MultiStage Quantum Secure Direct Communication Using Secure Shared Authentication Key
Abstract
:1. Introduction
 (1)
 The secret angle and authentication key are generated by Alice, and no third party is involved in the process to enhance the confidentiality of the communication. Thus, no preshared authentication key and initial secret angle are exchanged between Alice and Bob at the onset of the communication, which occurs in public channels.
 (2)
 The secret angles and the authentication key are updated using a mutually agreed algorithm after a number of bits sent to increase the security level.
 (3)
 The QSDC protocol is operated in singlestage, and the authentication is applied bitbybit, thus reducing the transmission time, and the security check is done along with the data transmission process.
2. The Importance of Authentication for QSDC
3. Related Works
4. Secure Shared Authentication Key (SSAK) Protocol
4.1. Initial Authentication Procedure
 First item, Alice 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 PauliX quantum gate operation to produce ${\theta}_{A}{}^{\prime}$. She then encrypts ${\theta}_{A}$ with ${\psi}_{0}$ to produce the quantum state ${\psi}_{1}$. The $TimeStamp$ is set to ${t}_{A}\left(1\right)=0.$
 Second item, Bob 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 ${t}_{B}\left(1\right)=2.$
 Third item, Alice decrypts the received ${\psi}_{2}$ with $({\theta}_{A})$ to generate ${\psi}_{3}$ and sends it back to Bob. At this stage, Alice is able to extract ${\theta}_{B}.$ Alice will verify the $TimeStamp$ after she gets the photon replied by Bob. Alice starts to analyze the difference between the sending and receiving time. If Alice gets $TimeStamp\text{}\ne 4$, an eavesdropper is detected and she will terminate the communication. Otherwise, the communication will be continued. Then, the $TimeStamp$ is set to 4.
 Bob applies $({\theta}_{B})$ to obtain the ${\psi}_{0}$ and successfully extracted ${\psi}_{0}$. Bob gets the value of ${\theta}_{A}$ and converts it into five binary digits. He then does the PauliX 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 Alice.
 Alice authenticates Bob 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 Bob. If the value is different, the communication will be terminated and needs to be restarted.
 Bob couples the receiving ${\psi}_{5}$ with $({\theta}_{B})$, to get the authentication key $\Phi $.
4.2. Secure Message Sharing Procedure
 Alice encrypts her secret message ${x}_{i}$ by generating a state with a linear polarization using a 0° polarizer as bit 0 or using 90° polarizer as bit 1 to get ${\theta}_{X}$.
 Quantum state ${\theta}_{X}$ is then coupled with initial ${\theta}_{A}$ and sent along with the initial authentication key $\Phi $ by Alice. The combination of ${\theta}_{X}$, ${\theta}_{A}$ and $\Phi $ generates ${\psi}_{A}$ are sent to Bob.
 Bob receives the quantum state ${\psi}_{A}$ and couples it with $({\theta}_{A})$ and $(\Phi )$ obtains information ${X}_{i}$.
 Alice and Bob frame the received bits and convert the last $n\mathrm{bits}$ to integer value $N$, given by$$N={\displaystyle \sum}_{i=kn+1}^{k}{b}_{i}\times {2}^{i}$$
 Alice and Bob compute new value of θ and $\mathsf{\Phi}$, given by$${\theta}_{Next}=\frac{N\pi}{{2}^{k}}+{\theta}_{initial}$$$${\Phi}_{Next}=\frac{N\pi}{{2}^{k}}+{\Phi}_{initial}$$
4.3. Security Checking Procedure
5. Example of the Proposed Protocol
5.1. Initial Authentication Procedure
 Suppose that Alice prepares a photon ${\psi}_{0}=0\u27e9$ and generates a random secret angle, ${\theta}_{A}=1\xb0$. Based on the decimal value of ${\theta}_{A}$, she converts it into binary digits $00001\u27e9$ and employs PauliX quantum gate operation to produce $11110\u27e9$. She converts it back to decimal value,${\theta}_{A}{}^{\prime}=30\xb0$. The new value will be used as the security check for the next procedure. She starts to encrypt$X=0\u27e9$ using ${\theta}_{A}$ and produce quantum state ${\psi}_{1}$. The $TimeStamp$ is set to ${t}_{A}\left(1\right)=0$.
 Bob generates a random secret angle ${\theta}_{B}=15\xb0$ and encrypts it with the received quantum state ${\psi}_{1}$ and produces ${\psi}_{2}$. The$TimeStamp$ is set to ${t}_{B}\left(1\right)=2$.
 Alice decrypts the received ${\psi}_{2}$ with ${\theta}_{A}$ to generate ${\psi}_{3}$ and sends it back to Bob. At this stage, Alice gets ${\theta}_{B}=15\xb0.$ Alice will verify the $TimeStamp=4$ after she gets the photon replied by Bob. If Alice gets the $TimeStamp\ne 4$, an eavesdropper is detected, and she will terminate the communication. Otherwise, the communication will be continued. The$TimeStamp$ is set to ${t}_{A}\left(2\right)=4$.
 Bob applies ${\theta}_{B}$ to obtain ${\psi}_{0}=0\u27e9$. He gets the value of ${\theta}_{A}=1\xb0$ and converts it into the binary digits $00001\u27e9$. Using the PauliX quantum gate, he gets $11110\u27e9$, and he converts it back into decimal value and generates ${\theta}_{B}=30\xb0$. He then encrypts it with the received quantum state ${\psi}_{0}=0\u27e9$ to produce quantum state ${\psi}_{4}$ and sends it to Alice. The$TimeStamp$ is set to ${t}_{B}\left(2\right)=6$.
 Alice authenticates Bob by comparing and analyzing ${\theta}_{B}$ using measurement. If ${\theta}_{B}={\theta}_{A}{}^{\prime}$, she sends the initial authentication key ${\Phi}_{initial}=20\xb0$ that is generated using a random number generator and encrypts it with ${\theta}_{B}=30\xb0$. If ${\theta}_{B}\ne {\theta}_{A}{}^{\prime}$, the communication will be terminated and need to be restarted.
 Finally, Bob couples the receiving ${\psi}_{5}$ with ${\theta}_{B}=30\xb0$ to get the authentication key ${\Phi}_{initial}$.
 It can be concluded that the security of the proposed scheme depends entirely on the initial authentication procedure, where the eavesdropping check and identity authentication are implemented at the same time.
5.2. Message Sharing Procedure
 Suppose that Alice prepares a photon. Alice wants to send the first qubit, $0\u27e9,$ the qubit is then encrypted to the photons using the first agreed angle from the first procedure, ${\theta}_{A}=30\xb0$. Alice prepares photons based on Equation (9) and encrypts it using the rotation of HWP based on Equation (6).$$\begin{array}{ccc}{\phi}_{1}& =& \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& cos(4\left(30\right))& sin\left(4\left(30\right)\right)& 0\\ 0& sin\left(4\left(30\right)\right)& cos\left(4\left(30\right)\right)& 0\\ 0& 0& 0& 1\end{array}\right]\times \left[\begin{array}{c}1\\ 1\\ 0\\ 0\end{array}\right]\\ & =& \left[\begin{array}{c}1\\ 0.5\\ 0.8660254\\ 0\end{array}\right].\end{array}$$
 Alice encrypts the ${\phi}_{1}$ with the authentication key, which is previously shared in the initial authentication procedure, $\Phi =20\xb0$.$$\begin{array}{ccc}{\phi}_{2}& =& \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& cos(4\left(20\right))& sin\left(4\left(20\right)\right)& 0\\ 0& sin\left(4\left(20\right)\right)& cos\left(4\left(20\right)\right)& 0\\ 0& 0& 0& 1\end{array}\right]\times \left[\begin{array}{c}1\\ 0.5\\ 0.8660254\\ 0\end{array}\right]\\ & =& \left[\begin{array}{c}1\\ 0.76604444\\ 0.64278761\\ 0\end{array}\right].\end{array}$$
 Alice then applies the transformation associated with the encoded bit. In the case of bit 0 is being sent, the angle is set at ${\theta}_{X}=$0° or ${\theta}_{X}=$45° if bit 1 is being sent.$$\begin{array}{ccc}{\phi}_{3}& =& \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& cos(4\left(0\right))& sin\left(4\left(0\right)\right)& 0\\ 0& sin\left(4\left(0\right)\right)& cos\left(4\left(0\right)\right)& 0\\ 0& 0& 0& 1\end{array}\right]\times \left[\begin{array}{c}1\\ 0.76604444\\ 0.64278761\\ 0\end{array}\right]\\ & =& \left[\begin{array}{c}1\\ 0.76604444\\ 0.64278761\\ 0\end{array}\right].\end{array}$$
 Bob receives ${\phi}_{3}$ and decrypts it by rotating it back with the angle $\u2013{\theta}_{A}$.$$\begin{array}{ccc}{\phi}_{4}& =& \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& cos(4\left(30\right))& sin\left(4\left(30\right)\right)& 0\\ 0& sin\left(4\left(30\right)\right)& cos\left(4\left(30\right)\right)& 0\\ 0& 0& 0& 1\end{array}\right]\times \left[\begin{array}{c}1\\ 0.76604444\\ 0.64278761\\ 0\end{array}\right]\phantom{\rule{0ex}{0ex}}\\ & =& \left[\begin{array}{c}1\\ 0.5\\ 0.8660254\\ 0\end{array}\right].\end{array}$$
 Bob receives ${\phi}_{4}$ and decrypts it by rotating it back using the angle of authentication key ${\Phi}_{A}.$ Bob receives the original message.$$\begin{array}{ccc}{\phi}_{5}& =& \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& cos(4\left(20\right))& sin\left(4\left(20\right)\right)& 0\\ 0& sin\left(4\left(20\right)\right)& cos\left(4\left(20\right)\right)& 0\\ 0& 0& 0& 1\end{array}\right]\times \left[\begin{array}{c}1\\ 0.5\\ 0.8660254\\ 0\end{array}\right]\phantom{\rule{0ex}{0ex}}\\ & =& \left[\begin{array}{c}1\\ 1\\ 0\\ 0\end{array}\right].\end{array}$$
5.3. Security Check Procedure
Algorithm 1 SSAK protocol 

6. Performance Analysis
6.1. Mutual Authentication
6.2. Low Cost and Low Complexity
6.3. Security Analysis
6.3.1. ManintheMiddle Attack
 Case 1:
 Eve 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, Eve needs to guess 45 possibilities of angle for each qubit transmitted. Eve can predict the true angle for ${\theta}_{initial}$ and ${\Phi}_{initial}$ with the probability $p=\frac{1}{45}\times \frac{1}{45}=\frac{1}{2025}$.
 Case 2:
 Eve succeeds in guessing the ${\theta}_{initial}$. However, Eve does not get any useful information about the message since she does not know ${\Phi}_{initial}$.
6.3.2. Intercept/Resend Attack
6.3.3. Beam Splitting Attack
7. Implementation Issues of the Proposed Protocol
8. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
 Long, G.L.; Liu, X.S. Theoretically efficient highcapacity quantumkeydistribution scheme G. Phys. Rev. A 2002, 65, 1–3. [Google Scholar] [CrossRef] [Green Version]
 Deng, F.; Long, G.L.; Liu, X. Twostep quantum direct communication protocol using the EinsteinPodolskyRosen pair block. Phys. Rev. A 2003, 68, 1–6. [Google Scholar] [CrossRef] [Green Version]
 Deng, F.G.; Long, G.L. Secure direct communication with a quantum onetime pad. Phys. Rev. A 2004, 052319, 1–4. [Google Scholar] [CrossRef] [Green Version]
 Li, J.; Pan, Z.; Sun, F.; Chen, Y.; Wang, Z.; Shi, Z. Quantum secure direct communication based on dense coding and detecting eavesdropping with fourparticle genuine entangled state. Entropy 2015, 17, 6743–6752. [Google Scholar] [CrossRef] [Green Version]
 Chang, Y.; Xu, C.X.; Zhang, S.; Yan, L.L. Quantum secure direct communication and authentication protocol with single photons. Chin. Sci. Bull. 2013, 58, 4571–4576. [Google Scholar] [CrossRef]
 Hu, J.Y.; Yu, B.; Jing, M.Y.; Xiao, L.T.; Jia, S.T.; Qin, G.Q.; Long, G.L. Experimental quantum secure direct communication with single photons. Light Sci. Appl. 2016, 5, 1–5. [Google Scholar] [CrossRef]
 Rifai, M.E.; Chan, K.W.C.; Verma, P.K. Multistage quantum secure communication using polarization hopping. Secur. Commun. Netw. 2015, 8, 4333–4342. [Google Scholar] [CrossRef]
 Alizo, M.T.D. Soft Processing Techniques for Quantum Key Distribution Applications, Politecnico di Torino Porto. Ph.D. Thesis, Politecnico di Torino, Torino, Italy, 2012. [Google Scholar]
 Darunkar, B.; Verma, P. The braided singlestage protocol for quantum secure communication. In Proceedings of the SPIE, Quantum Information and Computation XII, Baltimore, MD, USA, 22 May 2014; Volume 9123, pp. 1–8. [Google Scholar]
 Kak, S. A threestage Quantum Cryptography protocol. Found. Phys. Lett. 2006, 19, 293–296. [Google Scholar] [CrossRef] [Green Version]
 Chang, Y.; Zhang, S.; Yan, L.; Li, J. Deterministic secure quantum communication and authentication protocol based on threeparticle W state and quantum onetime pad. Chin. Sci. Bull. 2014, 59, 2835–2840. [Google Scholar] [CrossRef]
 Ellatif, A.A.A.; Abdelatty, B.; Hossain, M.S.; Samir, E.; Ghoneim, A. Secure Quantum Steganography Protocol for Fog Cloud Internet of Things. IEEE Access 2018, 6, 10332–10340. [Google Scholar] [CrossRef]
 Wu, L. Reconfigurable Optical Networks And MultiPhoton Quantum Cryptography. Ph.D. Thesis, University of Houston, Houston, TX, USA, 2015. [Google Scholar]
 Harun, N.Z.; Zukarnain, Z.A.; Hanapi, Z.M.; Ahmad, I. Hybrid MAry in Braided Single Stage Approach for Multiphoton Quantum Secure Direct Communication Protocol. IEEE Access 2019, 7, 22599–22612. [Google Scholar] [CrossRef]
 Li, Y.; Zhang, P.; Huang, R. Lightweight Quantum Encryption for Secure Transmission of Power Data in Smart Grid. IEEE Access 2019, 7, 36285–36293. [Google Scholar] [CrossRef]
 Chen, Y. Methods And Apparatuses For Authentication In Quantum Key Distribution And/Or Quantum Data Communication. U.S Patent 20180048466A1, 15 February 2018. [Google Scholar]
 Lai, X.; Fan, L.; Lei, X.; Li, J.; Yang, N.; Karagiannidis, G.K. Distributed Secure SwitchandStay Combining over Correlated Fading Channels. IEEE Trans. Inf. Forensics Secur. 2019, 14, 2088–2101. [Google Scholar] [CrossRef]
 Xu, Y.; Xia, J.; Wu, H.; Fan, L. QLearning Based PhysicalLayer Secure Game Against Multiagent Attacks. IEEE Access 2019, 7, 49212–49222. [Google Scholar] [CrossRef]
 Li, C.; Zhou, W.; Yu, K.; Fan, L.; Xia, J. Enhanced Secure Transmission Against Intelligent Attacks. IEEE Access 2019, 7, 53596–53602. [Google Scholar] [CrossRef]
 Thomas, J.H. Variations on Kak’s Three Stage Quantum Cryptography Protocol. arXiv 2007, arXiv:0706.2888, 1–7. [Google Scholar]
 Li, Q.; Le, D.; Wu, X.; Niu, X.; Guo, H. Efficient bit sifting scheme of postprocessing in quantum key distribution. Quantum Inf. Process. 2015, 14, 3785–3811. [Google Scholar] [CrossRef] [Green Version]
 Iwakoshi, T. On problems in security of quantum key distribution raised by Yuen. Quantum Inf. Sci. Technol. III 2017, 1044203, 3. [Google Scholar] [CrossRef] [Green Version]
 Chen, Y.; Kak, S.; Verma, P.K.; Macdonald, G.; El Rifai, M.; Punekar, N. Multiphoton tolerant secure quantum communication—From theory to practice. IEEE Int. Conf. Commun. 2013, 2111–2116. [Google Scholar] [CrossRef]
 Huang, W.; Xu, B.J.; Duan, J.T.; Liu, B.; Su, Q.; He, Y.H.; Jia, H.Y. Authenticated Quantum Key Distribution with Collective Detection using Single Photons. Int. J. Theor. Phys. 2016, 55, 4238–4256. [Google Scholar] [CrossRef]
 Li, C.M.; Yu, K.F.; Kao, S.H.; Hwang, T. Authenticated semiquantum key distributions without classical channel. Quantum Inf. Process. 2016, 15, 2881–2893. [Google Scholar] [CrossRef]
 Kak, S. Authentication Using Piggy Bank Approach to Secure DoubleLock Cryptography. arXiv 2014, arXiv:1411.3645, 1–8. [Google Scholar]
 Abushgra, A.; Elleithy, K. A Shared Secret Key Initiated by EPR Authentication and Qubit Transmission Channels. IEEE Access 2017, 17753–17763. [Google Scholar] [CrossRef]
 Darunkar, B.A. MultiPhoton Tolerant Quantum Key Distribution Protocols For Secured Global Communication. Ph.D. Thesis, University Of Oklahoma, Norman, OK, USA, 2017. [Google Scholar]
 Darunkar, B.; Punekar, N.; Verma, P.K. Secure Satellite Communication Using MultiPhoton tolerant quantum communication protocol. In Proceedings of the Quantum Communications and Quantum Imaging XIII, San Diego, CA, USA, 1 September 2015; Volume 9615, p. 961509. [Google Scholar]
 Verma, P.K.; El Rifai, M.; Chan, K.W.C. MultiPhoton Quantum Secure Communication; Springer: Singapore, 2019; ISBN 9789811086175. [Google Scholar]
 Liu, Z.H.; Chen, H.W.; Liu, W.J. Information Leakage Problem in Efficient Bidirectional Quantum Secure Direct Communication with Single Photons in Both Polarization and SpatialMode Degrees of Freedom. Int. J. Theor. Phys. 2016, 55, 4681–4686. [Google Scholar] [CrossRef]
 Ghilen, A.; Belmabrouk, H.; Bouallegue, R. Classification of quantum authentication protocols and calculation of their complexity. In Proceedings of the 15th International Conference on Sciences and Techniques of Automatic Control & Computer Engineering, Hammamet, Tunisia, 21–23 December 2014; pp. 169–173. [Google Scholar]
 Guedes, E.B.; de Assis, F.M. An Approach To Evaluate Quantum Authentication Protocols. In Proceedings of the Congresso Brasileiro de Inteligência Computacional, Fortaleza, Brazil, 8–11 November 2011; pp. 1–8. [Google Scholar]
 Wang, L.; Ma, W. Controlled quantum secure communication protocol with single photons in both polarization and spatialmode degrees of freedom. Mod. Phys. Lett. B 2016, 30, 1650051. [Google Scholar] [CrossRef]
 Wang, L.L.; Ma, W.P.; Wang, M.L.; Shen, D.S. Threeparty Quantum Secure Direct Communication with Single Photons in both Polarization and Spatialmode Degrees of Freedom. Int. J. Theor. Phys. 2016, 55, 2490–2499. [Google Scholar] [CrossRef]
Protocol  IV ThreeStage  Braided Single Stage  Proposed Protocol 

1. Public Communication (preshared angle)  Yes  Yes  No 
2. Authentication key  Yes  No  Yes 
3. No. of HWP for information exchange  7  5  5 
4. Information exchange stage  3 times  1 times  1 times 
5.Quantum communication complexity of authentication  ${Q}^{*}\left({f}_{I}\right)=\Omega \left(3n+3IV\right)$  ${Q}^{*}\left({f}_{I}\right)=\Omega \left(3n\right)$  $Q\left({f}_{I}\right)=5n$ 
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Harun, N.Z.; Ahmad Zukarnain, Z.; Hanapi, Z.M.; Ahmad, I. MultiStage Quantum Secure Direct Communication Using Secure Shared Authentication Key. Symmetry 2020, 12, 1481. https://doi.org/10.3390/sym12091481
Harun NZ, Ahmad Zukarnain Z, Hanapi ZM, Ahmad I. MultiStage Quantum Secure Direct Communication Using Secure Shared Authentication Key. Symmetry. 2020; 12(9):1481. https://doi.org/10.3390/sym12091481
Chicago/Turabian StyleHarun, Nur Ziadah, Zuriati Ahmad Zukarnain, Zurina Mohd Hanapi, and Idawaty Ahmad. 2020. "MultiStage Quantum Secure Direct Communication Using Secure Shared Authentication Key" Symmetry 12, no. 9: 1481. https://doi.org/10.3390/sym12091481