SPDZ_{2^k}: Efficient MPC mod 2^k for dishonest majority

Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime. In the more natural setting of integer computations modulo 2^k, which are useful for simplifying implementations and applications, no solutions with active security are known unless the majority of the participants are honest.

We present a new scheme for information-theoretic MACs that are homomorphic modulo 2^k, and are as efficient as the well-known standard solutions that are homomorphic over fields. We apply this to construct an MPC protocol for dishonest majority in the preprocessing model that has efficiency comparable to the well-known SPDZ protocol (Damgård et al., CRYPTO 2012), with operations modulo 2^k instead of over a field. We also construct a matching preprocessing protocol based on oblivious transfer, which is in the style of the MASCOT protocol (Keller et al., CCS 2016) and almost as efficient.