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 (Damgard 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.