In our protocol, Alice can run her topologically-protected quantum computation on Bob's quantum computer in such a way that Alice's [quid] privacy is kept secret to Bob (Fig. 2). More precisely, our protocol runs as follows (Fig.3). Like the BFK protocol, Alice first sends randomly-rotated [quid] qubits to Bob (Fig.3 (a)). By entangling these qubits, Bob next creates a certain three-dimensional system, which is a modification of the Raussendorf-Harrington-Goyal one (Fig.3 (b)). Then, Alice and Bob perform measurement-based quantum computing with exchanging classical messages (Fig.3 (c) and (d)). If Bob is honest, Alice can perform the correct topologically-protected quantum computation (Fig. 3 (e)). On the other hand, whatever evil Bob does, he cannot learn anything about Alice's input, output, and algorithm (Fig.3 (e)).