Computational SS and conversion protocols in both active and passive settings

Abstract

Secret sharing (SS) has been extensively studied as both a means of secure data storage and a fundamental building block for multiparty computation (MPC). For these purposes, code-efficiency and MPC-suitability are required for SS but they are incomparable. Recently, a computational SS and a conversion protocol were proposed. The computational SS is code-efficient and the conversion protocol converts shares of the computational (code-efficient) SS into those of an MPC-suitable SS, and it can be applied to reduce the amount of data storage while maintaining extendibility to MPC. However, this protocol is one-way: one cannot convert the share of MPC output value. In addition, it is only passively secure. The authors propose three protocols and a new computational SS. The first protocol is the inverse of the existing protocol, that is, it converts an MPC-suitable SS to the existing SS. The other two protocols are actively secure conversion protocols that convert shares between the new SS and an MPC-suitable SS. The new computational SS is code-efficient when the number of parties is small, so these two protocols are for converting between the code-efficient SS and an MPC-suitable SS. These two conversion protocols are actively secure in the honest majority.