Secure Computation on Additive Shares

The rapid development of cloud computing has probably benefited each of us. However, the privacy risks brought by untrusty cloud servers arise the attention of more and more people and legislatures. In the last two decades, plenty of works seek the way of outsourcing various specific tasks while ensuring the security of private data. Although the addition and multiplication are enough for implementing any functions, the direct utilization of existing schemes like homomorphic encryption will lead to significant efficiency and accuracy loss, which is not suitable for outsourcing computation tasks. The tasks to be outsourced are endless, however, the involved calculations are similar. In this paper, inspired by additive secret sharing and multiplicative secret sharing technologies, we construct a series of novel protocols which support the common secure calculations on numbers (e.g., basic elementary functions) or matrices (e.g., solve eigenvectors) in arbitrary $n$ number of servers ($n \geq 2$), and the $n$-party protocols ensure the security of the original data even if $n-1$ servers collude. All protocols we designed only need constant interaction rounds, and we demonstrate them under universally composability security. We believe that these protocols can provide a new basic tool for actual outsourced tasks.