I will present a new protocol that was developed entirely in the measurement-based model for quantum computation. Our protocol allows Alice to have Bob carry out a quantum computation for her such that Alice\'s inputs, outputs and computation remain perfectly private, and where Alice does not require any quantum computational power or memory. Alice only needs to be able to prepare single qubits from a finite set and send them to Bob, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, Alice and Bob use two-way classical communication which enables Alice to drive the computation, giving single-qubit measurement instructions to Bob, depending on previous measurement outcomes. Our protocol is efficient and is presented for the special case of a classical-input, and classical-output; modifications allow the general case of quantum inputs and outputs. We also discuss the use of authentication in order for Alice to detect an uncooperative Bob. Based on joint work with Joseph Fitzsimons and Elham Kashefi