MrNISC from LWE with polynomial modulus

Abstract

Introduced by Benhamouda and Lin [TCC'20], a multi-party reusable non-interactive secure computation protocol (mrNISC) consists of a commitment phase and an unbounded number of computation phases. In the commitment phase, a number of parties first commit to their input in a single broadcast round. Later in a computation phase, any subset of the parties can compute a function on their joint input by each sending a single broadcast message.Benhamouda and Lin [TCC'20] constructed the first mrNISC for all functions based on standard hardness assumptions in pairing groups. Soon after their work, two concurrent papers by Benhamouda et al. [EUROCRYPT'21] and Ananth et al. [EUROCRYPT'21] constructed mrNISC for all functions based on the hardness of LWE with super-polynomial modulus-to-noise ratio.In this work we build the first mrNISC for all functions based solely on LWE with polynomial modulus-to-noise ratio. We thus place mrNISC in the same category as public-key encryption and leveled fully homomorphic encryption in terms of the required LWE hardness assumption. We achieve our result by carefully introducing a bootstrapping step in the construction of Benhamouda et al.