  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 the inner product partition for
matrices $A$ and $B$. Our central technique relies on encoding matrices $A$ and
$B$ in a Hermitian code and its dual code, respectively. We present the
Hermitian Algebraic (HerA) scheme, which employs Hermitian codes and
characterizes the partitioning and security capacities given entries of
matrices belonging to a finite field with $q^2$ elements. We showcase that this
scheme performs the secure distributed matrix multiplication in a significantly
smaller finite field and expands security allowances compared to the existing
results in the literature.
