Abstract
We adapt the concept of a programmable hash function (PHF, Crypto 2008) to a setting in which a multilinear map is available. This enables new PHFs with previously unachieved parameters.
To demonstrate their usefulness, we show how our (standard-model) PHFs can replace random oracles in several well-known cryptographic constructions. Namely, we obtain standard-model versions of the Boneh-Franklin identity-based encryption scheme, the Boneh-Lynn-Shacham signature scheme, and the Sakai-Ohgishi-Kasahara identity-based non-interactive key exchange (ID-NIKE) scheme. The ID-NIKE scheme is the first scheme of its kind in the standard model.
Our abstraction also allows to derive hierarchical versions of the above schemes in settings with multilinear maps. This in particular yields simple and efficient hierarchical generalizations of the BF, BLS, and SOK schemes. In the case of hierarchical ID-NIKE, ours is the first such scheme with full security, in either the random oracle model or the standard model.
While our constructions are formulated with respect to a generic multilinear map, we also outline the necessary adaptations required for the recent “noisy” multilinear map candidate due to Garg, Gentry, and Halevi.
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Abdalla, M., Fiore, D., Lyubashevsky, V.: From selective to full security: Semi-generic transformations in the standard model. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 316–333. Springer, Heidelberg (2012)
Blundo, C., Santis, A.D., Herzberg, A., Kutten, S., Vaccaro, U., Yung, M.: Perfectly secure key distribution for dynamic conferences. Inf. Comput. 146(1), 1–23 (1998)
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)
Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, p. 213. Springer, Heidelberg (2001)
Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. Contemporary Mathematics 324, 71–90 (2002)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. J. Cryptology 17(4), 297–319 (2004)
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, pp. 523–552. Springer, Heidelberg (2010)
Çapar, Ç., Goeckel, D., Paterson, K.G., Quaglia, E.A., Towsley, D., Zafer, M.: Signal-flow-based analysis of wireless security protocols. Information and Computation 226, 37–56 (2013)
Cui, Y., Fujisaki, E., Hanaoka, G., Imai, H., Zhang, R.: Formal security treatments for signatures from identity-based encryption. In: Susilo, W., Liu, J.K., Mu, Y. (eds.) ProvSec 2007. LNCS, vol. 4784, pp. 218–227. Springer, Heidelberg (2007)
Dupont, R., Enge, A.: Provably secure non-interactive key distribution based on pairings. Discrete Applied Mathematics 154(2), 270–276 (2006)
Freire, E.S.V., Hofheinz, D., Kiltz, E., Paterson, K.G.: Non-interactive key exchange. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 254–271. Springer, Heidelberg (2013)
Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013), http://eprint.iacr.org/2012/610
Gennaro, R., Halevi, S., Krawczyk, H., Rabin, T., Reidt, S., Wolthusen, S.D.: Strongly-resilient and non-interactive hierarchical key-agreement in MANETs. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 49–65. Springer, Heidelberg (2008)
Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)
Guo, H., Mu, Y., Li, Z., Zhang, X.: An efficient and non-interactive hierarchical key agreement protocol. Computers & Security 30(1), 28–34 (2011)
Hanaoka, G., Matsuda, T., Schuldt, J.C.N.: On the impossibility of constructing efficient key encapsulation and programmable hash functions in prime order groups. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 812–831. Springer, Heidelberg (2012)
Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 21–38. Springer, Heidelberg (2008)
Lysyanskaya, A.: Unique signatures and verifiable random functions from the DH-DDH separation. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 597–612. Springer, Heidelberg (2002)
Paterson, K.G., Srinivasan, S.: On the relations between non-interactive key distribution, identity-based encryption and trapdoor discrete log groups. Des. Codes Cryptography 52(2), 219–241 (2009)
Ramkumar, M., Memon, N., Simha, R.: A hierarchical key pre-distribution scheme. In: 2005 IEEE International Conferenceon on Electro Information Technology (May 2005)
Rückert, M., Schröder, D.: Aggregate and verifiably encrypted signatures from multilinear maps without random oracles. In: Park, J.H., Chen, H.-H., Atiquzzaman, M., Lee, C., Kim, T.-h., Yeo, S.-S. (eds.) ISA 2009. LNCS, vol. 5576, pp. 750–759. Springer, Heidelberg (2009)
Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: SCIS 2000, Okinawa, Japan (January 2000)
Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
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Freire, E.S.V., Hofheinz, D., Paterson, K.G., Striecks, C. (2013). Programmable Hash Functions in the Multilinear Setting. In: Canetti, R., Garay, J.A. (eds) Advances in Cryptology – CRYPTO 2013. CRYPTO 2013. Lecture Notes in Computer Science, vol 8042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40041-4_28
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DOI: https://doi.org/10.1007/978-3-642-40041-4_28
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