Privacy-Preserving Singular Value Decomposition

In this paper, we propose secure protocols to perform singular value decomposition (SVD) for two parties over horizontally and vertically partitioned data. We propose various secure building blocks for the computations of QR algorithm so that it is privacy-preserving. Some of the proposed secure building blocks include secure matrix multiplication, (x+y)^-1, and radic(x+y). Together, they allow us to derive privacy-preserving SVD (PPSVD) based on a privacy-preserving QR algorithm. Finally we conduct experiments to evaluate the proposed secure building blocks and protocols. The results show that the proposed protocols for SVD achieve high accuracy for matrices of small and medium size.