  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 \emph{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. 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.
