Proofs of Data Possession and Retrievability Based on MRD Codes

Proofs of Data Possession (PoDP) scheme is essential to data outsourcing. It provides an efficient audit to convince a client that his/her file is available at the storage server, ready for retrieval when needed. An updated version of PoDP is Proofs of Retrievability (PoR), which proves the client’s file can be recovered by interactions with the storage server. We propose a PoDP/PoR scheme based on Maximum Rank Distance (MRD) codes. The client file is encoded block-wise to generate homomorphic tags with help of an MRD code. In an audit, the storage provider is able to aggregate the blocks and tags into one block and one tag, due to the homomorphic property of tags. The algebraic structure of MRD codewords enables the aggregation to be operated over a binary field, which simplifies the computation of storage provider to be the most efficient XOR operation. We also prove two security notions, unforgeability served for PoDP and soundness served for PoR with properties of MRD codes. Meanwhile, the storage provider can also audit itself to locate and correct errors in the data storage to improve the reliability of the system, thanks to the MRD code again.