SecFact: Secure Large-scale QR and LU Factorizations

We are now in the big data era. Due to the emerging various systems and applications, such as the Internet of Things, cyber-physical systems, smart cities, smart healthcare, we are able to collect more data than ever before. On the other hand, it makes it very difficult to analyze such massive data in order to advance our science and engineering fields. We note that QR and LU factorizations are two of the most fundamental mathematical tools for data analysis. However, conducting QR or LU factorization of an m x n matrix requires computational complexity of O(m(2)n). This incurs a formidable challenge in efficiently analyzing large-scale data sets by normal users or small companies on traditional resource-limited computers. To overcome this limitation, industry and academia propose to employ cloud computing that can offer abundant computing resources. This, however, obviously raises security concerns and hence a lot of users are reluctant to reveal their data to the cloud. To this end, we propose two secure outsourcing algorithms for efficiently performing large-scale QR and LU factorizations, respectively. We implement the proposed algorithms on the Amazon Elastic Compute Cloud (EC2) platform and a laptop. The experiment results show significant time saving for the user.