Multicast key distribution schemes based on Stinson-Van Trung designs PDF

Автори:A. N. Alekseichuk, S. N. Konyushok

A. N. Alekseichuk, S. N. Konyushok

UDC 621.391:517.95

Multicast key disrtribution schemes based on Stinson – van Trang designs / Alekseychuk A. N., Konushok S. N. // Cybernetika i sistemny analiz.

The efficiency characteristics of multicast key distribution schemes based on (v, b, r, λ)-designs are investigated. The stability and connectivity of such designs are estimated. These estimates generalize and enhance the well-known estimates for the efficiency characteristics of multicast key distribution schemes based on incomplete block designs.

Refs: 18 titles.


key distribution scheme, broadcast encoding, covering problem, combinatory design, block design, block code.

Author Affiliations

Institute of Special Communications and Information Protection, National Technical University of Ukraine "Kyiv Polytechnic Institute", Kyiv, Ukraine


1. S. Berkovits, “How to broadcast a secret,” in: Advances in Cryptology, EUROCRYPT’91, No. 547, Springer-Verlag, Berlin (1992), pp. 536–541.

2. A. Fiat and M. Naor, “Broadcast encryption,” in: Advances in Cryptology, CRYPTO’93, No. 773, Springer-Verlag, Berlin (1994), pp. 480–491.

3. D.R. Stinson, “On some methods for unconditionally secure key distribution and broadcast encryption, ” Designs, Codes and Cryptography, 12, 215–243 (1997). CrossRef

4. S.M. Konyushok and A.M. Oleksiichuk, “Unconditionally stable key distribution schemes in information and telecommunication systems with a large number of abonents: I. Schemes of preliminary distribution and key matching; II. Schemes of multicast key distribution,” Prikl. Radioelectronika, 5, No. 1, 83–104 (2006).

5. D. Naor, M. Naor, and J. Lotspiech, “Revocation and tracing schemes for stateless receivers,” in: Advances in Cryptology, CRYPTO’01, No. 2139, Springer-Verlag, Berlin, (2001), pp. 41–62.

6. T. Asano, “A revocation scheme with minimal storage at receivers,” ASIACRYPT’02, No. 2501, Springer-Verlag, Berlin, 433–450 (2002).

7. M. Naor and B. Pincas, “Efficient trace and revoke schemes,” Financial Cryptography’00, No. 1962, Springer-Verlag, Berlin (2000), pp. 1–20.

8. V. Korjik, M. Ivkov, Y. Merinovich, A. Barg, and H. van Tilborg, “A broadcast key distribution scheme based on block designs,” Cryptography and Coding, V, No. 1025, Springer-Verlag, Berlin (1995), pp. 12–21.

9. M. Hall, Combinatorial Theory, John Wiley&Sons, New York (1967).

10. H.J. Ryser, Combinatorial Mathematics, Mathematical Association of America, Washington (1963).

11. D.R. Stinson and T. van Trung, “Some new results on key distribution patterns and broadcast encryption,” Designs, Codes and Cryptography, 15, 261–279 (1998). CrossRef

12. A.N. Alekseichuk and S.N. Konyushok, “Asymptotic relationships for probabilities of the number of non-compromised keys in key distribution schemes based on block codes,” in: Legal, Normative, and Metrological Provision of Information Protection System in Ukraine [in Ukrainian], Issue 8, Kyiv (2004), pp. 85–90.

13. A.N. Alekseichuk and S.N. Konyushok, “Optimal schemes of multicast key distribution based on (v, b, r, λ)-designs,” in: Trans. Intern. Conf. on Optimization of Computations (POO-XXXII) dedicated to the memory of Acad. V. S. Mikhalevich [in Ukrainian], V. M. Glushkov Inst. of Cybernetics, NAS Ukr. (2005), pp. 22–23.

14. F. Delsarte, “An algebraic approach to the association schemes of coding theory,” Philips Res. Reports Suppl., 10, 1–97 (1973).

15. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, New York (1977).

16. A.P. Alfyorov, A.Yu. Zubov, A.S. Kuz’min, and A.V. Cheremushkin, Fundamentals of Cryptography [in Russian], Gelios ARV, Moscow (2001).

17. Yu.L. Vasil’ev, F.Ya. Vetukhnovskii, V.V. Glagolev, et al., Discrete Mathematics and Mathematical Problems of Cybernetics [in Russian], Vol. 1, Nauka, Moscow (1974).

18. V.N. Sachkov, Introduction to Combinatory Methods of Discrete Mathematics [in Russian], Nauka, Moscow (1982).

Cybernetics and Systems Analysis

May 2007, Volume 43, Issue 3, pp 397-406

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 100–111, May–June 2007