In this work we introduce the notion of Subset Predicate Encryption, a form of attribute-based encryption (ABE) in which a message is encrypted with respect to a set s' and the resulting ciphertext can be decrypted by a key that is associated with a set s if and only if s ⊆ s'. We formally define our primitive and identify several applications. We also propose two new constructions based on standard assumptions in bilinear groups; the constructions have very efficient decryption algorithms (consisting of one and two pairing computations, respectively) and small keys: in both our schemes, private keys contain only two group elements. We prove selective security of our constructions without random oracles. We demonstrate the usefulness of Subset Predicate Encryption by describing several black-box transformations to more complex primitives, such as identity-based encryption with wildcards and ciphertext-policy ABE for DNF formulas over a small universe of attributes. All of the resulting schemes are as efficient as the base Subset Predicate Encryption scheme in terms of decryption and key generation.
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