Abstract
In order to increase security of identity-based encryption (IBE) scheme in the standard model from lattice, and reduce the size of master public key, we propose a new lattice-based IBE scheme. This scheme mainly uses the identity-based lossy trapdoor function to generate trapdoor, and get the master public key, master private key and ciphertext from programmable hash function. Comparative analysis shows that, compared to MP12 trapdoor delegation algorithm, identity-based lossy trapdoor function is directly related to user’s identity, at the same time the trapdoor is lossy, each different identity corresponds to a different trapdoor, it is impossible to distinguish that the master public key whether is lossy or injective for the adversary, so that the adversary is unable to obtain complete information about how to construct the trapdoor functions, this feature makes the trapdoor function more secure than other trapdoor functions. In addition, the size of master public of previous scheme is \( {\rm O}\left( n \right) \) (\( n \) denotes the length of the user’s identity), using programmable hash function constructs master public key of our scheme, so that our scheme master public key size is reduced to \( {\rm O}\left( {\log n} \right) \), the size of the master public key of our scheme is reduced and the efficiency of our scheme is improved. Finally, we can prove our scheme is indistinguishability from random under adaptive chosen ciphertext and chosen-identity attacks (INDr-ID-CCA) secure based on learning with error hard problem in the standard model.
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References
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). https://doi.org/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). https://doi.org/10.1007/3-540-44647-8_13
Boneh, D., Raghunathan, A., Segev, G.: Function-private identity-based encryption: hiding the function in functional encryption. In: Canetti, R., Garay, Juan A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 461–478. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_26
Tessaro, S., Wilson, D.A.: Bounded-collusion identity-based encryption from semantically-secure public-key encryption: generic constructions with short ciphertexts. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 257–274. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_15
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008 Proceedings of the Fortieth Annual ACM Symposium on Theory of computing, pp. 197–206. ACM, New York (2008)
Zhandry, M.: Secure identity-based encryption in the quantum random oracle model. Int. J. Quantum Inf. 13(04), 1484–1510 (2015)
Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_27
Agrawal, S., Boyen, X.: Identity-based encryption from lattices in the standard model. Manuscript (2009)
Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. J. Cryptol. 25(3), 484–527 (2012)
Hofheinz, D., Jager, T., Kiltz, E.: Short signatures from weaker assumptions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 647–666. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_35
Zhang, J., Chen, Yu., Zhang, Z.: Programmable hash functions from lattices: short signatures and IBEs with small key sizes. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 303–332. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_11
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC 2008 Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 187–196. ACM, New York (2008)
Bellare, M., Kiltz, E., Peikert, C., Waters, B.: Identity-based (lossy) trapdoor functions and applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 228–245. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_15
Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_41
Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656. Springer, Heidelberg (2014). https://doi.org/10.1007/3-540-39200-9_16
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). https://doi.org/10.1007/978-3-642-13190-5_28
Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98–115. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_6
Acknowledgements
This work is supported by “13th Five-Year” National Crypto Development Fund under Grant (No. MMJJ20170122), the Project of Education Department of Henan Province (No. 18A413001, No. 16A520013), Natural Science Foundation of Henan Polytechnic University (No. T2018-1).
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Tang, Y., Wang, M., Zhao, Z., Ye, Q. (2018). Adaptively Chosen Ciphertext Secure Lattice IBE Based Programmable Hash Function in the Standard Model. In: Sun, X., Pan, Z., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2018. Lecture Notes in Computer Science(), vol 11065. Springer, Cham. https://doi.org/10.1007/978-3-030-00012-7_43
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