Secure multiparty matrix multiplication based on Strassen-Winograd algorithm

Abstract

This paper presents the first recursive secure multiparty computation protocol for matrix multiplication, based on Strassen-Winograd algorithm. We focus on the setting in which any given player knows only one row of both input matrices and learns the corresponding row of the resulting product matrix. Neither the player initial data, nor the intermediate values, even during the recurrence part of the algorithm, are ever revealed to other players. We use a combination of partial homomorphic encryption schemes and additive masking techniques together with a novel schedule for the location and encryption layout of all intermediate computations that preserves privacy. Compared to state of the art protocols, the asymptotic communication volume and computational time is reduced from O(n3) to O(n2.81. This improvement in terms of communication volume arises with matrices of dimension as small as n=96 which is confirmed by experiments.