Secure Computation with Low Communication from Cross-checking.

We construct new four-party protocols for secure computation that are secure against a single malicious corruption. Our protocols can perform computations over a binary ring, and require sending just 1.5 ring elements per party, per gate. In the special case of Boolean circuits, this amounts to sending 1.5 bits per party, per gate. One of our protocols is robust, yet requires almost no additional communication. Our key technique can be viewed as a variant of the “dual execution” approach, but, because we rely on four parties instead of two, we can avoid any leakage, achieving the standard notion of security.