Abstract
Inner product encryption (IPE) generates a secret key for a predicate vector and encrypts a message under an attribute vector such that recovery of the message from a ciphertext requires the vectors to satisfy a linear relation. In the case of zero IPE (ZIPE), the relation holds if the inner product between the predicate and attribute vectors is zero. Over the years, several ZIPE schemes have been proposed with numerous applications. However, most of the schemes compute inner products for bounded length vectors in the sense that a pre-specified bound on the length of predicate/attribute vectors must be fixed while producing the system parameters. On the other hand, an unbounded ZIPE (UZIPE) provides freedom to select the length of vectors at the time of generating keys or producing ciphertexts. The feature of unboundedness expands the applicability of ZIPE in the scenario where the length of vectors varies or is not known in advance. Achieving UZIPE with short secret keys and ciphertexts is the main goal of this paper. More specifically, we present an efficient UZIPE scheme based on symmetric external Diffie-Hellman assumption (SXDH) in the standard model. Our UZIPE enjoys short secret keys and ciphertexts which reduce storage and communication costs. Moreover, we prove security in the adaptively fully attribute-hiding model meaning that the ciphertexts of our UZIPE hide the payload along with the attribute vector. On the technical side, our work takes inspiration from the unbounded inner product functional encryption (UIPFE) of Tomida and Takashima (ASIACRYPT’18) and modifies their framework to UZIPE with efficiency improvements regarding the sizes of ciphertexts and keys. As UIPFE does not generically imply UZIPE, our scheme goes through several technical modifications in the construction and security analysis over the UIPFE.
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References
Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: 2007 IEEE symposium on security and privacy (SP 2007), pp. 321–334. IEEE (2007)
Boneh, D., Boyen, X.: Secure identity based encryption without random oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_27
Boneh, D., Waters, B.: Conjunctive, subset, and range queries on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 535–554. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_29
Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_9
Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_4
Lewko, A., Waters, B.: Unbounded hibe and attribute-based encryption. Cryptology ePrint Archive, Report 2011/049 (2011). https://eprint.iacr.org/2011/049
Okamoto, T., Takashima, K.: Hierarchical predicate encryption for inner-products. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 214–231. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_13
Okamoto, T., Takashima, K.: Fully secure functional encryption with general relations from the decisional linear assumption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 191–208. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_11
Okamoto, T., Takashima, K.: Adaptively attribute-hiding (hierarchical) inner product encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 591–608. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_35
Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349–366. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_22
Okamoto, T., Takashima, K.: Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption. Des. Codes Cryptogr., 725–771 (2015). https://doi.org/10.1007/s10623-015-0131-1
Okamoto, T., Takashima, K.: Dual pairing vector spaces and their applications. IEICE Trans. Fund. Electron. Commun. Comput. Sci. E98.A(1), 3–15 (2015). https://doi.org/10.1587/transfun.E98.A.3
Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, pp. 195–203 (2007)
Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27
Tomida, J., Takashima, K.: Unbounded inner product functional encryption from bilinear maps. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 609–639. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_21
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Dutta, S., Pal, T., Dutta, R. (2021). Fully Secure Unbounded Zero Inner Product Encryption with Short Ciphertexts and Keys. In: Huang, Q., Yu, Y. (eds) Provable and Practical Security. ProvSec 2021. Lecture Notes in Computer Science(), vol 13059. Springer, Cham. https://doi.org/10.1007/978-3-030-90402-9_13
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