# Multi-Stage Quantum Secure Direct Communication Using Secure Shared Authentication Key
## 5 Example of the Proposed Protocol
### Security Check Procedure
Instead of the classical authentication, which is based on the computational complexity of certain mathematical problems, quantum authentication utilizes quantum mechanics, which provides absolute security [15; 16; 31]. Thus, to evaluate the quantum authentication protocol, quantum communication complexity measurement was conducted. Quantum communication complexity can be defined as the amount of communications carried out between the parties to accomplish information distribution tasks [32]. The protocol that uses quantum and classical resources to authenticate users is denoted by \(Q^{*}(f_{l})\), while the protocol that fully uses quantum channel to authenticate users is denoted by \(Q(f_{l})\), where \(Q\) is the quantum communication complexity and \(f_{l}\) is the identity authentication [32; 33]. It can be seen from Table 1 that the IV Three-stage and Braided Single Stage protocol require a classical channel (\(\Omega\)) to share a set of polarization states predetermined amongst them for authentication functionalities [30]. For the IV Three-stage protocol, a three-stage transformation over the quantum channel (\(n\)) is required to perform the authentication process between the parties and to exchange the initialization vector that acts as an authentication key. Due to no authentication key in the Braided Single Stage [9], the three-stage transformation is only used for authentication tasks. Indeed, the proposed protocol does not need a predetermined polarization state before the effective authentication process starts. The secret polarization angle and authentication key can be shared in a fully quantum channel within five stages. It can be considered a good quantum authentication protocol if a minimum number of communications are held between parties. In order to make the authentication process more secure and efficient, classical communication is not necessary. ### Security Analysis

Security analysis is the critical assessment standard for any quantum protocol to ensure that the proposed protocol is secure against any eavesdropper attacks. The security of the proposed QSDC authentication protocol relies not only on the quantum non-cloning theorem and the quantum uncertainty principle of the secret message to prevent an unconditional attack, but the quantum state is also applied to the authentication key that secures the messages. The security analysis is explained in detail herein. #### 6.3.1 Man-in-the-Middle Attack

Due to the two secret polarization angles, the attacker must know the value of \(\theta_{A}\) and \(\Phi\) at the same time. However, it is very difficult for the attacker to guess the exact value due to the secure handshake mechanism that has been conducted to share that value between [PERSON] and [PERSON]. If the \(\Phi\) and the quantum states \(\theta_{X}\) are exposed to [PERSON] during transmission, she has no means to understand the value of \(\Phi\) or X. Even if [PERSON] sends multiple photons with the same polarization, [PERSON] cannot obtain the useful information since different values of authentication keys are generated for each block of the bit transfer. [PERSON] is able to decode the information X if he possesses the correct \(\theta_{A}\) and \(\Phi\). Hence, [PERSON] cannot pretend to be [PERSON] or [PERSON] if she does not know the authentication key. As shown in Figure 4, [PERSON] and [PERSON] will compare the bits to determine if a MITM attack has been launched. For example, [PERSON] may disturb the message by interrupting the quantum channel several times, and this situation will lead to the re-initialization of the communication between the legitimate parties. If an interception