This thesis deals with the security of the storage, the access and themaintenance of outsourced data. Indeed, outsourced storage raises newthreats for users. We focus on the three following protocols. First,Proofs of Retrievability (PoR) allows a user who rarely accesses itsdata to be sure that it is effectively stored on the server and that itdid not suffer any alterations. Second, Updatable Encryption (UE)permits the user of an encrypted database to rotate potentiallycompromised cryptographic keys with low bandwith usage. Third, PrivateInformation Retrieval (PIR) allows a user to make the way it accessesoutsourced data confidential. The goal of this thesis can be summarizein three steps. In step one, we develop modular security notions andmodels that closely match the security expectations of real-worldsolutions for the three above problems. Then, in step two, we check ifexisting security definitions are sufficient, and sometimes alsonecessary, to provide the security guarantees identified in step one.Finally, we determine if existing cryptographic schemes reach oursecurity definitions and, if not, we improve them or propose newconstructions that do. Our security statements are phrased in theConstructive Cryptography (CC) model of Maurer. The contributions madein this thesis are the following. We solve three open problems inpost-quantum UE. Indeed, we propose the first post-quantum UE schemethat is secure against chosen ciphertexts attacks. Moreover, we proposethe first post-quantum UE schemes that support an unbounded number ofkey updates. Third, our new schemes are based on three differentproblems that are not lattice-based. We do so by studying the problem ofbuilding UE in the group action framework. As for PoRs, we show that thesecurity of a PoR of Lavauzelle and Levy-dit-Vehel was overestimated. Wepropose a framework for the design of secure and efficient PoR schemesbased on Locally Correctable Codes. We use our framework to give asecure generalization of the previously mentioned PoR. Furthermore, weuse expander codes to design another PoR scheme with better parameters.We also extend CC so as to handle interactive protocols. We use ourextension to model UE and PIR. As for UE, we give the first composablemodeling of UE by circumventing an impossibility result known as thecommitment problem. We use this modeling to understand which securitynotion for UE is best suited for different real-world applications. Asfor PIR, we give a composable and unified treatment of many PIR variants.