Fast Secure Computation Method based on a Secret Sharing Scheme Even for n<2k-1 Which Can Deal with the Secret Zero

Abstract

Secure computation is a major issue that affects the utilization of Big Data. Two main approaches are employed to achieve secure computation: homomorphic encryption (HE) and secret sharing schemes (SSSs), where the computational cost of the latter is generally much less than that of HE. Aminuddin et al. proposed a secure product-sum computation that allows secure multiplication for n<2k-1 by using the (scalar value × polynomial) approach. However, this approach requires a polynomial calculation because it uses Shamir's SSS, so it cannot be processed rapidly. In this study, we propose a fast secure computation method based on the XOR method, and we evaluate its performance and security.