Proofs of Reliability

We consider the following cloud storage scenario. A client outsources a file F to a CSP. To handle large files, F is first partitioned into subfiles of equal length, which are then individually processed. Let F be divided to ns subfiles f1, f2, . . . fns . Each fi is independently encoded to yi through the application of a linear ECC C of length n, dimension k, and minimum distance d over a finite field Fq, an (n, k, d)q code for short. This is common practice in most cloud systems [1, 2, 3, 4]. The order of Fq is q = 2`, so that C operates on `-bit blocks, also referred to as symbols. The SLA between the client and the CSP specifies a reliability degree ω for F . The reliability degree defines the maximum number of tolerated erasures, before F becomes irretrievable. Note that although the application of code C provides a reliability of d−1, the SLA may specify any desired reliability degree ω ≤ d. A CSP offering a higher reliability degree can require a higher monetary compensation. To verify compliance to the SLA, the client (or a designated verifier) periodically performs an integrity verification test. This is achieved by executing an interactive proof-of-reliability (PoRL) protocol. In a PoRL, the CSP is challenged to prove the retrievability of n − (d − ω) symbols per subfile. When ω = 0, a PoRL is equivalent to a PoR. A PoRL poses a stronger requirement to the CSP compared to classical PoR protocols. In the latter, it is sufficient to assure the integrity of each subfile, and therefore of F , by retrieving the minimum number of symbols required for retrievability. In a PoRL, the CSP must additionally prove that redundant symbols are stored per subfile. A PoRL assurance implies a PoR assurance, but the converse does not hold. As an additional requirement, the CSP must be able to efficiently recover lost symbols, when symbol erasures occur due to hardware failures.