Most of the existing secret sharing schemes are constructed to realize general access structure, which is defined in term of authorized groups of participants, and is unable to be applied directly to the design of an intrusion tolerant syst em. Instead, the generalized adversary structure, which specifies the corruptibl e subsets of participants, can be determined directly by exploiting the system s etting and the attributes of all participants. An efficient secret sharing schem e realizing graph-based adversary structures is proposed. The scheme requires le ss computational costs and storage overhead than the existing ones. Furthermore, it is proved that the scheme satisfy both the required properties of the secret sharing scheme, i.e., the reconstruction property and the perfect property.