We define and construct a new primitive called a fully homomorphic message authenticator. With such scheme, anybody can perform arbitrary computations over authenticated data and produce a short tag that authenticates the result of the computation (without knowing the secret key). This tag can be verified using the secret key to ensure that the claimed result is indeed the correct output of the specified computation over previously authenticated data (without knowing the underlying data). For example, Alice can upload authenticated data to "the cloud", which then performs some specified computations over this data and sends the output to Bob, along with a short tag that convinces Bob of correctness. Alice and Bob only share a secret key, and Bob never needs to know Alice's underlying data. Our construction relies on fully homomorphic encryption to build fully homomorphic message authenticators.
The work of Gennaro and Wichs REF defines and achieves fully homomorphic MACs using fully homomorphic encryption.
Fully homomorphic message authenticators
IACR Cryptology ePrint Archive
Computer Science