In order to improve the audit efficiency of big data storage, we propose a big data storage audit method based on the remote data checking (RDC) of the finite field algebraic signature partition table. Firstly, after obtaining the algebraic signature of outsourced files, we use the arithmetic operation of the underlying field to complete the remote detection of data integrity in the cloud storage. The proposed data audit method has relatively low computation and communication costs for both the client and the cloud server. Secondly, we design a divide and conquer table (D&CTs) as a new data structure to effectively support dynamic data operations such as insert, add, delete, and modify operations. The D&CTs method can enable the proposed RDC scheme to be applied to cloud storage process analysis with varied size of files. Finally, simulation experiments are carried out to verify the effectiveness of the proposed method in big data cloud storage process.