Multi-prover Proof-of-Retrievability

TL;DR

This paper extends proof-of-retrievability systems to multiple servers, formalizing security definitions for threshold and average success, and introduces schemes with confidentiality guarantees, including an unconditionally secure instantiation based on the Shacham-Waters scheme.

Contribution

It introduces formal security definitions for multi-server PoR systems and provides secure schemes with confidentiality, including an unconditionally secure version based on existing cryptographic techniques.

Findings

Secure multi-server PoR schemes with threshold and average-case guarantees.

Extension of classical statistical techniques for response verification.

An unconditionally secure multi-server PoR scheme based on Shacham-Waters.

Abstract

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 \emph{proof-of-retrievability} ($\mathsf{PoR}$) systems. In this paper, we study multiple server $\mathsf{PoR}$ systems. We formalize security definitions for two possible scenarios: (i) when a threshold of servers succeed with high enough probability (worst-case) and (ii) when 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 $\mathsf{M}\mbox{-}\mathsf{PoR}$ 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 used by Paterson, Stinson and Upadhyay (Journal of Mathematical Cryptology: 7(3)) 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 (Asiacrypt, 2008). 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.