Private Coded Matrix Multiplication

Abstract

In distributed computing system for the master-worker framework, an erasure code is able to mitigate the effects of slow workers, also called stragglers. The distributed computing system combined with coding is referred to as coded computation. For a matrix multiplication, we consider a variation of coded computation that ensures the master's privacy from the workers, which is referred to as private coded matrix multiplication. In the private coded matrix multiplication, the master needs to compute a matrix multiplication on its own matrix and one of the matrices in a library exclusively shared by the external workers. After the master recovers the matrix multiplication through coded matrix multiplication, the workers should not know which matrix in the library was desired by the master, which implies that the master's privacy is ensured. Our problem is a special case of linear private computation, where a linear combination of matrices in the library should be concealed. We propose a private coded matrix multiplication scheme, based on the conventional coded matrix multiplication scheme. In terms of computation time and communication load, we compare our proposed scheme with a conventional robust private information retrieval scheme and private computation schemes.