Minimising communication in honest-majority MPC by batchwise multiplication verification

Abstract

In this paper, we present two new and very communication-efficient protocols for maliciously secure multi-party computation over fields in the honest-majority setting with abort. Our first protocol improves a recent protocol by Lindell and Nof. Using the so far overlooked tool of batchwise multiplication verification, we speed up their technique for checking correctness of multiplications (with some other improvements), reducing communication by 2 × to 7 ×. In particular, in the 3PC setting, each party sends only two field elements per multiplication. We also show how to achieve fairness, which Lindell and Nof left as an open problem. Our second protocol again applies batchwise multiplication verification, this time to perform 3PC by letting two parties perform the SPDZ protocol using triples generated by a third party and verified batchwise. In this protocol, each party sends only 4/3 field elements during the online phase and 5/3 field elements during the preprocessing phase.