Abstract
This paper proposes a broadcast encryption scheme with traitor tracing based on the ternary tree structure. The subset difference method with ternary tree reduces the communication cost and tracing cost of the original method with the binary tree. However, straightforward expansion of the method ends in failure due to the vulnerability to coalition attacks. Thus, we design a new cover-finding algorithm and label assignment algorithm in order to achieve a coalition-resistant revocation and tracing schemes. Our analysis on efficiency and security shows that our scheme is an improvement of the existing broadcast encryption schemes: complete subtree and subset difference methods.
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References
Berkovits, S.: How to Broadcast a Secret. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 535–541. Springer, Heidelberg (1991)
Fiat, A., Naor, M.: Broadcast Encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)
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), eprint.iacr.org/2001/059
Halevy, D., Shamir, A.: The LSD Broadcast Encryption Scheme. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 47–161. Springer, Heidelberg (2002)
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)
Jho, N.S., Hwang, J.Y., Cheon, J.H., Kim, M.H., Lee, D.H., Yoo, E.S.: One-Way Chain Based Broadcast Encryption Schemes. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 559–574. Springer, Heidelberg (2005)
Hwang, J.Y., Lee, D.H., Lim, J.: Generic Transformation for Scalable Broadcast Encryption Schemes. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 276–292. Springer, Heidelberg (2005)
Attrapadung, N., Imai, H.: Practical broadcast encryption from graph-theoretic techniques and subset-incremental-chain structure. IEICE Transaction on Fundamental of Electronics, Communications and Computer Sciences, Special Section on Cryptography and Information Security E90-A, 187–203 (2007)
Asano, T.: A Revocation Scheme with Minimal Storage at Receivers. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 433–450. Springer, Heidelberg (2002)
Attrapadung, N., Kobara, K., Imai, H.: Sequential Key Derivation Patterns for Broadcast Encryption and Key Predistribution Schemes. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 374–391. Springer, Heidelberg (2003)
Gentry, C., Ramzan, Z.: RSA Accumulator Based Broadcast Encryption. In: Zhang, K., Zheng, Y. (eds.) ISC 2004. LNCS, vol. 3225, pp. 73–86. Springer, Heidelberg (2004)
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)
Wang, W., Ma, J., Moon, S.: Ternary Tree Based Group Key Management in Dynamic Peer Networks. In: Wang, Y., Cheung, Y.-M., Liu, H. (eds.) CIS 2006. LNCS (LNAI), vol. 4456, pp. 513–522. Springer, Heidelberg (2007)
Graham, R.L., Li, M., Yao, F.F.: Optimal tree structures for group key management with batch updates. SIAM J. on Discrete Mathematics 21, 532–547 (2007)
Tripathi, S., Biswas, G.P.: Design of efficient ternary-tree based group key agreement protocol for dynamic groups. In: Proc. of First International Conference on Communication Systems and Networks, COMSNET 2009 (2009)
Fukushima, K., Kiyomoto, S., Tanaka, T., Sakurai, K.: Ternary Subset Difference Method and Its Quantitative Analysis. In: Chung, K.-I., Sohn, K., Yung, M. (eds.) WISA 2008. LNCS, vol. 5379, pp. 225–239. Springer, Heidelberg (2009)
Fukushima, K., Kiyomoto, S., Miyake, Y., Sakurai, K.: Towards optimal revocation and tracing schemes — the power of the ternary tree —. In: Proc. of International Conference on Security and Cryptography (SECRYPT 2011), pp. 37–49 (2011)
Chor, B., Fiat, A., Naor, M.: Tracing Traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994)
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)
Boneh, D., Franklin, M.: An Efficient Public Key Traitor Scheme (Extended Abstract). In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 338–353. Springer, Heidelberg (1999)
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)
Chabanne, H., Phan, D.H., Pointcheval, D.: Public Traceability in Traitor Tracing Schemes. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 542–558. Springer, Heidelberg (2005)
Boneh, D., Sahai, A., Waters, B.: Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 573–592. Springer, Heidelberg (2006)
Shin, S., Kobara, K., Imai, H.: A secure network storage system with information privacy. In: Proc. of Western European Workshop on Research in Cryptology (WEWoRC 2005). LNI, vol. P-74, pp. 22–31 (2005)
Okuaki, S., Kunihiro, N., Ohta, K.: Estimation of a message length for subset difference method. In: Proc. of Symposium on Cryptography and Information Security (SCIS 2008), vol. 2E1-2 (2008) (in Japanese)
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Fukushima, K., Kiyomoto, S., Miyake, Y., Sakurai, K. (2012). Revocation and Tracing Based on Ternary Tree: Towards Optimal Broadcast Encryption Scheme. In: Obaidat, M.S., Sevillano, J.L., Filipe, J. (eds) E-Business and Telecommunications. ICETE 2011. Communications in Computer and Information Science, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35755-8_17
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DOI: https://doi.org/10.1007/978-3-642-35755-8_17
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