Abstract
In this paper we present a general framework for constructing efficient multicast cryptosystems with provable security and show that a line of previous work on multicast encryption are all special cases of this general approach. We provide new methods for building such cryptosystems with various levels of security (e.g., IND-CPA, IND-CCA2). The results we obtained enable the construction of a whole class of new multicast schemes with guaranteed security using a broader range of common primitives such as OAEP. Moreover, we show that multicast cryptosystems with high level of security (e.g. IND-CCA2) can be based upon public key cryptosystems with weaker (e.g. CPA) security as long as the decryption can be securely and efficiently “shared”. Our constructions feature truly constant-size decryption keys whereas the lengths of both the encryption key and ciphertext are independent of group size.
This work was supported by National Science Foundation award #EIA-0122599 (Title: “ITR/SI: Societal Scale Information Systems: Technologies, Design, and Applications”).
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Fenner, W.: Internet group management protocol, version 2. RFC-2236 (1997)
Harney, H., Muckenhirn, C.: Group key management protocol (gkmp) architecture. IETF Request for Comments, RFC 2094 (1997)
Wallner, D., Harder, E., Agee, R.: Key management for multicast: Issues and architectures. IETF Request For Comments, RFC 2627 (1999)
Wong, C.K., Gouda, M., Lam, S.S.: Secure group communications using key graphs. IEEE/ACM Trans. Netw. 8, 16–30 (2000)
Canetti, R., Garay, J., Itkis, G., Micciancio, D., Naor, M., Pinkas, B.: Multicast security: A taxonomy and some efficient constructions. In: INFOCOMM 1999 (1999)
Chang, I., Engel, R., Kandlur, D., Pendarakis, D., Saha, D.: Key management for secure internet multicast using boolean function minimization techniques. In: Proceedings IEEE Infocomm 1999, vol. 2, pp. 689–698 (1999)
Wong, C.K., Lam, S.S.: Keystone: A group key management service. In: International Conference on Telecommunications, ICT 2000 (2000)
Li, X.S., Yang, Y.R., Gouda, M.G., Lam, S.S.: Batch rekeying for secure group communications. In: Proceedings of the tenth international World Wide Web conference on World Wide Web, Orlando, FL USA, pp. 525–534 (2001)
Setia, S., Koussih, S., Jajodia, S., Harder, E.: A scalable group re-keying approach for secure multicast. In: IEEE Symposium on Security and Privacy, pp. 215–228 (2000)
Yang, Y.R., Li, X.S., Zhang, X.B., Lam, S.S.: Reliable group rekeying: a performance analysis. In: Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications, pp. 27–38. ACM Press, New York (2001)
Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994)
Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)
Boneh, D., Franklin, M.: An efficient public key traitor tracing scheme. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 338–353. Springer, Heidelberg (1999)
Anzai, J., Matsuzaki, N., Matsumoto, T.: A quick group 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)
Luby, M., Staddon, J.: Combinatorial bounds for broadcast encryption. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 512–526. Springer, Heidelberg (1998)
Garay, J.A., Staddon, J., Wool, A.: Long-lived broadcast encryption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 333–352. Springer, Heidelberg (2000)
Naor, M., Pinkas, B.: Efficient trace and revoke schemes. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, p. 1. Springer, Heidelberg (2001)
Halevy, D., Shamir, A.: The LSD broadcast encryption scheme. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 47–60. Springer, Heidelberg (2002)
Naor, D., Naor, M., Lotspiech, J.B.: Revocation and tracing schemes for stateless receivers. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 41–62. Springer, Heidelberg (2001)
Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)
Boneh, D., Gentry, C., Waters, B.: Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 258–275. Springer, Heidelberg (2005)
Tzeng, W.G., Tzeng, Z.J.: A public-key traitor tracing scheme with revocation using dynamic shares. In: Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography, pp. 207–224. Springer, Heidelberg (2001)
Dodis, Y., Fazio, N.: Public key trace and revoke scheme secure against adaptive chosen ciphertext attack. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 100–115. Springer, Heidelberg (2002)
Kim, C.H., Hwang, Y.H., Lee, P.J.: An efficient public key trace and revoke scheme secure against adaptive chosen ciphertext attack. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 359–373. Springer, Heidelberg (2003)
Liu, D., Ning, P., Sun, K.: Efficient self-healing group key distribution with revocation capability. In: Proceedings of the 10th ACM conference on Computer and communication security, pp. 231–240. ACM Press, New York (2003)
Staddon, J., Miner, S., Franklin, M., Balfanz, D., Malkin, M., Dean, D.: Self-healing key distribution with revocation. In: Proceedings of the 2002 IEEE Symposium on Security and Privacy, p. 241. IEEE Computer Society, Los Alamitos (2002)
Wang, H.: Resilient lkh: Secure multicast key distribution schemes. In: Proceedings of the 2003 International Workshop on Advanced Developments in Software and Systems Security, WADIS (2003)
Boyd, C.: Digital multisignatures. Cryptography and Coding, 241–246 (1986)
Desmedt, Y.: Society and group oriented cryptography: A new concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988)
Desmedt, Y.G., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)
De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely. In: Proceedings of the twenty-sixth annual ACM symposium on Theory of computing, pp. 522–533. ACM Press, New York (1994)
Canetti, R., Goldwasser, S.: An efficient threshold public key cryptosystem secure against adaptive chosen ciphertext attack. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 90–106. Springer, Heidelberg (1999)
Abe, M.: Robust distributed multiplication without interaction. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 130–147. Springer, Heidelberg (1999)
Jarecki, S., Lysyanskaya, A.: Adaptively secure threshold cryptography: Introducing concurrency, removing erasures (extended abstract). In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 221–242. Springer, Heidelberg (2000)
Shoup, V., Gennaro, R.: Securing threshold cryptosystems against chosen ciphertext attack. J. Cryptology 15, 75–96 (2002)
Fouque, P.A., Pointcheval, D.: Threshold cryptosystems secure against chosen-ciphertext attacks. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 351–368. Springer, Heidelberg (2001)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 223. Springer, Heidelberg (1999)
RSA Labs: PKCS#1 v2.1: RSA cryptography standard (2002)
Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM conference on Computer and communications security, pp. 62–73. ACM Press, New York (1993)
Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Shoup, V.: OAEP reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001)
Fujisaki, E., Okamoto, T., Pointcheval, D., Stern, J.: RSA-OAEP is secure under the rsa assumption. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 260–274. Springer, Heidelberg (2001)
Lim, C.H., Lee, P.J.: Another method for attaining security against adaptively chosen ciphertext attacks. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 420–434. Springer, Heidelberg (1994)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust and efficient sharing of RSA functions. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 157–172. Springer, Heidelberg (1996)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Proceedings of the twenty-second annual ACM symposium on Theory of computing, pp. 427–437. ACM Press, New York (1990)
Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Duan, Y., Canny, J. (2006). How to Construct Multicast Cryptosystems Provably Secure Against Adaptive Chosen Ciphertext Attack. In: Pointcheval, D. (eds) Topics in Cryptology – CT-RSA 2006. CT-RSA 2006. Lecture Notes in Computer Science, vol 3860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605805_16
Download citation
DOI: https://doi.org/10.1007/11605805_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31033-4
Online ISBN: 978-3-540-32648-9
eBook Packages: Computer ScienceComputer Science (R0)