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There has been considerable recent interest in "cloud storage" wherein a userasks a server to store a large file. One issue is whether the user can verifythat the server is actually storing the file, and typically achallenge-response protocol is employed to convince the user that the file isindeed being stored correctly. The security of these schemes is phrased interms of an extractor which will recover or retrieve the file given any"proving algorithm" that has a sufficiently high success probability.  This paper treats proof-of-retrievability schemes in the model ofunconditional security, where an adversary has unlimited computational power.In this case retrievability of the file can be modelled as error-correction ina certain code. We provide a general analytical framework for such schemes thatyields exact (non-asymptotic) reductions that precisely quantify conditions forextraction to succeed as a function of the success probability of a provingalgorithm, and we apply this analysis to several archetypal schemes. Inaddition, we provide a new methodology for the analysis of keyed POR schemes inan unconditionally secure setting, and use it to prove the security of amodified version of a scheme due to Shacham and Waters under a slightlyrestricted attack model, thus providing the first example of a keyed POR schemewith unconditional security. We also show how classical statistical techniquescan be used to evaluate whether the responses of the prover are accurate enoughto permit successful extraction. Finally, we prove a new lower bound on storageand communication complexity of POR schemes.

A coding theory foundation for the analysis of general unconditionally secure proof-of-retrievability schemes for cloud storage