Abstract
In this paper we propose three public key BE schemes that have efficient complexity measures. The first scheme, called the BE-PI scheme, has O(r) header size, O(1) public keys and O(logN) private keys per user, where r is the number of revoked users. This is the first public key BE scheme that has both public and private keys under O(logN) while the header size is O(r). These complexity measures match those of efficient secret key BE schemes.
Our second scheme, called the PK-SD-PI scheme, has O(r) header size, O(1) public key and O(log2 N) private keys per user. They are the same as those of the SD scheme. Nevertheless, the decryption time is remarkably O(1). This is the first public key BE scheme that has O(1) decryption time while other complexity measures are kept low. The third scheme, called, the PK-LSD-PI scheme, is constructed in the same way, but based on the LSD method. It has O(r/ε) ciphertext size and O(log1 + ε N) private keys per user, where 0 < ε< 1. The decryption time is also O(1).
Our basic schemes are one-way secure against full collusion of revoked users in the random oracle model under the BDH assumption. We can modify our schemes to have indistinguishably security against adaptive chosen ciphertext attacks.
Research supported in part by NSC projects 96-2628-E-009-011-MY3, 96-3114-P-001-002-Y (iCAST), and 96-2219-E-009-013 (TWISC).
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Attrapadung, N., Imai, H.: Graph-decomposition-based frameworks for subset-cover broadcast encryption and efficient instantiations. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 100–120. Springer, Heidelberg (2005)
Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)
Boneh, D., Franklin, M.: An efficient public key traitor tracing scheme. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 338–353. Springer, Heidelberg (1999)
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)
Boneh, D., Waters, B.: A fully collusion resistant broadcast, trace, and revoke system. In: Proceedings of the ACM Conference on Computer and Communications Security - CCS 2006, pp. 211–220. ACM Press, New York (2006)
Dodis, Y., Fazio, N.: Public key broadcast encryption for stateless receivers. In: Feigenbaum, J. (ed.) DRM 2002. LNCS, vol. 2696, pp. 61–80. Springer, Heidelberg (2003)
Dodis, Y., Fazio, N.: Public key broadcast encryption secure against adaptive chosen ciphertext attack. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 100–115. Springer, Heidelberg (2002)
Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)
Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999)
Galindo, D.: Boneh-Franklin identity based encryption revisited. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 791–802. Springer, Heidelberg (2005)
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)
Halevy, D., Shamir, A.: The LSD broadcast encryption scheme. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 47–60. Springer, Heidelberg (2002)
Kurosawa, K., Desmedt, Y.: Optimum traitor tracing and asymmetric schemes. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 145–157. Springer, Heidelberg (1998)
Kurosawa, K., Yoshida, T.: Linear code implies public-key traitor tracing. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 172–187. Springer, Heidelberg (2002)
Lee, J.W., Hwang, Y.H., Lee, P.J.: Efficient public key broadcast encryption using identifier of receivers. In: Chen, K., Deng, R., Lai, X., Zhou, J. (eds.) ISPEC 2006. LNCS, vol. 3903, pp. 153–164. Springer, Heidelberg (2006)
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, pp. 1–20. Springer, Heidelberg (2001)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Tzeng, W.-G., Tzeng, Z.-J.: A public-key traitor tracing scheme with revocation using dynamic shares. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 207–224. Springer, Heidelberg (2001)
Wang, P., Ning, P., Reeves, D.S.: Storage-efficient stateless group key revocation. In: Zhang, K., Zheng, Y. (eds.) ISC 2004. LNCS, vol. 3225, pp. 25–38. Springer, Heidelberg (2004)
Yoo, E.S., Jho, N.-S., Cheon, J.J., Kim, M.-H.: Efficient broadcast encryption using multiple interpolation methods. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 87–103. Springer, Heidelberg (2005)
Yoshida, M., Fujiwara, T.: An efficient traitor tracing scheme for broadcast encryption. In: Proceedings of 2000 IEEE International Symposium on Information Theory, p. 463. IEEE Press, Los Alamitos (2000)
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Liu, YR., Tzeng, WG. (2008). Public Key Broadcast Encryption with Low Number of Keys and Constant Decryption Time. In: Cramer, R. (eds) Public Key Cryptography – PKC 2008. PKC 2008. Lecture Notes in Computer Science, vol 4939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78440-1_22
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