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.

翻译：我们提出面向安全分布式矩阵乘法（SDMM）的模块化多项式（MP）码。该构造基于如下观察：通过较少的求值次数即可解码多项式系数的特定真子集，而无需完整插值整个多项式。我们还提出了广义间隙加性安全多项式（GGASP）码。实验表明，与采用网格划分的其他SDMM多项式码相比，MP码和GGASP码在恢复阈值方面均具有更优性能。针对掉队节点的鲁棒性，MP码与GGASP码均能实现纠缠多项式码的恢复阈值，但MP码可根据实际故障工作节点集合在低于该阈值的条件下进行解码。由于用户无需承担完整多项式插值的任务，MP码的解码复杂度低于现有文献中的其他方案。