A computing system includes an array of storage devices configured to provide access to storage data and check data corresponding to a data block length; and a storage engine, coupled to the array of storage devices, configured to: detect one more erroneous data, one more erroneous check data, or a combination thereof for representing the storage data, the check data, or a combination thereof inaccessible or failing a status check process after initial storage thereof, determine a prime shift factor for representing a smallest prime number not less than a block unit-quantity, wherein the block unit-quantity is for representing a quantity of shift units within the data block length, and iteratively generate a target recovery set based on a circular-shift mechanism utilizing the prime shift factor for recovering the one more erroneous data, the one more erroneous check data, or a combination thereof.