Duality in ABE: Converting Attribute Based Encryption for Dual Predicate and Dual Policy via Computational Encodings

摘要

We show a generic conversion that converts an attribute based encryption (ABE) scheme for arbitrary predicate into an ABE scheme for its dual predicate. In particular, it can convert key-policy ABE (KP-ABE) into ciphertext-policy ABE (CP-ABE), and vice versa, for dually related predicates. It is generic in the sense that it can be applied to arbitrary predicates. On the other hand, it works only within the generic ABE framework recently proposed by Attrapadung (Euro-crypt'14), which provides a generic compiler that compiles a simple primitive called pair encodings into fully secure ABE. Inside this framework, Attrapadung proposed the first generic dual conversion that works only for subclass of encodings, namely, perfectly secure encodings. However, there are many predicates for which realizations of such encodings are not known, and hence the problems of constructing fully secure ABE for their dual predicates were left unsolved. In this paper, we revisit the dual conversion of Attrapadung, and show that, somewhat surprisingly, the very same conversion indeed also works for broader classes of encodings, namely, computationally secure encodings. Consequently, we thus solve the above open problems as we obtain the first fully secure realizations of completely-unbounded CP-ABE and CP-ABE with short keys for Boolean formulae, via applying the conversion to previously proposed KP-ABE. Moreover, we provide a generic conversion that converts ABE into its dual-policy variant. Dual-policy ABE (DP-ABE) conjunctively combines both KP-ABE and CP-ABE into one primitive, and hence can be useful in general-purpose applications. As for instantiations, we obtain the first realizations of fully secure DP-ABE for formulae, unbounded DP-ABE for formulae, and DP-ABE for regular languages. The latter two systems are the first to realize such functionalities, let alone are fully secure.