CAT and DOG: Improved Codes for Private Distributed Matrix Multiplication

Abstract: We present novel constructions of polynomial codes for private distributed matrix multiplication (PDMM/SDMM) using outer product partitioning (OPP). We extend the degree table framework from the literature to cyclic-addition degree tables (CATs). By using roots of unity as evaluation points, we enable modulo-addition in the table. Based on CATs, we present an explicit construction, called CATx, that requires fewer workers than existing schemes in the low-privacy regime. Additionally, we present new families of schemes based on conventional degree tables, called GASPrs and DOGrs, that outperform the state-of-the-art for a wide range of parameters.