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

In this work1, we consider the problem of secure multi-party computation (MPC), consisting of F sources, each has access to a large private matrix, N processing nodes or workers, and one 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 server. The workers process their shares in interaction with each other, and send some results to the master such that it can derive the final results. There are several constraints: (1) each worker has a constraint on its storage, such that it can store equivalent of $\displaystyle \frac{1}{m}$ fraction of size of each input matrices from each source, 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 of the workers, called recovery threshold, such that the final result is correct, servers 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 main challenge is to manage the errors propagated through the network by the adversarial nodes when the workers interact with each other in each round.