  In order to prevent eavesdropping and tampering, the network security
protocols use a handshake with an asymmetric cipher to establish a
session-specific shared key with which further communication is encrypted using
a symmetric cipher. The commonly used asymmetric algorithms include public key
encryption, key exchange and identity-based encryption(IBE). However, the
network security protocols based on classic identity-based encryption do not
have perfect forward security. To solve the problem, we construct the first
quantum IBE (QIBE) scheme based on the learning with errors problem, and prove
that our scheme is fully secure under the random oracle. Moreover, we construct
the quantum circuit of our QIBE scheme and give an estimate of the quantum
resource of our circuit including the numbers of Hadamard gate, phase gate, T
gate, CNOT gate and the total qubits used in the circuit, and conclude that the
quantum resources required by our scheme increase linearly with the number of
bits of the encrypted quantum plaintext. Our scheme exhibits the following
advantages: (i) The classic key generation center (KGC) system still can be
used for our QIBE scheme to generate and distribute the secret identity keys so
that the cost can be reduced when the scheme is implemented. The reason why the
classic KGC can be used is that the public and private keys are in the form of
classic bits. (ii) The network security protocols using a handshake with our
QIBE scheme can provide perfect forward security. In our scheme, the ciphertext
is transmitted in the form of a quantum state that is unknown to the adversary
and therefore cannot be copied and stored. Thus, in the network security
protocols based on our QIBE construction, the adversary cannot decrypt the
previous quantum ciphertext to threat the previous session keys even if the
identity secret key is threatened.
