International Association for Cryptologic Research (IACR)
Abstract
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 F_2 and F_p with log(p) \approx log(N). For semi-honest security we achieve communication O(N)2^{O(log∗(N))} using only secure operations over F_2. This improves over the straightforward solution of simulating a Boolean multiplication circuit, both asymptotically and in practice
