Fast Multiparty Multiplications from shared bits

We study the question of securely multiplying N -bit integers that are stored in binary representation, in the context of protocols for dishonest majority with preprocessing. We achieve communication complexity O(N) using only secure operations over small fields F2 and Fp with log(p) ≈ log(N). For semi-honest security we achieve communication O(N)2 ∗(N)) using only secure operations over F2. This improves over the straightforward solution of simulating a Boolean multiplication circuit, both asymptotically and in practice.