Abstract
Quantum computer is regarded as a threat to the cryptosystem at present. Lattice with a rich mathematics structure gave a choice for building post-quantum secure hierarchical identity-based encryption (HIBE) system. But in the existing works, there are many shortcomings such as large public/private key space and weak security model. To overcome these shortcomings, a method for delegating a short lattice basis is discussed in this paper. It maintains the lattice dimension is constant. This distinct feature is used to construct the secure HIBE. The issued scheme has many advantages over the available, such as short public/private keys, achieving adaptive security. It is fair that our scheme is the first one which achieves both constant size private key space and adaptive security. In addition, we also convert our scheme from an one-bit version to an N-bit version. Based learning with errors (LWE) problem, we prove the security in the standard model.
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References
Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1–9. Springer, Heidelberg (1999). doi:10.1007/3-540-48523-6_1
Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions from worst-case complexity assumptions. In: Proceedings of the 43rd Symposium on Foundations of Computer Science (FOCS), pp. 356–365. IEEE press, New York (2002). doi:10.1007/s00037-007-0234-9
Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing(STOC 2009), pp. 333–342. ACM, New York (2009). doi:10.1145/1536414.1536461
Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: a ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267–288. Springer, Heidelberg (1998). doi:10.1007/BFb0054868
Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13190-5_28
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing (STOC), pp. 187–196. ACM, New York (2008). doi:10.1145/1374376.1374406
Waters, B.: Functional encryption for regular languages. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 218–235. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32009-5_14
Boyen, X.: Attribute-based functional encryption on lattices. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 122–142. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36594-2_8
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing (STOC), pp. 169–178. ACM, New York (2009). doi:10.1145/1536414.1536440
Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) Advances in Cryptology-CRYPTO 2010. LNCS, vol. 6223, pp. 98–115. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14623-7-6
Singh, K., Rangan, C.P., Banerjee, A.K.: Efficient lattice HIBE in the standard model with shorter public parameters. In: Linawati, Mahendra, M.S., Neuhold, E.J., Tjoa, A.M., You, I. (eds.) Information and Communication Technology, ICT-EurAsia 2014. LNCS, vol. 8407. Springer, Heidelberg (2014). doi:10.1007/978-3-642-55032-4-56
Agrawal, S., Boyen, X., Vaikunthanathan, V., Voulgaris, P., Wee, H.: Functional encryption for threshold functions (or, fuzzy IBE) from lattices. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) CPKC 2012. LNCS, vol. 7293, pp. 280–297. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30057-8-17
Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011, vol. 6841, pp. 505–524. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22792-9-29
Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002). doi:10.1007/3-540-36178-2_34
Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004). doi:10.1007/978-3-540-24676-3_14
Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005). doi:10.1007/11426639_26
Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03356-8_36
Zhang, L.Y., Wu, Q., Hu, Y.: Hierarchical identity-based encryption with constant size ciphertexts. ETRI J. 34(1), 142–145 (2012). doi:10.4218/etrij.12.0211.0140
Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). doi:10.1007/3-540-39568-7_5
Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). doi:10.1007/3-540-44647-8_13
Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees or, how to delegate a lattice basis. J. Cryptol. 25(4), 601–639 (2012). doi:10.1007/s00145-011-9105-2
Singh, K., Pandurangan, C., Banerjee, A.K.: Adaptively secure efficient lattice (H)IBE in standard model with short public parameters. In: Bogdanov, A., Sanadhya, S. (eds.) SPACE 2012. LNCS, pp. 153–172. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34416-9_11
Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). doi:10.1007/11426639_7
Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: A Cryptographic Perspective, vol. 671. Kluwer Academic Publishers, Boston (2002)
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. In: Proceedings of FOCS 2004, pp. 372–381. IEEE press, New York (2004). doi:10.1109/FOCS.2004.72
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 84–93. ACM, New York (2005). doi:10.1145/1060590.1060603
Peikert, C.: Bonsai trees (or, arboriculture in lattice-based cryptography). Cryptology ePrint Archive, Report 2009/359 (2009). http://eprint.iacr.org/
Acknowledgments
This work was supported in part by the Nature Science Foundation of China under Grant (61472307, 61402112, 61100165, 61100231), Natural Science Basic Research Plan in Shaanxi Province of China (Program NO. 2016JM6004).
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Zhang, L., Wu, Q. (2017). Adaptively Secure Hierarchical Identity-Based Encryption over Lattice. In: Yan, Z., Molva, R., Mazurczyk, W., Kantola, R. (eds) Network and System Security. NSS 2017. Lecture Notes in Computer Science(), vol 10394. Springer, Cham. https://doi.org/10.1007/978-3-319-64701-2_4
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