Privacy-Preserving Outsourcing Computation of QR Decomposition in the Encrypted Domain

Signal processing in encrypted domain has become an important mean to protect privacy in an untrusted network environment. Due to the limitations of the underlying encryption methods, many useful algorithms that are sophisticated are not well implemented. Considering that QR decomposition is widely used in many fields, in this paper, we propose to implement QR decomposition in homomorphic encrypted domain. We firstly realize some necessary primitive operations in homomorphic encrypted domain, including division and open square operation. Gram-Schmidt process is then studied in the encrypted domain. We propose the implementation of QR decomposition in the encrypted domain by using the secure implementation of Gram-Schmidt process. We conduct experiments to demonstrate the effectiveness and analyze the performance of the proposed outsourced QR decomposition.