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Verifiable computation (VC) allows a computationally weak client to outsource evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation to obtain an encoding of its function which is then given to the server. The server returns both the evaluation of the function on the client's input and a proof with which the client can verify the correctness of the evaluation using substantially less effort than doing the evaluation on its own. We consider privacy preserving VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with input privacy for univariate polynomial evaluation and matrix multiplication and then extend them to achieve function privacy. Our main tool is the recently proposed mutilinear maps. We show that the proposed VC schemes can be used to implement verifiable outsourcing of private information retrieval (PIR).

Private Outsourcing of Polynomial Evaluation and Matrix Multiplication Using Multilinear Maps