Ideal and perfect multi-secret sharing schemes whose access structure are Q3

The characterization of access structure is one of the main open problems in secret sharing schemes. We are particularly interested in determining which Q3 access structures can be realized and the requirement should be achieved even in the presence of an adversary who is able to corrupt some players in an ideal secret sharing scheme. The problems are studied in our paper. Above all, we present a concrete scheme that can meet all above requirements. In our scheme, it is not only a dynamic multi-secret and multi-use sharing protocol, but participants from access structure can recover the secret using their shares, while the same number of participants from adversary structure can´t recover the secret using their shares, which is different from general access structure schemes. Moreover, in the whole dynamic process, the coefficients of polynomial and private secret shares always stay the same. Therefore, it enjoys high practical value.