Paper 2018/482

SPDZ2k: Efficient MPC mod 2^k for Dishonest Majority

Ronald Cramer and Ivan Damgård and Daniel Escudero and Peter Scholl and Chaoping Xing

Abstract

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.

Note: Fixed a bug in the batch MAC check protocol, explained in Section 3.4. The online communication is now O(k+s) bits per opening, instead of O(k).