In a threshold secret sharing (SS) scheme, whether or not a shareholder set is an authorized set totally depends on the number of shareholders in the set. When the access structure is not threshold, (t,n) threshold SS is not suitable. This paper proposes a new kind of SS named grouped secret sharing (GSS), which is specific multipartite SS. Moreover, in order to implement GSS, we utilize both Lagrange interpolation polynomials and Chinese remainder theorem to design two GSS schemes, respectively. Detailed analysis shows that both GSS schemes are correct and perfect, which means any authorized set can recover the secret while an unauthorized set cannot get any information about the secret.

Traditional threshold secret sharing cannot realizing all access structures of secret sharing. So, Ito introduced the concept of Secret sharing scheme realizing general access structure. But Its scheme has to send multiple shares to each trustee. In this paper, we proposed two new secret sharing schemes realizing general access structures by only assigning one share to each trustee. Our proposed second scheme is a perfect secret sharing scheme. Furthermore, our schemes can realize any access structures.