Abstract
In a recent work, Katz et al. (CANS’17) generalized the notion of Broadcast Encryption to define Subset Predicate Encryption (SPE) that emulates subset containment predicate in the encrypted domain. They proposed two selective secure constructions of SPE in the small universe settings. Their first construction is based on q-type assumption while the second one is based on DBDH. Both achieve constant size secret key while the ciphertext size depends on the size of the privileged set. They also showed some black-box transformation of SPE to well-known primitives like WIBE and ABE to establish the richness of the SPE structure.
This work investigates the question of large universe realization of SPE scheme based on static assumption without random oracle. We propose two constructions both of which achieve constant size secret key. First construction \(\mathsf {SPE}_1\), instantiated in composite order bilinear groups, achieves constant size ciphertext and is proven secure in a restricted version of selective security model under the subgroup decision assumption (SDP). Our main construction \(\mathsf {SPE}_2\) is adaptive secure in the prime order bilinear group under the symmetric external Diffie-Hellman assumption (SXDH). Thus \(\mathsf {SPE}_2\) is the first large universe instantiation of SPE to achieve adaptive security without random oracle. Both our constructions have efficient decryption function suggesting their practical applicability. Thus the primitives like WIBE and ABE resulting through black-box transformation of our constructions become more practical.
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References
Abdalla, M., Catalano, D., Dent, A.W., Malone-Lee, J., Neven, G., Smart, N.P.: Identity-based encryption gone wild. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 300–311. Springer, Heidelberg (2006). https://doi.org/10.1007/11787006_26
Abdalla, M., Kiltz, E., Neven, G.: Generalized key delegation for hierarchical identity-based encryption. In: Biskup, J., López, J. (eds.) ESORICS 2007. LNCS, vol. 4734, pp. 139–154. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74835-9_10
Attrapadung, N.: Dual system encryption via doubly selective security: framework, fully secure functional encryption for regular languages, and more. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 557–577. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_31
Attrapadung, N.: Dual system encryption framework in prime-order groups. In: IACR Cryptology ePrint Archive 2015, 390 (2015)
Attrapadung, N., Libert, B.: Functional encryption for inner product: achieving constant-size ciphertexts with adaptive security or support for negation. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 384–402. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_23
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). https://doi.org/10.1007/978-3-540-24676-3_14
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., 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). https://doi.org/10.1007/11535218_16
Boyen, X.: General Ad Hoc encryption from exponent inversion IBE. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 394–411. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_23
Chase, M., Meiklejohn, S.: Déjà Q: using dual systems to revisit q-type assumptions. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 622–639. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_34
Chatterjee, S., Mukherjee, S.: Large universe subset predicate encryption based on static assumption (without random oracle). Cryptology ePrint Archive, Report 2018/1190 (2018). https://eprint.iacr.org/2018/1190
Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_20
Chen, J., Gong, J.: ABE with tag made easy. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 35–65. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_2
Delerablée, C.: Identity-based broadcast encryption with constant size ciphertexts and private keys. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 200–215. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_12
Delerablée, C., Paillier, P., Pointcheval, D.: Fully collusion secure dynamic broadcast encryption with constant-size ciphertexts or decryption keys. In: Takagi, T., Okamoto, E., Okamoto, T., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 39–59. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73489-5_4
Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008). Applications of Algebra to Cryptography
Gong, J., Libert, B., Ramanna, S.C.: Compact IBBE and Fuzzy IBE from simple assumptions. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 563–582. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_30
Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM CCS, pp. 89–98 (2006)
Jutla, C.S., Roy, A.: Shorter quasi-adaptive NIZK proofs for linear subspaces. J. Cryptol. 30(4), 1116–1156 (2017)
Katz, J., Maffei, M., Malavolta, G., Schröder, D.: Subset predicate encryption and its applications. In: Capkun, S., Chow, S.S.M. (eds.) CANS 2017. LNCS, vol. 11261, pp. 115–134. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-02641-7_6
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
Ramanna, S.C., Sarkar, P.: Efficient adaptively secure IBBE from the SXDH assumption. IEEE IT 62(10), 5709–5726 (2016)
Waters, B.: Efficient identity-based encryption without random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_7
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). https://doi.org/10.1007/978-3-642-03356-8_36
Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_26
Wee, H.: Déjà Q: Encore! un petit IBE. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 237–258. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49099-0_9
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Chatterjee, S., Mukherjee, S. (2019). Large Universe Subset Predicate Encryption Based on Static Assumption (Without Random Oracle). In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_4
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