Hierarchical Key Assignment Schemes can be used to enforce access control policies by cryptographic means. In this paper, we present a new, enhanced security model for such schemes. We also give simple, efficient, and strongly-secure constructions for Hierarchical Key Assignment Schemes for arbitrary hierarchies using pseudorandom functions and forward-secure pseudorandom generators. We compare instantiations of our constructions with state-of-the-art Hierarchical Key Assignment Schemes, demonstrating that our new schemes possess an attractive trade-off between storage requirements and efficiency of key derivation.

Non-interactive key exchange (NIKE) is a fundamental but much-overlooked cryptographic primitive. It appears as a major contribution in the ground-breaking paper of Diffie and Hellman, but NIKE has remained largely unstudied since then. In this paper, we provide different security models for this primitive and explore the relationships between them. We then give constructions for secure NIKE in the Random Oracle Model based on the hardness of factoring and in the standard model based on the hardness of a variant of the decisional Bilinear Diffie Hellman Problem for asymmetric pairings. We also study the relationship between NIKE and public key encryption (PKE), showing that a secure NIKE scheme can be generically converted into an IND-CCA secure PKE scheme. This conversion also illustrates the fundamental nature of NIKE in public key cryptography.

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 BonehFranklin identity-based encryption scheme, the Boneh-Lynn-Shacham signature scheme, and the Sakai-Ohgishi-Kasahara identity-based noninteractive 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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