Feel the Quantum Functioning: Instantiating Generic Multi-Input Functional Encryption from Learning with Errors (extended version)

Functional Encryption (FE) allows users who hold a specific decryption key, to learn a specific function of encrypted data while the actual plaintexts remain private. While FE is still in its infancy, it is our strong belief that in the years to come, this remarkable cryptographic primitive will have matured to the degree that will make it an integral part of access control systems, especially cloud-based ones. To this end, we believe it is of great importance to provide not only theoretical and generic constructions but also concrete instantiations of FE schemes from well-studied cryptographic assumptions. Therefore, in this paper, we undertake the task of presenting two instantiations of the generic work presented in [8] from the Decisional Diffie-Hellman (DDH) problem that also satisfies the property of verifiable decryption. Moreover, we present a novel multi-input FE (MIFE) scheme, that can be instantiated from Regev's cryptosystem, and thus remains secure even against quantum adversaries. Finally, we provide a multi-party computation (MPC) protocol that allows our MIFE construction to be deployed in the multi-client mode