International Association
for Cryptologic Research

In recent years, actively secure SPDZ-like protocols for dishonest majority, like SPD$\mathbb Z_{2^k}$, Overdrive2k, and MHz2k, over base rings $\mathbb Z_{2^k}$ have become more and more efficient. In this paper, we present a new actively secure MPC protocol Multipars that outperforms these state-of-the-art protocols over $\mathbb Z_{2^k}$ by more than a factor of 2 in the two-party setup in terms of communication. Multipars is the first actively secure N-party protocol over $\mathbb Z_{2^k}$ that is based on linear homomorphic encryption (LHE) in the offline phase (instead of oblivious transfer or somewhat homomorphic encryption in previous works). The strong performance of Multipars relies on a new adaptive packing for BGV ciphertexts that allows us to reduce the parameter size of the encryption scheme and the overall communication cost. Additionally, we use modulus switching for further size reduction, a new type of enhanced CPA security over $\mathbb Z_{2^k}$, a truncation protocol for Beaver triples, and a new LHE-based offline protocol without sacrificing over $\mathbb Z_{2^k}$.

We have implemented Multipars and therewith provide the fastest preprocessing phase over $\mathbb Z_{2^k}$. Our evaluation shows that Multipars offers at least a factor of 8 lower communication costs and up to a factor of 15 faster runtime in the WAN setting compared to the currently best available actively secure MPC implementation over $\mathbb Z_{2^k}$.