Prover efficient public verification of dense or sparse/structured matrix-vector multiplication
This addresses the need for efficient public verification in cloud computing for computationally weak devices, offering a significant speed improvement over prior methods.
The paper tackles the problem of verifying matrix-vector multiplications delegated to cloud servers, presenting protocols that are secure against malicious servers and achieve essentially optimal overhead with a small constant factor for the server and linear verification time. The result is protocols that are more than two orders of magnitude faster than existing ones.
With the emergence of cloud computing services, computationally weak devices (Clients) can delegate expensive tasks to more powerful entities (Servers). This raises the question of verifying a result at a lower cost than that of recomputing it. This verification can be private, between the Client and the Server, or public, when the result can be verified by any third party. We here present protocols for the verification of matrix-vector multiplications, that are secure against malicious Servers. The obtained algorithms are essentially optimal in the amortized model: the overhead for the Server is limited to a very small constant factor, even in the sparse or structured matrix case; and the computational time for the public Verifier is linear in the dimension. Our protocols combine probabilistic checks and cryptographic operations, but minimize the latter to preserve practical efficiency. Therefore our protocols are overall more than two orders of magnitude faster than existing ones.