol. 117, no. 8, pp. 049–1057.
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.
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.
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.
Van Trung, T. and Martirosyan, S., On a Class of Traceability Codes, Des. Codes Cryptogr., 2004, vol. 31, no. 2, pp. 25–132.
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.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.M. Deundyak, S.A. Yevpak, V.V. Mkrtichyan, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 4, pp. 99–111.
Rights and permissions
About this article
Cite this article
Deundyak, V.M., Yevpak, S.A. & Mkrtichyan, V.V. Analysis of properties of q-ary Reed–Muller error-correcting codes viewed as codes for copyright protection. Probl Inf Transm 51, 398–408 (2015). https://doi.org/10.1134/S0032946015040092
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0032946015040092