We give a construction of mrNISC that achieves standard simulation security, as classical multi-round MPC protocols achieve. Our construction relies on the Learning With Errors (LWE) assumption with polynomial modulus, and on the existence of a pseudorandom function (PRF) in $\mathsf{NC}^1$. We achieve semi-malicious security in the plain model and malicious security by further relying on trusted setup (which is unavoidable for mrNISC). In comparison, the only previously known constructions of mrNISC were either using bilinear maps or using strong primitives such as program obfuscation.
We use our mrNISC to obtain new Multi-Key FHE (MKFHE) schemes with threshold decryption:
$\bullet$ In the CRS model, we obtain threshold MKFHE for $\mathsf{NC}^1$ based on LWE with only $\textit{polynomial}$ modulus and PRFs in $\mathsf{NC}^1$, whereas all previous constructions rely on LWE with super-polynomial modulus-to-noise ratio.
$\bullet$ In the plain model, we obtain threshold levelled MKFHE for $\mathsf{P}$ based on LWE with $\textit{polynomial}$ modulus, PRF in $\mathsf{NC}^1$, and NTRU, and another scheme for constant number of parties from LWE with sub-exponential modulus-to-noise ratio. The only known prior construction of threshold MKFHE (Ananth et al., TCC 2020) in the plain model restricts the set of parties who can compute together at the onset.
Category / Keywords: foundations / Multiparty computation, non-interactive secure computation, LWE Original Publication (with major differences): IACR-EUROCRYPT-2021 Date: received 21 Mar 2021, last revised 21 Mar 2021 Contact author: fabrice benhamouda at gmail com,aayushjain@cs ucla edu,ilank@cs huji ac il,rachel@cs washington edu Available format(s): PDF | BibTeX Citation Version: 20210322:193903 (All versions of this report) Short URL: ia.cr/2021/378