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Lecture notes in computer science

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

Danilo Francati, Daniele Friolo, Giulio Malavolta, Daniele Venturi

Published Jan 1, 2023• 23 citations
Publisher
DOI
10.1007/978-3-031-30620-4_19

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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 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-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.
Fully Homomorphic Encryption (FHE) is a powerful encryption system in cloud computing that allows homomorphic computations on encrypted data without decrypting them. Multi-key fully homomorphic encryption (MFHE), as an extension to FHE, allows homomorphic computations on ciphertexts encrypted under different keys. However, most MFHE schemes require a Common Random/Reference String (CRS), while the few that do not are based on the Learning With Errors (LWE) problem, which means that they can only deal with single bit plaintext. Consequently, MFHE schemes based on the Ring Learning With Errors (RLWE) problem are more desirable, as they can handle polynomial plaintext. Requiring the CRS seems to weaken the semantic definition of MFHE, where all users generate their own keys independently. In this paper, we study the RLWE-based MFHE in the CRS model and propose the first RLWE-based MFHE without a CRS. To this end, we remove the CRS by designing a relinearization algorithm without a CRS. Like previous MFHE schemes, our RLWE-based MFHE without CRS has a simple 1-round threshold decryption, which implies a 3-round secure MPC protocol in the plain model from the RLWE assumption.