Actively Secure Setup for SPDZ

We present an actively secure, practical protocol to generate the distributed secret keys needed in the SPDZ offline protocol. The resulting distribution of the public and secret keys is such that the associated SHE `noise\u27 analysis is the same as if the distributed keys were generated by a trusted setup. We implemented the presented protocol for distributed BGV key generation within the SCALE-MAMBA framework. Our method makes use of a new method for creating doubly (or even more) authenticated bits in different MPC engines, which has applications in other areas of MPC-based secure computation. We were able to generate keys for two parties and a plaintext size of 64 bits in around five minutes, and approximately eighteen minutes for a 128 bit prime