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

Coded Secure Multi-Party Computation for Massive Matrices with Adversarial Nodes