Overdrive2k: Efficient Secure MPC over Z2k from Somewhat Homomorphic Encryption

Recently, Cramer et al. (CRYPTO 2018) presented a protocol, SPDZ2k, for actively secure multiparty computation for dishonest majority in the pre-processing model over the ring Z2k , instead of over a prime field Fp. Their technique used oblivious transfer for the pre-processing phase, more specifically the MASCOT protocol (Keller et al. CCS 2016). In this paper we describe a more efficient technique for secure multiparty computation over Z2k based on somewhat homomorphic encryption. In particular we adapt the Overdrive approach (Keller et al. EUROCRYPT 2018) to obtain a protocol which is more like the original SPDZ protocol (Damg̊ard et al. CRYPTO 2012). To accomplish this we introduce a special packing technique for the BGV encryption scheme operating on the plaintext space defined by the SPDZ2k protocol, extending the ciphertext packing method used in SPDZ to the case of Z2k . We also present a more complete pre-processing phase for secure computation modulo 2 by adding a new technique to produce shared random bits.