A Universal Secret Sharing Scheme with General Access Structure Based on CRT

Abstract

In a (t, n) threshold secret sharing ((t, n)-SS) scheme, any equal to or more than t shareholders are able to reconstruct the secret by pooling shares together. However, (t, n)-SS cannot work when the access structure is not threshold. Later, the notion of secret sharing scheme with general access structure (GAS) was proposed. In a GAS scheme, access structure can be designed for any requirements. If and only if a set of shareholders satisfies required access structure, the secret can be recovered. Because access structures are more complex than simple (t, n) threshold, users need plenty of storage to keep multiple private shares in most GAS schemes. In order to reduce private shares of shareholder, this paper proposes a universal GAS scheme which breaks the hierarchical limitation of levels in a multilevel secret sharing scheme based on Chinese remainder theorem to make the GAS scheme available for any general access structure. More importantly, each shareholder just needs less storage to keep one private share in the proposed scheme.