An Efficient Matrix Multiplication with Enhanced Privacy Protection in Cloud Computing and Its Applications

As one of the most important basic operations, matrix multiplication computation (MMC) has varieties of applications in the scientific and engineering community such as linear regression, k-nearest neighbor classification and biometric identification. However handling these tasks with large-scale datasets will lead to huge computation beyond resource-constrained client s computation power. With the rapid development of cloud computing, outsourcing intensive tasks to cloud server has become a promising method. While the cloud server is generally out of the control of clients, there are still many challenges concerned with the privacy security of clients sensitive data. Motivated by this, Lei et al. presented an efficient encryption scheme based on random permutation to protect the privacy of client s data in outsourcing MMC task. Nevertheless, there exists inherent security flaws in their scheme, revealing the statistic information of zero elements in the original data thus not satisfying the computational indistinguishability (IND-ZEA). Aiming to enhance the security of the outsourcing MMC task, we propose a new encryption scheme based on subtly designed invertible matrix where the additive perturbation is introduced besides the multiplicative perturbation. Furthermore, we show that the proposed encryption scheme can be applied to not only MMC task but also other kinds of outsourced tasks such as linear regression and principal component analysis. Theoretical analyses and experiments indicate that our methods are more secure in terms of data privacy, with comparable performance to the state-of-the-art scheme based on matrix transformation.