Functional Encryption for Pattern Matching with a Hidden String

Abstract

We propose a new functional encryption for pattern matching scheme with a hidden string. In functional encryption for pattern matching (FEPM), access to a message is controlled by its description and a private key that is used to evaluate the description for decryption. In particular, the description with which the ciphertext is associated is an arbitrary string w and the ciphertext can only be decrypted if its description matches the predicate of a private key which is also a string. Therefore, it provides fine-grained access control through pattern matching alone. Unlike related schemes in the literature, our scheme hides the description that the ciphertext is associated with. In many practical scenarios, the description of the ciphertext cannot be public information as an attacker may abuse the message description to identify the data owner or classify the target ciphertext before decrypting it. Moreover, some data owners may not agree to reveal any ciphertext information since it simply gives greater advantage to the adversary. In this paper, we introduce the first FEPM scheme with a hidden string, such that the adversary cannot get any information about the ciphertext from its description. The security of our scheme is formally analyzed. The proposed scheme provides both confidentiality and anonymity while maintaining its expressiveness. We prove these security properties under the interactive general Diffie–Hellman assumption (i-GDH) and a static assumption introduced in this paper.