Thresholdizing lattice based encryption schemes

Abstract

In this thesis, we examine a variety of constructions based on secret sharing techniques applied on lattice-based cryptographic primitives constructed from the learning with erros (LWE) assumption. Using secret sharing techniques from [BGG⁺17], we show how to construct paradigms of threshold multi-key fully homomorphic encryption and predicate encryption. Through multi-key fully homomorphic encryption [MW16] and threshold fully homomorphic encryption, we can construct a low-round multi party computation (MPC) scheme with guaranteed output delivery, assuming honest majority in the semi-honest and malicious settings. Applying the secret sharing scheme on predicate encryption constructions from LWE [GVW15], we can obtain a distributed predicate encryption scheme.