Attribute hiding subset predicate encryption: Quantum-resistant construction with efficient decryption

Predicate encryption is well studied due to its flexibility in supporting fine-grained access control. In Katz et al. (2018) proposed a predicate encryption for a new predicate family, called subset predicate encryption. In such a scheme, a ciphertext and a private key are associated with sets. A private key can successfully decrypt a ciphertext if and only if the set for the private key is a subset of the set for the ciphertext. However, we found that, all the existing schemes are not able to hide the sets associated to ciphertexts, i.e., the information of receivers will be revealed. To enhance the privacy for receivers, we proposed the first subset predicate encryption schemes with weakly attribute hiding. Moreover, our first scheme is constructed over lattices, which is believed to be secure against quantum computers. The security of our scheme is formally proven in the standard model under well-studied complexity assumptions.