Functional encryption is an important generalization of several types of encryption such as publickey, identity-based, and attribute-based encryption. Numerous different security definitions for functional encryption have been proposed, most of them being rather complex and involving several algorithms. Many of these definitions differ in details such as which algorithm has oracle access to which oracle, while the consequences of specific choices are often unclear. This spans a large space of possible definitions without a consensus on the adequacy of specific points in this space. What a particular definition means and for which applications it is suitable remains unsettled. To remedy this situation, we propose a novel interpretation of functional encryption, based on the Constructive Cryptography framework, in which a protocol is seen as a construction of an ideal resource with desired properties from a real resource, which is assumed to be available. The resulting ideal resource can then be used as a real resource in other protocols to construct more advanced resources. The real resource we consider here corresponds to a public repository that allows everyone to read its contents. Such repositories are indeed widely available on the internet. Using functional encryption, we construct, as the ideal resource, a repository with fine-grained access control. Based on this constructive viewpoint, we propose a new security definition, called FA-security, for functional encryption by adequately modifying an established definition, and prove the equivalence to our notion of construction. This gives evidence that FA-security is an appropriate definition. We further consider known impossibility results and examine a weaker security definition. We show that this weaker definition, for which secure schemes exist, is sufficient to construct a repository that restricts the number and order of interactions. This makes explicit how such schemes can be used. 1
Abstract: Query algorithms are used to compute Boolean functions. The definition of the function is known, but input is hidden in a black box. The aim is to com-pute the function value using as few queries to the black box as possible. As in other computational models, different kinds of query algorithms are possible: deterministic, probabilistic, as well as nondeterministic. In this paper, we present a new alternative definition of nondeterministic query algorithms and study algorithm complexity in this model. We demonstrate the power of our model with an example of computing the Fano plane Boolean function. We show that for this function the difference between deterministic and nondeterministic query complexity is 7N versus O(3N).
We construct a functional encryption scheme for circuits which simultaneously achieves and improves upon the security of the current best known, and incomparable, constructions from standard assumptions: reusable garbled circuits by Goldwasser, Kalai, Popa, Vaikuntanathan and Zeldovich (STOC 2013) [GKP+13] and predicate encryption for circuits by Gorbunov, Vaikuntanathan and Wee (CRYPTO 2015) [GVW15]. Our scheme is secure based on the learning with errors (LWE) assumption. Our construction implies:
1.
A new construction for reusable garbled circuits that achieves stronger security than the only known prior construction [GKP+13].
2.
A new construction for bounded collusion functional encryption with substantial efficiency benefits: our public parameters and ciphertext size incur an additive growth of
O(Q2), where Q is the number of permissible queries (We note that due to a lower bound [AGVW13], the ciphertext size must necessarily grow with Q). Additionally, the ciphertext of our scheme is succinct, in that it does not depend on the size of the circuit. By contrast, the prior best construction [GKP+13, GVW12] incurred a multiplicative blowup of
O(Q4) in both the public parameters and ciphertext size. However, our scheme is secure in a weaker game than [GVW12].