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We consider the problem of secure distributed matrix multiplication (SDMM),where a user has two matrices and wishes to compute their product with the helpof $N$ honest but curious servers under the security constraint that anyinformation about either $A$ or $B$ is not leaked to any server. This paperpresents a \emph{new scheme} that considers the inner product partition formatrices $A$ and $B$. Our central technique relies on encoding matrices $A$ and$B$ in a Hermitian code and its dual code, respectively. We present theHermitian Algebraic (HerA) scheme, which employs Hermitian codes andcharacterizes the partitioning and security capacities given entries ofmatrices belonging to a finite field with $q^2$ elements. We showcase that thisscheme performs the secure distributed matrix multiplication in a significantlysmaller finite field and expands security allowances compared to the existingresults in the literature.

HerA Scheme: Secure Distributed Matrix Multiplication via Hermitian Codes