Root of Unity for Secure Distributed Matrix Multiplication: Grid Partition Case

We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of N honest but curious servers under the security constraint that any information about either A or B is not leaked to any server. This paper presents a new scheme that considers a grid product partition for matrices A and B, which achieves an upload cost significantly lower than the existing results in the literature. Also, it significantly reduces the recovery threshold compared to the PolyDot codes presented for grid partition when T > 0. Since the grid partition is a general partition that incorporates the inner and outer ones, it turns out that the communication load of the proposed scheme matches the best-known protocols for those extreme cases.