  Based on $d$-dimensional quantum full homomorphic encryption, an efficient
and secure quantum network coding protocol is proposed in this paper. First, a
quantum full homomorphic encryption protocol is constructed utilizing
$d$-dimensional universal quantum gates. On this basis, an efficient quantum
network coding protocol is proposed. In the protocol, two source nodes encrypt
their respective prepared quantum states with the quantum full homomorphic
encryption protocol. The two intermediate nodes successively perform
homomorphic evaluation of the received quantum states. Finally, the two sink
nodes recover the quantum states transmitted by the two source nodes in the
butterfly network depending on their measurement results. The performance
analysis shows that the proposed quantum network coding protocol is correct and
resistant to attacks launched by dishonest intermediate nodes and external
eavesdroppers. Compared to related protocols, the proposed protocol not only
enables to transfer information in $d$-dimensional quantum system, but also
requires only 1 quantum gate and a key of length 2 in the encryption phase,
which makes the protocol has higher efficiency.
