# Multi-Stage Quantum Secure Direct Communication Using Secure Shared Authentication Key
## 5 Example of the Proposed Protocol
### Security Check Procedure
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Protocol** & **IV Three-Stage** & **Braided Single Stage** & **Proposed Protocol** \\ \hline
1. Public Communication & Yes & Yes & No \\ (pre-shared angle) & Yes & No & Yes \\
2. Authentication key & Yes & No & Yes \\
3. No. of HWP for information & 7 & 5 & 5 \\ exchange & 4. Information exchange stage & 3 times & 1 times \\
5.Quantum communication & \(Q^{*}(f_{l})=\Omega\left(3n+3 IV\right)\) & \(Q^{*}(f_{l})=\Omega(3n)\) & \(Q(f_{l})=5n\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison between three-stage variants and proposed authentication protocol. occurs, [PERSON] and [PERSON] will immediately detect it, and [PERSON] will never get the original message. If the bit error rate is high, this means that [PERSON]'s attack has been started as the quantum states are disturbed. Thus, if the error rate is higher than the threshold, the transmission will be canceled. During the MITM attack, [PERSON] will impersonate [PERSON] and [PERSON] to extract information. [PERSON] does not know the value of \(\theta_{A}\) and \(\Phi\) to send a fake sequence of messages prepared by herself to [PERSON] because [PERSON] and [PERSON] share the \(\theta_{initial}\) and \(\Phi_{initial}\) by utilizing a quantum handshake scheme. The possible cases on how the proposed protocol defends MITM attacks are discussed here. 1. [PERSON] has no knowledge of the \(\theta_{initial}\) or the \(\Phi_{initial}\), thus she is incapable of getting anything about the secret message. Thus, the proposed protocol is secure against MITM attack. As stated in Section 5, [PERSON] needs to guess 45 possibilities of angle for each qubit transmitted. [PERSON] can predict the true angle for \(\theta_{initial}\) and \(\Phi_{initial}\) with the probability \(p=\frac{1}{45}\times\frac{1}{45}=\frac{1}{2025}\). 2. [PERSON] succeeds in guessing the \(\theta_{initial}\). However, [PERSON] does not get any useful information about the message since she does not know \(\Phi_{initial}\). In order to investigate the impact of [PERSON]'s information on the secret angles of the SSAK and the benchmark protocol, a random character from 5 to 25 with random message generation is selected. The messages are shared over the QSDC protocol. The simulations have been tested using Python programming language. Figure 5 shows an average of 30 simulation runs for each data point. The leakage angle in average, \(Leak_{AB}\) can be calculated as:

\[Leak_{AB}=\frac{LeakAngle}{SecretAngle} \tag{19}\]

where \(LeakAngle\) is the number of angles that are successfully recovered by [PERSON] and \(SecretAngle\) is the number of secret angles agreed by [PERSON] and [PERSON]. As shown in Figure 5, the average covered angle by [PERSON] is 0% in the proposed protocol. This means that [PERSON] does not have any clue to guess the true angles, \(\Phi\) and \(\theta\) simultaneously. Therefore, [PERSON] has completely no knowledge about the polarized photon that represents the message. However, in benchmark protocols (IV Three-stage and Braided Single Stage), as the number of bits increases, [PERSON] still has chances to guess the secret angle by 2% on average. The line plotted in the graph shows the maximum average covered angles by [PERSON] after 30 simulation runs for the benchmark protocol. It can be seen that [PERSON] is able to guess up to 7% of the secret angles in the lowest number of characters shared. Figure 5: The implementation of the sender and receiver side authentication controller. #### 6.3.2 Intercept/Resend Attack

After [PERSON] encodes the photons, [PERSON] attempts to steal the photons and substitutes them with fake photons prepared in advance. In the proposed SSAK protocol, [PERSON] shares the secret \(\theta\) and \(\Phi\) securely with [PERSON] that is only known to them. [PERSON] cannot measure the intercepted photons correctly because she cannot know the right value of \(\theta\) and \(\Phi\).