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 propose a framework for the design of secure and efficient PoR schemes that is based on Locally Correctable Codes, and whose security is phrased in the Constructive Cryptography model by Maurer. We give a first instantiation of our framework using the high rate lifted codes introduced by Guo et al. 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. Moreover, we show that the security of a PoR of Lavauzelle and Levy-dit-Vehel was overestimated and propose new secure parameters for it. Finally, 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.