How to Construct Multicast Cryptosystems Provably Secure Against Adaptive Chosen Ciphertext Attack

  • Yitao Duan
  • John Canny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3860)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fenner, W.: Internet group management protocol, version 2. RFC-2236 (1997)Google Scholar
  2. 2.
    Harney, H., Muckenhirn, C.: Group key management protocol (gkmp) architecture. IETF Request for Comments, RFC 2094 (1997)Google Scholar
  3. 3.
    Wallner, D., Harder, E., Agee, R.: Key management for multicast: Issues and architectures. IETF Request For Comments, RFC 2627 (1999)Google Scholar
  4. 4.
    Wong, C.K., Gouda, M., Lam, S.S.: Secure group communications using key graphs. IEEE/ACM Trans. Netw. 8, 16–30 (2000)CrossRefGoogle Scholar
  5. 5.
    Canetti, R., Garay, J., Itkis, G., Micciancio, D., Naor, M., Pinkas, B.: Multicast security: A taxonomy and some efficient constructions. In: INFOCOMM 1999 (1999)Google Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Wong, C.K., Lam, S.S.: Keystone: A group key management service. In: International Conference on Telecommunications, ICT 2000 (2000)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994)Google Scholar
  12. 12.
    Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)Google Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Luby, M., Staddon, J.: Combinatorial bounds for broadcast encryption. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 512–526. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Naor, M., Pinkas, B.: Efficient trace and revoke schemes. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, p. 1. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Halevy, D., Shamir, A.: The LSD broadcast encryption scheme. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 47–60. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    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)Google Scholar
  21. 21.
    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)Google Scholar
  22. 22.
    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)Google Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    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)Google Scholar
  28. 28.
    Boyd, C.: Digital multisignatures. Cryptography and Coding, 241–246 (1986)Google Scholar
  29. 29.
    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)Google Scholar
  30. 30.
    Desmedt, Y.G., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)Google Scholar
  31. 31.
    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)CrossRefGoogle Scholar
  32. 32.
    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)Google Scholar
  33. 33.
    Abe, M.: Robust distributed multiplication without interaction. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 130–147. Springer, Heidelberg (1999)Google Scholar
  34. 34.
    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)CrossRefGoogle Scholar
  35. 35.
    Shoup, V., Gennaro, R.: Securing threshold cryptosystems against chosen ciphertext attack. J. Cryptology 15, 75–96 (2002)MATHMathSciNetGoogle Scholar
  36. 36.
    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)CrossRefGoogle Scholar
  37. 37.
    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)Google Scholar
  38. 38.
    RSA Labs: PKCS#1 v2.1: RSA cryptography standard (2002)Google Scholar
  39. 39.
    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)CrossRefGoogle Scholar
  40. 40.
    Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  41. 41.
    Shoup, V.: OAEP reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    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)Google Scholar
  44. 44.
    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)Google Scholar
  45. 45.
    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)CrossRefGoogle Scholar
  46. 46.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yitao Duan
    • 1
  • John Canny
    • 1
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

Personalised recommendations