Attribute-Based Encryption for Circuits

In an attribute -based encryption (ABE) scheme, a, ciphertext is associated with an f-bit public index inci and a message en, and a secret key is associated with a Boolean predicate P. The secret key allows to decrypt the ciphertext and -lean' in. iff P(ind) = 1. Moreover, the scheme should be secure against collusions of users, namely, given secret keys for polynomially many predicates, an adversary learns nothing about the message if none of the secret keys can individually decrypt the ciphertext. We present attribute-based encryption schemes for circuits of any arbitrary polynomial size, where the public parameters and the ciphertext grow linearly with the depth of the circuit. Our construction is secure under the standard learning with errors (LWE) assumption. Previous constructions of attribute-based encryption were for Boolean formulas, captured by the complexity class NC'. In the course of our construction, we present a new framework for constructing ABE schemes. As a by-product of our framework, we obtain ABE schemes for polynomialsize branching programs, corresponding to the complexity class L00,9PACE, under quantitatively better assumptions.