The existing ADSs do not support the append-only feature and fork consistency of transparent logs. Therefore, it is very necessary and urgent to research new types of ADSs. To solve the data integrity problem in the transparent log system, this thesis improves the existing ADS and designs an Append-only Authenticated Data Sets (AADS) model. The formal definition, correctness definition, and security definition of the model are given. Based on the RSA accumulator, the construction method of AADS is given, and the algorithms of initialization, adding data, searching data, and verifying evidence are designed. During the process of adding data, it can be dynamically built according to the size of the dataset, and precompute the (non-)membership of the data. The security of the model and the complexity of the algorithm are analyzed, and the results show that the model is safe under the strong RSA assumption and the adaptive root assumption, and has certain advantages in reducing the algorithm space complexity.