A novel fully homomorphic robust secret sharing scheme

As an enhancement to traditional secret sharing, robust secret sharing provides additional fault tolerance. The fault tolerance means that the original secret can be recovered even if some shares used in reconstruction are incorrect. So far, there is a lot of research work on robust secret sharing, however the current schemes are all based on Shamir's scheme. Because Shamir's scheme is constructed on polynomials, it has only additive homomorphism and has a narrow range of applications. In this article, we will analyze the existence of robust secret sharing scheme based on Chinese Remainder Theorem from the perspective of redundant residue number system. Based on the existence, we construct a new robust secret sharing scheme and we analyze the time complexity, share size, robustness and homomorphism of our scheme. Compared with the existing scheme, our new scheme has both additive and multiplicative homomorphisms under the premise of achieving the same robustness and share size.