In this work the first linearly homomorphic authenticated encryption scheme with public verifiability and provable correctness, called LEPCoV, is presented. It improves the initial proposal by avoiding false negatives during the verification algorithm. This work provides a detailed description of LEPCoV, a comparison with the original scheme, a security and correctness proof, and a performance analysis showing that all algorithms run in reasonable time for parameters that are currently considered secure. The scheme presented here allows a user to outsource computations on encrypted data to the cloud, such that any third party can verify the correctness of the computations without having access to the original data. This makes this work an important contribution to cloud computing and applications where operations on sensitive data have to be performed, such as statistics on medical records and tallying of electronically cast votes.
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