Graph-Decomposition-Based Frameworks for Subset-Cover Broadcast Encryption and Efficient Instantiations
- 1.8k Downloads
We present generic frameworks for constructing efficient broadcast encryption schemes in the subset-cover paradigm, introduced by Naor et.al., based on various key derivation techniques. Our frameworks characterize any instantiation completely to its underlying graph decompositions, which are purely combinatorial in nature. This abstracts away the security of each instantiated scheme to be guaranteed by the generic one of the frameworks; thus, gives flexibilities in designing schemes. Behind these are new techniques based on (trapdoor) RSA accumulators utilized to obtain practical performances.
We then give some efficient instantiations from the frameworks. Our first construction improves the currently best schemes, including the one proposed by Goodrich et.al., without any further assumptions (only pseudo-random generators are used) by some factors. The second instantiation, which is the most efficient, is instantiated based on RSA and directly improves the first scheme. Its ciphertext length is of order O(r), the key size is O(1), and its computational cost is O(n 1/klog2 n) for any (arbitrary large) constant k; where r and n are the number of revoked users and all users respectively. To the best of our knowledge, this is the first explicit collusion-secure scheme in the literature that achieves both ciphertext size and key size independent of n simultaneously while keeping all other costs efficient, in particular, sub-linear in n. The third scheme improves Gentry and Ramzan’s scheme, which itself is more efficient than the above schemes in the aspect of asymptotic computational cost.
KeywordsBroadcast Encryption Revocation Scheme Subset-cover Optimal Key Storage
- 3.Attrapadung, N., Kobara, K., Imai, H.: Broadcast Encryption with Short Keys and Transmissions. ACM Workshop on Digital Rights Management (2003)Google Scholar
- 5.Benaloh, J., de Mare, M.: One-way accumulators: A decentralized alternative to digital signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1994)Google Scholar
- 7.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) (to appear)Google Scholar
- 8.Chick, G.C., Tavares, S.E.: Flexible Access Control with Master Keys. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 316–322. Springer, Heidelberg (1990)Google Scholar
- 9.Diestel, R.: Graph theory. In: Graduate texts in mathematics, 2nd edn., vol. 173 (2000)Google Scholar
- 12.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)Google Scholar
- 13.Fiat, A., Naor, M.: Broadcast Encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)Google Scholar
- 19.Star, Z.: An Asymptotic Formula in the Theory of Compositions. Aequationes Math (1976)Google Scholar