Proofs of Encrypted Data Retrievability with Probabilistic and Homomorphic Message Authenticators

When users store their data on a cloud, they may concern on whether their data is stored correctly and can be fully retrieved. Proofs of Retrivability (PoR) is a cryptographic concept that allows users to remotely check the integrity of their data without downloading. This check is usually done by attaching data with message authenticators that contain data integrity information. The existing PoR schemes consider only the retrievability of unencrypted data and their message authenticators are usually deterministic. In this paper, we propose a PoR scheme that is built over homomorphic encryption schemes. Our PoR scheme can prove the retrievability of homomorphically encrypted data by generating probabilistic and homomorphic message authenticators. Moreover, the homomorphically encrypted data can be processed by the cloud directly and our PoR scheme can verify the integrity of such outsourced computations over ciphertexts. A prototype of our scheme is implemented to evaluate its performance.