Multi-Key Homomorphic MACs with Efficient Verification for Quadratic Arithmetic Circuits

Abstract

Multi-key homomorphic MACs (MKHomMACs) allow multiple clients to authenticate data with their own secret keys and outsource their data together with the tags to an untrusted server. Upon receiving any user 's request of computing a function on the data, the server is able to generate both the computation result and a short tag that vouches for the correctness of the result. MKHomMACs provide a solution with minimal communication and interaction to the problem of delegating computations over outsourced data. Fiore, Mitrokotsa, Nizzardo, and Pagnin (Asiacrypt 2016) constructed a PRF-based MKHomMAC where the result verification could be as costly as the delegated computation. In this paper, we show a PRF-based MKHomMAC for quadratic arithmetic circuits such that the verification can be substantially faster than the delegated computation in an amortized setting. The efficiency improvement is achieved by using PRFs with multi-key amortized closed-form efficiency.