More efficient constant-round multi-party computation from BMR and SHE


We present a multi-party computation protocol in the case of dishonest majority which has very low round complexity. Our protocol sits philosophically between Gentrys Fully Homomorphic Encryption based protocol and the SPDZ-BMR protocol of Lindell et al (CRYPTO 2015). Our protocol avoids various inefficiencies of the previous two protocols. Compared to Gentrys protocol we only require Somewhat Homomorphic Encryption (SHE). Whilst in comparison to the SPDZ-BMR protocol we require only a quadratic complexity in the number of players (as opposed to cubic), we have fewer rounds, and we require less proofs of correctness of ciphertexts. Additionally, we present a variant of our protocol which trades the depth of the garbling circuit (computed using SHE) for some more multiplications in the offline and online phases.

Theory of Cryptography Conference 2016-B