Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation (Full Version)

We give improved upper bounds on the communication complexity of optimally-resilient secure multiparty computation in the cryptographic model. We consider evaluating an n-party randomized function and show that if f can be computed by a circuit of size c, then O(cnκ) is an upper bound for active security with optimal resilience t < n/2 and security parameter κ. This improves on the communication complexity of previous protocols by a factor of at least n. This improvement comes from the fact that in the new protocol, only O(n) messages (of size O(κ) each) are broadcast during the whole protocol execution, in contrast to previous protocols which require at least O(n) broadcasts per gate. Furthermore, we improve the upper bound on the communication complexity of passive secure multiparty computation with resilience t < n from O(cnκ) to O(cnκ). This improvement is mainly due to a simple observation.