Multi-key and Multi-input Predicate Encryption (for Conjunctions) from Learning with Errors

We put forward two natural generalizations of predicate encryption (PE), dubbed multi-key and multi-input PE. More in details, our contributions are threefold. In particular, plugging in our constructions of multi-key and multi-input PE, under the sub-exponential LWE assumption, we obtain the first ME supporting arbitrary policies with unbounded collusions, as well as robust (resp. non-robust) NI-MPC for so-called all-or-nothing functions satisfying a non-trivial notion of reusability and supporting a constant (resp. polynomial) number of parties. Prior to our work, both of these applications required much heavier tools such as indistinguishability obfuscation or compact functional encryption.