Field Trace Polynomial Codes for Secure Distributed Matrix\n Multiplication

Abstract

We consider the problem of communication efficient secure distributed matrix\nmultiplication. The previous literature has focused on reducing the number of\nservers as a proxy for minimizing communication costs. The intuition being,\nthat the more servers used, the higher the communication cost. We show that\nthis is not the case. Our central technique relies on adapting results from the\nliterature on repairing Reed-Solomon codes where instead of downloading the\nwhole of the computing task, a user downloads field traces of these\ncomputations. We present field trace polynomial codes, a family of codes, that\nexplore this technique and characterize regimes for which our codes outperform\nthe existing codes in the literature.\n