Practical Covertly Secure MPC for Dishonest Majority – or: Breaking the SPDZ Limits

Abstract. SPDZ (pronounced “Speedz”) is the nickname of the MPC protocol of Damgard et al. from Crypto 2012. ˚

SPDZ provided various efficiency innovations on both the theoretical and practical sides compared to previous work in the preprocessing model. In this paper we both resolve a number of open problems with SPDZ; and present several theoretical and practical improvements to the protocol. In detail, we start by designing and implementing a covertly secure key generation protocol for obtaining a BGV public key and a shared associated secret key. In prior work this was assumed to be provided by a given setup functionality. Protocols for generating such shared BGV secret keys are likely to be of wider applicability than to the SPDZ protocol alone. We then construct both a covertly and actively secure preprocessing phase, both of which compare favourably with previous work in terms of efficiency and provable security. We also build a new online phase, which solves a major problem of the SPDZ protocol: namely prior to this work preprocessed data could be used for only one function evaluation and then had to be recomputed from scratch for the next evaluation, while our online phase can support reactive functionalities. This improvement comes mainly from the fact that our construction does not require players to reveal the MAC keys to check correctness of MAC’d values. Since our focus is also on practical instantiations, our implementation offloads as much computation as possible into the preprocessing phase, thus resulting in a faster online phase. Moreover, a better analysis of the parameters of the underlying cryptoscheme and a more specific choice of the field where computation is performed allow us to obtain a better optimized implementation. Improvements are also due to the fact that our construction is in the random oracle model, and the practical implementation is multi-threaded.