Abstract
We propose a new broadcast encryption scheme based on polynomial interpolations. Our scheme, obtained from the Naor-Pinkas scheme by partitioning the user set and interpolating multiple polynomials, turns out to be better in efficiency than the best known broadcast schemes like the Subset Difference and the Layered Subset Difference methods, which are tree based schemes. More precisely, when r users are revoked among n users, our method requires O(log (n/m)) user keys and O(αr + m) transmission overhead in the worst case, where m is the number of partitions of the user set and can be chosen to optimize its efficiency, and α is a predetermined constant satisfying 1 < α < 2. So, our scheme is always better in the storage than the tree based schemes (whose storage overhead is O(log2 n) or O(log3/2 n)). In the transmission overhead, our scheme beats those schemes except for a very small r/n. The computation cost is worse than the other schemes but is reasonable for systems with moderate computing power. The security proof is given based on the computational Diffie-Hellman problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anzai, J., Matsuzaki, N., Matsumoto, T.: A quick key distribution scheme with “Entity Revocation”. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 333–347. Springer, Heidelberg (1999)
Berkovits, S.: How to Broadcast a secret. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 536–541. Springer, Heidelberg (1991)
Chick, G., Tavares, S.: Flexible access control with master keys. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 316–322. Springer, Heidelberg (1990)
D’Aroco, P., Stinson, D.R.: Fault Tolerant and Distributed Broadcast Encrytion. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 263–280. Springer, Heidelberg (2003)
Fiat, A., Naor, M.: Broadcast Encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)
Goodrich, M.T., Sun, J.Z., Tamassia, R.: Efficient Tree-Based Revocation in Groups of Low-State Devices. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 511–527. Springer, Heidelberg (2004)
Garay, J., Staddon, J., Wool, A.: Long-Lived Broadcast Encryption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 333–352. Springer, Heidelberg (2000)
Halevi, D., Shamir, A.: The LSD Broadcast Encryption Scheme. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 47–60. Springer, Heidelberg (2002)
Kumar, R., Rajagopalan, S., Sahai, A.: Coding Constructions for blacklisting problems without Computational Assumptions. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 609–623. Springer, Heidelberg (1999)
Möller, B.: Algorithms for Multi-exponentiation. In: Vaudenay, S., Youssef, A.M. (eds.) SAC 2001. LNCS, vol. 2259, pp. 165–180. Springer, Heidelberg (2001)
Naor, D., Naor, M., Lotspiech, J.: Revocation and Tracing Schemes for Stateless Receivers. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 41–62. Springer, Heidelberg (2001)
Naor, M., Pinkas, B.: Efficient trace and revoke schemes. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, p. 1. Springer, Heidelberg (2001)
Wong, C.K., Gouda, M., Lam, S.S.: Secure Group Communication using Key Graphs. In: ACM SIGGCOM 1998. ACM, New York (1998)
Luby, M., Staddon, J.: Combinatorial Bounds for Broadcast Encryption. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 512–526. Springer, Heidelberg (1998)
Shamir, A.: How to Share a Secret. Comm. ACM 22, 612–613
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yoo, E.S., Jho, NS., Cheon, J.H., Kim, MH. (2005). Efficient Broadcast Encryption Using Multiple Interpolation Methods. In: Park, Cs., Chee, S. (eds) Information Security and Cryptology – ICISC 2004. ICISC 2004. Lecture Notes in Computer Science, vol 3506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496618_8
Download citation
DOI: https://doi.org/10.1007/11496618_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26226-8
Online ISBN: 978-3-540-32083-8
eBook Packages: Computer ScienceComputer Science (R0)