Privacy preserving multi-party multiplication of polynomials based on (k,n) threshold secret sharing

In applications such as cloud analytics, multi-party computation enables a set of participants to compute an arbitrary function of their inputs jointly, without revealing these inputs to one another. In this study, we introduce secure multi-party multiplication using (k,n) threshold secret sharing without increasing the required number of computing servers. This is achieved using encrypted shares and a recombination vector, whereby two encrypted shares of the same secret are sent to each server. Moreover, our method supports multi-input (as opposed to only two-input) multiplication. This is important for operations such as exponential functions that are commonly used in domains including deep learning.