The popularity of the cloud storage systems has brought a number of challenges. Two of them are data integrity and energy efficiency. There are many proposed static solutions to prove the integrity of a file. For the dynamic case, Rank-Based Authenticated Skip List (RBASL) has been presented. It provides the update operations with logarithmic complexity. However, an RBASL expects the block size to be fixed. In a realistic scenario, where the updates can be of variable size, an RBASL performs O(n) update operations on the data structure when a change in the file occurs, where n is the number of blocks.