Optimized algorithms for flexible length-based authenticated skip list

With the growing trend toward using cloud storage, the problem of efficiently checking and proving data integrity needs more consideration. Many cryptography and security schemes, such as PDP (Provable Data Possession) and POR (Proofs of Retrievability) were proposed for this problem. Although many efficient schemes for static data have been constructed, only a few dynamic schemes exist, such as DPDP (Dynamic Provable Data Possession). But the DPDP scheme falls short when updates are not proportional to a fixed block size. The FlexList-based Dynamic Provable Data Possession (FlexDPDP) was an optimized scheme for DPDP. However, the update operations (insertion, remove, modification) in Flex DPDP scheme only apply to single node at a time, while multiple consecutive nodes operation is more common in practice. To solve this problem, we propose optimized algorithms for multiple consecutive nodes, which including MultiNodes Insert and Verification, MultiNodes Remove and Verification, MultiNodes Modify and Verification. The cost of our optimized algorithms is also analyzed. For m consecutive nodes, an insertion takes O(m) + O(log N) + O(log m), where N is the number of leaf nodes of FlexList, a remove takes O(log N), and a modification is the same as the original algorithm. Finally, we compare the optimized algorithms with original Flex-List through experiences, and the results show that our scheme has the higher efficiency of time and space.