  In secure distributed matrix multiplication (SDMM) the multiplication
$\mathbf{A}\mathbf{B}$ from two private matrices $\mathbf{A}$ and $\mathbf{B}$
is outsourced by a user to $N$ distributed servers. In $\ell$-SDMM, the goal is
to a design a joint communication-computation procedure that optimally balances
conflicting communication and computation metrics without leaking any
information on both $\mathbf{A}$ and $\mathbf{B}$ to any set of $\ell\leq N$
servers. To this end, the user applies coding with $\tilde{\mathbf{A}}_i$ and
$\tilde{\mathbf{B}}_i$ representing encoded versions of $\mathbf{A}$ and
$\mathbf{B}$ destined to the $i$-th server. Now, SDMM involves multiple
tradeoffs. One such tradeoff is the tradeoff between uplink (UL) and downlink
(DL) costs. To find a good balance between these two metrics, we propose two
schemes which we term USCSA and GSCSA that are based on secure cross subspace
alignment (SCSA). We show that there are various scenarios where they
outperform existing SDMM schemes from the literature with respect to the UL-DL
efficiency. Next, we implement schemes from the literature, including USCSA and
GSCSA, and test their performance on Amazon EC2. Our numerical results show
that USCSA and GSCSA establish a good balance between the time spend on the
communication and computation in SDMMs. This is because they combine advantages
of polynomial codes, namely low time for the upload of
$\left(\tilde{\mathbf{A}}_i,\tilde{\mathbf{B}}_i\right)_{i=1}^{N}$ and the
computation of $\mathbf{O}_i=\tilde{\mathbf{A}}_i\tilde{\mathbf{B}}_i$, with
those of SCSA, being a low timing overhead for the download of
$\left(\mathbf{O}_i\right)_{i=1}^{N}$ and the decoding of
$\mathbf{A}\mathbf{B}$.
