Improved Private and Secure Distributed Matrix Multiplication

Abstract

Consider the problem of a user having a private matrix A and N non-colluding servers sharing a library of L (L > 1) matrices B (0) , B (1) , . . . , B (L−1) , for which the user wishes to compute AB (θ) for some θ ∈ [0, L) without revealing any information of the matrix A to the servers, and keeping the index θ private to the servers. This problem is known as private and secure distributed matrix multiplication (PSDMM) and is supposed to have wide application potential. However, studies of PSDMM are still scarce in the literature. In this paper, we propose a new efficient private and secure distributed matrix multiplication coding scheme, which has a better performance than state-of-the-art schemes in that it achieves a smaller recovery threshold and download cost as well as providing a more flexible tradeoff between the upload and download costs.