Degree Tables for Secure Distributed Matrix Multiplication

We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute product two matrices with assistance honest but curious servers. construct polynomial codes for SDMM by studying recently introduced combinatorial tool called degree table. For fixed partitioning, minimizing total communication cost code is equivalent $N$ , number distinct elements corresponding propose new constructions tables low elements. These lead general family SDMM, we call notation="LaTeX">$\mathsf {GASP}_{r}$ (Gap Additive Secure Polynomial codes) parameterized an integer notation="LaTeX">$r$ . outperforms all previously known under outer partitioning. also present lower bounds on and prove optimality or asymptotic our certain regimes. Moreover, formulate construction optimal as linear program use it system parameters that were able test.