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

Quantum Identity-Based Encryption from the Learning with Errors Problem