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

Abstract

We put forward two natural generalizations of predicate encryption (PE), dubbed multikey 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 adaptively secure multi-key and multi-input PE supporting the conjunction of poly-many arbitrary single-input predicates, assuming the

sub-exponential hardness of the 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 non-interactive

multi-party computation (NI-MPC) and matchmaking encryption (ME).

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-ornothing 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.