STR: Secure computation on additive shares using the share-transform-reveal strategy

The rapid development of cloud computing has probably benefited each of us. However, the privacy risks brought by untrustworthy cloud servers arise the attention of more and more people and legislatures. In the last two decades, plenty of works seek to outsource various specific tasks while ensuring the security of private data. The tasks to be outsourced are countless; however, the computations involved are similar. In this paper, we construct a series of novel protocols that support the secure computation of various functions on numbers (e.g., the basic elementary functions) and matrices (e.g., the calculation of eigenvectors and eigenvalues) in arbitrary $n\geq 2$ servers. All protocols only require constant rounds of interactions and achieve the low computation complexity. Moreover, the proposed $n$-party protocols ensure the security of private data even though $n-1$ servers collude. The convolutional neural network models are utilized as the case studies to verify the protocols. The theoretical analysis and experimental results demonstrate the correctness, efficiency, and security of the proposed protocols.