Private Predicate Encryption for Inner Product from Key-Homomorphic Pseudorandom Function

Predicate encryption (PE), formalized by Katz et al., is a new paradigm of public-key encryption that conceptually captures the public-key encryption that supports fine-grained access control policy. Because of the nature of PE, it is used for cloud storage so that users can retrieve encrypted data without revealing any information about the data to cloud servers and other users. Although lots of PE schemes have been studied, the predicate-hiding security is seldom considered; that is, the user’s secret key may leak sensitive information of the predicate. Additionally, the security of the current predicate-hiding PE schemes relies on the discrete logarithm assumption which cannot resist the quantum attacks in the future. In this paper, we propose a generic PE for inner product under symmetric-key setting, called private IPE, from specific key-homomorphic pseudorandom function (PRF). The rigorous proofs are provided to show that the construction is payload-hiding, attribute-hiding, and predicate-hiding secure. With the advantage of the generic construction, if the underlying PRF can resist quantum attacks, then, through our proposed generic construction, a quantum-resistant private IPE can be obtained.