# Multi-Stage Quantum Secure Direct Communication Using Secure Shared Authentication Key
## 5 Example of the Proposed Protocol
### Security Check Procedure
44:Notation:
45:\(\{\text{fB},\ \text{$\theta$},\ \text{$\varphi$}\}\leftarrow\) is the function that returns the updated secret polarization angle and authentication key for every block of photon (\(\mathbf{\Phi}\) photons per block)
46:for\(\{\text{fB},\ \text{$\theta$},\ \text{$\varphi$}\}\) in enumerate ({\text{f(B},\ \text{$\theta$},\ \text{$\varphi$)}}\)do
47:for\(\text{j}=1\) in range \(\mathbf{B}\)do
48: Transmission of photon using single-stage
49:if\(\text{i}^{+}\ \text{B}+\text{j}\ \text{$\geq$ len(\mathbf{B})}\)then
50:break transmission;
51:endif
52:endfor
53:endfor
54:[PERSON] and [PERSON] checks for authenticity
55:if\((\theta_{A},\text{$\varphi$})\)\(\times(-\theta_{A},-\text{$\varphi$})=\)\(I\)then
56:[PERSON] and [PERSON] are authenticated
57:else
58:detect [PERSON] and terminate communication
59:endif
```

**Algorithm 1** SSAK protocol

## 6 Performance Analysis

### Mutual Authentication

It has been found that the authentication procedure in the IV Three-stage and Braided Single Stage protocol is unidirectional, which means that only [PERSON] can authenticate [PERSON]. In this work, a mutual authentication procedure is presented by applying the unitary transformation in the process of authentication. Mutual authentication between legal parties is necessary to avoid an eavesdropper stealing the secret message. Mutual authentication requires the parties to prove their identity with each other in the communication. Therefore, the mutually agreed algorithm of the authentication keys is changed every eight bits of transactions. The keys are updated based on every last \(n\) bit photons to prevent the message from leaking. The frequent change of the authentication key has helped to enhance the level of security, but a longer time is needed to change the polarization angle due to the limitations of the mechanical components [28]. As discussed in the previous section, the transformation needs to be commutative in which the rotation is only known to the parties that apply them [30]. Therefore, in the case where [PERSON] and [PERSON] are not mutually authenticated, Equation (5) is fulfilled, where \(\theta_{A}.\Phi\) is the polarization at [PERSON] that acts as encryption angle, \(-\theta_{A}.-\Phi\) is the polarization at [PERSON] that acts as decryption angle and \(I\) is the identity matrix, as shown in Equation (18). As shown in Figure 4, the sender and receiver authentication controllers provide an authentication function by the evaluation of information sent by both parties [16]. Besides, the controller also monitors the bit error rate of the received photons. For instance, [PERSON] and [PERSON] can check the legitimacy of each other by comparing their polarizations. If the result is not equal to \(I\), the failed authentication alarm will be triggered, and the procedure would be stopped. The procedure needs to start over again. ### Low Cost and Low Complexity

Table 1 shows that the previous protocols, IV Three-stage and Braided Single Stage, use the public channel to share the initial secret angle between [PERSON] and [PERSON], therefore, making the secret angle vulnerable to attacks. The proposed protocol, on the other hand, uses the quantum channel to share the initial angle and the authentication key. Thus it is hard for the attacker to obtain the value since the quantum state is implemented from the beginning of the procedure. It makes the authentication of the users simpler without sharing the secret polarization angle and authentication key onset of the protocol. Similar to previous protocols, there is no need for a third party to verify the authentication in the proposed protocol. Despite the IV Three-stage protocol that used four variables [7] during the message sharing, the proposed authentication only consists of three variables, which are \(\theta_{X}\), \(\theta_{A}\), and \(\Phi\). It shows that the consumption of photonic devices is less compared to the previous protocols. Figure 4: The implementation of the sender and receiver side authentication controller.