Generic constructions of PoRs from codes and instantiations

In this paper, we show how to construct – from any linear code – a Proof of Retrievability ( {\mathsf{PoR}} ) which features very low computation complexity on both the client ( {\mathsf{Verifier}} ) and the server ( {\mathsf{Prover}} ) sides, as well as small client storage (typically 512 bits). We adapt the security model initiated by Juels and Kaliski [PoRs: Proofs of retrievability for large files, Proceedings of the 2007 ACM Conference on Computer and Communications Security—CCS 2007, ACM, New York 2007, 584–597] to fit into the framework of Paterson, Stinson and Upadhyay [A coding theory foundation for the analysis of general unconditionally secure proof-of-retrievability schemes for cloud storage, J. Math. Cryptol. 7 2013, 3, 183–216], from which our construction evolves. We thus provide a rigorous treatment of the security of our generic design; more precisely, we sharply bound the extraction failure of our protocol according to this security model. Next we instantiate our formal construction with codes built from tensor-products as well as with Reed–Muller codes and lifted codes, yielding {\mathsf{PoR}} s with moderate communication complexity and (server) storage overhead, in addition to the aforementioned features.

Multi-prover proof of retrievability

There has been considerable recent interest in “cloud storage” wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover the file given any “proving algorithm” that has a sufficiently high success probability. This forms the basis of proof-of-retrievability (PoR) systems. In this paper, we study multiple server PoR systems. We formalize security definitions for two possible scenarios: (i) A threshold of servers succeeds with high enough probability (worst case), and (ii) the average of the success probability of all the servers is above a threshold (average case). We also motivate the study of confidentiality of the outsourced message. We give MPoR schemes which are secure under both these security definitions and provide reasonable confidentiality guarantees even when there is no restriction on the computational power of the servers. We also show how classical statistical techniques previously used by us can be extended to evaluate whether the responses of the provers are accurate enough to permit successful extraction. We also look at one specific instantiation of our construction when instantiated with the unconditionally secure version of the Shacham–Waters scheme. This scheme gives reasonable security and privacy guarantee. We show that, in the multi-server setting with computationally unbounded provers, one can overcome the limitation that the verifier needs to store as much secret information as the provers.