Cryptology ePrint Archive: Report 2022/064

A Framework for the Design of Secure and Efficient Proofs of Retrievability

Françoise Levy-dit-Vehel and Maxime Roméas

Abstract: Proofs of Retrievability (PoR) protocols ensure that a client can fully retrieve a large outsourced file from an untrusted server. Good PoRs should have low communication complexity, small storage overhead and clear security guarantees with tight security bounds. The focus of this work is to design good PoR schemes with simple security proofs. To this end, we use the Constructive Cryptography (CC) setting by Maurer [13]. We propose a framework for the design of secure and efficient PoR schemes based on Locally Correctable Codes (LCC). We give a first instantiation of our framework using the high rate lifted codes introduced by Guo et al. [5]. This yields an infinite family of good PoRs. We assert their security by solving a finite geometry problem, giving an explicit formula for the probability of an adversary to fool the client. Using the local correctability properties of Tanner codes, we get another instantiation of our framework and derive an analogous formula for the success probability of the audit.

Category / Keywords: cryptographic protocols / Proofs of Retrievability, Locally Correctable Codes, Constructive Cryptography, Server Memory Resource

Date: received 18 Jan 2022

Contact author: maxime romeas at inria fr

Available format(s): PDF | BibTeX Citation

Version: 20220118:200138 (All versions of this report)

Short URL: ia.cr/2022/064