  We present Modular Polynomial (MP) Codes for Secure Distributed Matrix
Multiplication (SDMM). The construction is based on the observation that one
can decode certain proper subsets of the coefficients of a polynomial with
fewer evaluations than is necessary to interpolate the entire polynomial. We
also present Generalized Gap Additive Secure Polynomial (GGASP) codes. Both MP
and GGASP codes are shown experimentally to perform favorably in terms of
recovery threshold when compared to other comparable polynomials codes for SDMM
which use the grid partition. Both MP and GGASP codes achieve the recovery
threshold of Entangled Polynomial Codes for robustness against stragglers, but
MP codes can decode below this recovery threshold depending on the set of
worker nodes which fails. The decoding complexity of MP codes is shown to be
lower than other approaches in the literature, due to the user not being tasked
with interpolating an entire polynomial.
