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 anew 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 q2 elements. We showcase this scheme performs the secure
distributed matrix multiplication in a significantly smaller finite field than
the existing results in the literature