  In this work, we consider the problem of secure multi-party computation
(MPC), consisting of $\Gamma$ sources, each has access to a large private
matrix, $N$ processing nodes or workers, and one data collector or master. The
master is interested in the result of a polynomial function of the input
matrices. Each source sends a randomized functions of its matrix, called as its
share, to each worker. The workers process their shares in interaction with
each other, and send some results to the master such that it can derive the
final result. There are several constraints: (1) each worker can store a
function of each input matrix, with the size of $\frac{1}{m}$ fraction of that
input matrix, (2) up to $t$ of the workers, for some integer $t$, are adversary
and may collude to gain information about the private inputs or can do
malicious actions to make the final result incorrect. The objective is to
design an MPC scheme with the minimum number the workers, called the recovery
threshold, such that the final result is correct, workers learn no information
about the input matrices, and the master learns nothing beyond the final
result. In this paper, we propose an MPC scheme that achieves the recovery
threshold of $3t+2m-1$ workers, which is order-wise less than the recovery
threshold of the conventional methods. The challenge in dealing with this set
up is that when nodes interact with each other, the malicious messages that
adversarial nodes generate propagate through the system, and can mislead the
honest nodes. To deal with this challenge, we design some subroutines that can
detect erroneous messages, and correct or drop them.
