# Multi-Stage Quantum Secure Direct Communication Using Secure Shared Authentication Key
## 4 Secure Shared Authentication Key (SSAK) Protocol
### Initial Authentication Procedure  
[PERSON] is the party that supposedly sends a message to [PERSON]. For [PERSON], it is extremely important to ensure the messages are only received by the authenticated user who is [PERSON]. However, [PERSON] faces difficulties when he receives the message; he does not know whether it comes from [PERSON] or an eavesdropper. The initial part of authentication is important to verify the party that initiates the communication. Therefore, in this paper, a novel quantum handshake for sharing initial secret angle and authentication key, which is utilized before the quantum communication session is proposed. The objective of the proposed protocol is to allow [PERSON] to identify herself to [PERSON] and [PERSON] can prove that [PERSON] is a legitimate party. Note that operator \(E_{K}[\cdot]\) and \(D_{K}[\cdot]\) operators in Figure 2 are defined as encrypt and decrypt operations with key \(K\).  
Figure 2: Procedure of the secure shared authentication key (SSAK) protocol.  
The steps of the proposed protocol are discussed below:  
1. First item, [PERSON] prepares a private orthogonal state \(\psi_{0}\) and generates a random quantum state \(\theta_{A}\) using a random number generator. Based on the decimal value of \(\theta_{A}\), she prepares five binary digits and do Pauli-X quantum gate operation to produce \(\theta_{A}\)'. She then encrypts \(\theta_{A}\) with \(\psi_{0}\) to produce the quantum state \(\psi_{1}\). The _TimeStamp_ is set to \(t_{A}(1)=0\).
2. Second item, [PERSON] generates a random quantum state \(\theta_{B}\) using a random number generator and encrypts it with the received quantum state \(\psi_{1}\) and produces \(\psi_{2}\). The _TimeStamp_ is set to \(t_{B}(1)=2\).
3. Third item, [PERSON] decrypts the received \(\psi_{2}\) with \((-\theta_{A})\) to generate \(\psi_{3}\) and sends it back to [PERSON]. At this stage, [PERSON] is able to extract \(\theta_{B}\). [PERSON] will verify the _TimeStamp_ after she gets the photon replied by [PERSON]. [PERSON] starts to analyze the difference between the sending and receiving time. If [PERSON] gets \(TimeStamp\
eq 4\), an eavesdropper is detected and she will terminate the communication. Otherwise, the communication will be continued. Then, the _TimeStamp_ is set to 4.
4. [PERSON] applies \((-\theta_{B})\) to obtain the \(\psi_{0}\) and successfully extracted \(\psi_{0}\). [PERSON] gets the value of \(\theta_{A}\) and converts it into five binary digits. He then does the Pauli-X quantum gate operation to generate new value of \(\theta_{B}\). Next, he encrypts it with the received quantum state \(\psi_{0}\) to produce quantum state \(\psi_{4}\) and sends it to [PERSON].
5. [PERSON] authenticates [PERSON] by comparing and analysing \(\theta_{B}\) using measurement. If the value is correct, she will then send the authentication key \(\Phi_{initial}\) that is generated using a random number generator. The \(\Phi_{initial}\) is then encrypted with the \(\theta_{B}\) that she had extracted in step 3 to produce \(\psi_{5}\) and passed it back to [PERSON]. If the value is different, the communication will be terminated and needs to be restarted.
6. [PERSON] couples the receiving \(\psi_{5}\) with \((-\theta_{B})\), to get the authentication key \(\Phi\).  
After the authentication is successfully completed, [PERSON] will start to convert the string of bit message into the photons and directly sends it to [PERSON] using the initial secret polarization angle (\(\theta_{initial}\)) and authentication key (\(\Phi_{initial}\)).