A data integrity verification method and system based on a root random number to ensure secure distributed data storage on a public cloud. A new root random number can be generated in response to receiving a file for storage to the public cloud. A unique random number tag for each data chunk associated with the file can be calculated via a shift operation and the tag can be added to the data chunk. A hash function (message digests) can be then generated and concatenated with the data chunk and the random number tag. The data chunk in conjunction with the hash and the random number tag can be encrypted by an encryption module and stored to the public cloud in order to provide multiple levels of security with respect to the distributed public cloud storage. Upon file retrieval, the encryption module decrypts all data chunks and recalculates the hash in order to verify the data integrity of the file.