Paper 2022/806

Multi-key and Multi-input Predicate Encryption from Learning with Errors

Abstract

We put forward two natural generalizations of predicate encryption (PE) dubbed multi-key and multi-input PE. More in details, our contributions are threefold. - Definitions. We formalize security of multi-key PE and multi-input PE following the standard indistinguishability paradigm, and modeling security both against malicious senders (i.e., corruption of encryption keys) and malicious receivers (i.e., collusions). - Constructions. We construct multi-key and multi-input PE supporting the conjunction of poly-many arbitrary single-input predicates, assuming the hardness of the standard learning with errors (LWE) problem. - Applications. We show that multi-key and multi-input PE for expressive enough predicates suffices for interesting cryptographic applications, including matchmaking encryption (ME) and non-interactive multi-party computation (NI-MPC). As a corollary, plugging in our concrete constructions of multi-key and multi-input PE, we obtain the first construction of ME for arbitrary policies, as well as NI-MPC with partial re-usability for all-or-nothing functions and a constant number of parties, under the standard LWE assumption. Prior to our work, all of these applications required much heavier tools such as indistinguishability obfuscation or compact functional encryption.