Fully Homomorphic Message Authenticators

We define and construct fully homomorphic message authenticators. In such a scheme, anybody can perform arbitrary computations over authenticated data and produce a short tag that authenticates the result of the computation. The user verifies this tag with her private key to ensure that the claimed result is indeed the correct output of the specified computation over previously authenticated data, without needing to know the underlying data itself. For example, a user can outsource the storage of large amounts of authenticated data to a remote server, and the server can later non-interactively certify the outputs of various computations over this data with only a short tag. Our construction uses fully homomorphic encryption in a novel way