Searchable and Verifiable As a crucial method of cloud security, symmetric encryption enables users to search for encrypted data in the cloud using keywords and validate the accuracy of the results. One of the most prevalent and important requirements for data owners in such schemes is dynamic update for cloud data. To our knowledge, all of the verifiable SSE systems that permit data dynamic update currently in use are based on asymmetric -key cryptography verification, which necessitates time-consuming processes. The sheer volume of cloud data could make the overhead of verification a major burden. Consequently, a crucial unsolved topic is how to implement keyword search over dynamic encrypted cloud data with effective verification. In this research, we investigate how to accomplish keyword search over dynamically encrypted cloud data with symmetric-key based verification and suggest a workable technique. In order to support the efficient verification of dynamic data, we design a novel Accumulative Authentication Tag (AAT) based on the symmetric -key cryptography to generate an authentication tag for each keyword. Benefiting from the accumulation property of our designed AAT, the authentication tag can be conveniently updated when dynamic operations on cloud data occur. In order to achieve efficient data update, we design a new secure index composed by a search table ST based on the orthogonal list and a verification list VL containing AATs. Owing to the connectivity and the flexibility of ST, the update efficiency can be significantly improved. The security analysis and the performance evaluation results show that the proposed scheme is secure and efficient