# Efficient Authentication Protocol and Its Application in Resonant Inductive Coupling Wireless Power Transfer Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Related Work

#### 1.2. Organization

## 2. Preliminaries

#### 2.1. Wireless Power Transfer Scenario

#### 2.2. Chebyshev Chaotic Map

#### 2.3. Hard Problem

- (1)
- Quadratic Residue Assumption: Given p and q as two large primes and n = p ∗ q. Let the symbol ${QR}_{n}$ denote the set of all quadratic residues in [1, n − 1]. If ${y=x}^{2}modn$ has a solution, i.e., $\exists $ a square root for y, then y is named as a quadratic residue modulo n where $y\in {QR}_{n}$. To find x satisfying ${y=x}^{2}modn$ when p and q are unknown is computationally intractable since no polynomial algorithm has been found to solve the factoring problem.
- (2)
- Chaotic-based Discrete Logarithm (CDL) Problem: Given the variable x and the result y, it is infeasible to find the integer n, such that ${T}_{n}\left(x\right)\equiv ymodp$
- (3)
- Chaotic-based Diffie–Hellman (CDH) Problem: Given the variable x, ${T}_{n}\left(x\right)modp$ and ${T}_{m}\left(x\right)modp$, it is infeasible to compute ${T}_{nm}\left(x\right)modp$ without knowing n or m.

## 3. A Chaos-Based Authentication Key Exchange Scheme

- ▪
- First, the ER chooses integers r and y at random and computes x${=H}_{1}\left(y\right){,T}_{r}\left(x\right){=r}_{pub}{,k=y*r}_{pub}{,\mu =\left(k\right|\left|PW\right),r=\mu}^{2}{modn,EID}_{ER}{=U}_{ER}\oplus {H}_{2}\left(\mu \right){\mathrm{and}UAuth}_{ER}=$ ${H}_{2}\left({\mu ,T}_{r}\left(x\right){,T}_{1}{,EID}_{ER}\right).$ Here, ${T}_{1}$ is the initial timestamp. The ER sends ${C}_{1}{=\{UAuth}_{ER}{,r,T}_{r}\left(x\right){,T}_{1}{,EID}_{ER}\}$ to the ET.
- ▪
- Given C
_{1}, the ET validates whether ${T}_{2}-{T}_{1}\le \u25b3T$ is true or not. Here, ${T}_{2}$ is the ET’s current timestamp. Upon successful verification, the Chinese remainder theorem is used to solve R using p and q to get ${\mu}_{1},{\mu}_{2},{\mu}_{3},{\mu}_{4}$ and then the ET determines whether ${\mu}^{\prime}=\left({k}^{\prime}\right||P{W}^{\prime})$ by verifying whether ${UAuth}_{ER}{=H}_{2}{(\mu}_{i}{,T}_{r}\left(x\right){,T}_{2}{,EID}_{ER})$ for i = 1, 2, 3, 4. Subsequently, the ET computes ${U}_{ER}{=EID}_{ER}\oplus {H}_{2}{(\mu}^{\prime})$ and validates whether ${PW}^{\prime}=PW$ is right or not. If true, the ET successfully authenticates the ER and selects a random integer s and computes ${x=H}_{1}{(y}^{\prime})$, ${T}_{s}\left(x\right),\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{sr}\left(x\right))$, ${UAuth}_{ET}{=H}_{2}{(\gamma ,PW,U}_{ET}{,U}_{ER}{,T}_{2})$. The ET then sends ${C}_{2}{=\{UAuth}_{ET}{,U}_{ET}{,T}_{s}\left(x\right){,T}_{2}\}$ to the ER. - ▪
- It is verified whether ${T}_{3}-{T}_{2}\le \u25b3T$ is true or not once C
_{2}is received by the ER. Note that ${T}_{3}$ is the current timestamp here. The ER then computes ${\gamma}^{\prime}={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{sr}\left(x\right))$ and validates the rightness of ${UAuth}_{ET}{=H}_{2}{(\gamma}^{\prime}{,PW,U}_{ET}{,U}_{ER}{,T}_{2})$. Once verified as right, the ER successfully authenticates the ET; otherwise, the ER aborts this request. Now, the ER and the ET possess $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$. Thus, $\gamma $ is the shared session key, which is relevant for computing the switching frequency.

#### Security Analysis of the CBAKE Scheme

- Mutual Authentication: In the proposed scheme, the ET authenticates the ER by verifying ${H}_{2}\left({EID}_{ER}{,\mu}_{i}{,T}_{r}\left(x\right){,T}_{1}\right){=UAuth}_{ER}$ and ${PW}^{\prime}=PW$. Subsequently, the ER authenticates the ET by verifying ${H}_{2}{(\gamma}^{\prime}{,PW,U}_{ET}{,U}_{ER}{)=UAuth}_{ET}$ as stated in the third step, where ${\gamma}^{\prime}={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{s}{(T}_{r}\left(x\right)\left)\right)$. Hence, the proposed scheme has mutual authentication capability.
- Resistance to Replay Attack: The proposed scheme guarantees the freshness of the key due to the timestamps being utilized. These can be seen as follows: T
_{1}in C_{1}, T_{2}in C_{2}and T_{3}in C_{3}. Therefore, our proposed scheme prevents replaying attacks. - Contribution Property of Key Agreement: In the proposed scheme, the chaotic session key is $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$. In the process, no party is able to determine the session key alone since s and r are random numbers secretly generated by the power transmitter and the receiver, respectively. Notably, the proposed scheme satisfies the contribution feature of the key agreement.
- Private Key Security: Given T(·), T
_{r}(x) and T_{s}(x). T_{rs}(x) = T_{r}(T_{s}(x)) = T_{s}(T_{r}(x)), the session key $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$ cannot be calculated if r, s and x remain unknown, due to the chaotic maps Diffie–Hellman problem [46]. Therefore, the session key cannot be derived by an unauthorized user in our proposed CBAKE scheme. - Known Key Security: The session key $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$ generated in distinct rounds are not dependent on each other due to the fact that r, s and x are chosen randomly by the ER and the ET, respectively, and, in the scheme executions, they are independent of each other. Hence, the proposed scheme achieves the known-key security.
- Perfect Forward Secrecy: In our scheme, a false password PW will not result in any previous session key $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$ since the short-lived numbers r, s and x are picked randomly and independent among the executions of the scheme’s algorithms. More specifically, the proposed scheme has perfect forward secrecy. However, an attacker can use the strategy of Bergamo et al. [44] to realize the secret key y and derive previous session keys $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$, where ${x=H}_{1}\left(y\right)$ if the private keys p and q of T are known.
- Resistance to Password Guessing Attack: For ${V=H}_{2}{(EID}_{ER}{,\mu ,T}_{r}\left(x\right))$, where $\mu =\left(k\right|\left|PW\right)$, ${UAuth}_{ET}{=H}_{2}{(\gamma ,PW,U}_{ET}{,U}_{ER})$ involve password related information. Even though some of the messages are revealed, PW cannot be obtained due to the hash function ${H}_{2}(\xb7)$, which has a one-way property. Moreover, PW is protected by the secret value k. Additionally, there exists no information that can aid an attacker to directly confirm the authenticity of the guessed passwords. In this way, offline password guessing attacks fail with respect to our proposed scheme.
- User Anonymity: The temporary identity ${EID}_{ER}{=U}_{ER}\oplus {H}_{2}\left(\mu \right)$, where $\mu =\left(k\right|\left|PW\right)$ and k represent a random secret generated by the ER is not dependent on scheme executions. Therefore, ${ID}_{ER}$ cannot be obtained from ${EID}_{ER}$ when k, PW and likewise ${ID}_{ET}$ are unknown. Moreover, due to the quadratic residue assumption, one cannot decipher $\mu $ from R if the power transmitter’s secret keys p and q are not known, where ${R=\mu}^{2}modn$. In addition, ${U}_{ER}$ and ${U}_{ET}$ cannot be generated from ${UAuth}_{ER}{=H}_{2}{(\gamma ,U}_{ER}{,U}_{ET})$, ${UAuth}_{ET}{=H}_{2}{(\gamma ,PWU}_{ER}{,U}_{ET})$ because of the inherent one-way property of the hash function. Hence, our proposed CBAKE scheme achieves the user anonymity feature.

## 4. Performance Analysis

## 5. Application to WPT System

_{ET}. C

_{ET}is computed as follows: if the chaotic session key for both parties is the Chebyshev polynomial $\gamma ={H}_{2}{(T}_{r}\left(x\right){,T}_{s}\left(x\right){,T}_{rs}\left(x\right))$ then the ET can compute a switching frequency as ${\beta}_{ET}{=\gamma}_{i}{\omega}_{0},\forall i0.$ Assuming ${\omega}_{ET}={\beta}_{ET}$ then the ET can compute C

_{ET}as:

_{ER}. C

_{ER}is computed as follows:

#### Functionality Comparison

## 6. Open Research Problems

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Tesla, N. Experiments with Alternate Currents of Very High Frequency and their Application to Methods of Artificial Illumination. Trans. Am. Inst. Electr. Eng.
**1891**, VIII, 266–319. [Google Scholar] [CrossRef] - Kurs, A.; Karalis, A.; Moffatt, R.; Joannopoulos, J.D.; Fisher, P.; Soljačic, M. Wireless Power Transfer via Strongly Coupled Magnetic Resonances. Science
**2007**, 317, 83–86. [Google Scholar] [CrossRef] [Green Version] - Das, S.; Wasif, A.; Kumar, N.; Karim, E. Wireless powering by magnetic resonant coupling: Recent trends in wireless power transfer system and its applications. Renew. Sustain. Energy Rev.
**2015**, 51, 1525–1552. [Google Scholar] - Liu, Q.; Yildirim, K.S.; Pawełczak, P.; Warnier, M. Safe and secure wireless power transfer networks: Challenges and opportunities in RF-based systems. IEEE Commun. Mag.
**2016**, 54, 74–79. [Google Scholar] [CrossRef] - Shinohara, N. Wireless Power Transfer via Radiowaves; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2014. [Google Scholar]
- Lee, C.K.; Zhong, W.X.; Hui, S.Y.R. Recent progress in mid-range wireless power transfer. In Proceedings of the 2012 IEEE Energy Conversion Congress and Exposition, ECCE 2012, Raleigh, NC, USA, 15–20 September 2012. [Google Scholar]
- Huh, J.; Lee, S.W.; Lee, W.Y.; Cho, G.H.; Rim, C.T. Narrow-Width Inductive Power Transfer System for Online Electrical Vehicles. IEEE Trans. Power Electron.
**2011**, 26, 3666–3679. [Google Scholar] [CrossRef] - Jawad, A.M.; Nordin, R.; Gharghan, S.K.; Jawad, H.M.; Ismail, M. Opportunities and Challenges for Near-Field Wireless Power Transfer: A Review. Energies
**2017**, 10, 1022. [Google Scholar] [CrossRef] - Zhang, Z.; Chau, K.T.; Wang, Z.; Li, W. Improvement of Electromagnetic Compatibility of Motor Drives Using Hybrid Chaotic Pulse Width Modulation. IEEE Trans. Magn.
**2011**, 47, 4018–4021. [Google Scholar] [CrossRef] - Ye, S.; Chau, K.T. Chaoization of DC Motors for Industrial Mixing. IEEE Trans. Ind. Electron.
**2007**, 54, 2024–2032. [Google Scholar] [CrossRef] [Green Version] - Budhia, M.; Boys, J.T.; Covic, G.A.; Huang, C.-Y. Development of a Single-Sided Flux Magnetic Coupler for Electric Vehicle IPT Charging Systems. IEEE Trans. Ind. Electron.
**2013**, 60, 318–328. [Google Scholar] [CrossRef] - Lee, W.Y.; Huh, J.; Choi, S.Y.; Thai, X.V.; Kim, J.H.; Al-Ammar, E.; El-Kady, M.A.; Rim, C.T. Finite-Width Magnetic Mirror Models of Mono and Dual Coils for Wireless Electric Vehicles. IEEE Trans. Power Electron.
**2013**, 28, 1413–1428. [Google Scholar] [CrossRef] - Zhang, Z.; Chau, K.T.; Qiu, C.; Liu, C. Energy Encryption for Wireless Power Transfer. IEEE Trans. Power Electron.
**2015**, 30, 5237–5246. [Google Scholar] [CrossRef] - Zhang, Z.; Chau, K.T.; Liu, C.; Qiu, C. Energy-security-based contactless battery charging system for roadway-powered electric vehicles. In Proceedings of the 2015 IEEE PELS Workshop on Emerging Technologies: Wireless Power (2015 WoW), Daejeon, Korea, 5–6 June 2015. [Google Scholar]
- Liu, W.; Chau, K.T.; Lee, C.H.T.; Jiang, C.; Han, W. A Switched-Capacitorless Energy-Encrypted Transmitter for Roadway-Charging Electric Vehicles. IEEE Trans. Magn.
**2018**, 54, 1–6. [Google Scholar] [CrossRef] - Lee, K.; Pantic, Z.; Lukic, S. Reflexive Field Containment in Dynamic Inductive Power Transfer Systems. IEEE Trans. Power Electron.
**2014**, 29, 4592–4602. [Google Scholar] [CrossRef] - Cannon, B.L.; Hoburg, J.F.; Stancil, D.D.; Goldstein, S.C. Magnetic Resonant Coupling as a Potential Means for Wireless Power Transfer to Multiple Small Receivers. IEEE Trans. Power Electron.
**2009**, 24, 1819–1825. [Google Scholar] [CrossRef] [Green Version] - Madawala, U.K.; Thrimawithana, D.J. A Bidirectional Inductive Power Interface for Electric Vehicles in V2G Systems. IEEE Trans. Ind. Electron.
**2011**, 58, 4789–4796. [Google Scholar] [CrossRef] - Nadeau, P.; Mimee, M.; Carim, S.; Lu, T.K.; Chandrakasan, A.P. 21.1 Nanowatt Circuit Interface to Whole-Cell Bacterial. In ISSCC 2017/Session 21/Smart SoCs for Innovative Applications; IEEE: Piscataway, NJ, USA, 2017; pp. 352–354. [Google Scholar]
- Ahene, E.; Ofori-Oduro, M.; Agyemang, B. Secure Energy Encryption for Wireless Power Transfer. In Proceedings of the 2017 IEEE 7th International Advance Computing Conference (IACC), Hyderabad, India, 5–7 January 2017; pp. 199–204. [Google Scholar]
- Cai, C.; Yang, M.; Qin, M.; Wu, S. High Transmission Capacity P.U.A Wireless Power Transfer for AUV Using an Optimized Magnetic Coupler. In Proceedings of the 2018 IEEE International Magnetics Conference (INTERMAG), Singapore, 23–27 April 2018; IEEE: Piscataway, NJ, USA, 2018; pp. 1–2. [Google Scholar]
- Diffie, W.; Hellman, M.E. New directions in cryptography. IEEE Trans. Inf. Theory
**1976**, 22, 644–654. [Google Scholar] [CrossRef] [Green Version] - Lee, C.-C.; Hsu, C.-W. A secure biometric-based remote user authentication with key agreement scheme using extended chaotic maps. Nonlinear Dyn.
**2012**, 71, 201–211. [Google Scholar] [CrossRef] - Tan, Z. A chaotic maps-based authenticated key agreement protocol with strong anonymity. Nonlinear Dyn.
**2013**, 72, 311–320. [Google Scholar] [CrossRef] - Xiang, T.; Wong, K.-W.; Liao, X. On the security of a novel key agreement protocol based on chaotic maps. Chaos Solitons Fractals
**2009**, 40, 672–675. [Google Scholar] [CrossRef] - Lee, C.-C.; Chen, C.-L.; Wu, C.-Y.; Huang, S.-Y. An extended chaotic maps-based key agreement protocol with user anonymity. Nonlinear Dyn.
**2012**, 69, 79–87. [Google Scholar] [CrossRef] - Alvarez, E.; Fernández, A.; Garcia, P.; Jiménez, J.; Marcano, A. New approach to chaotic encryption. Phys. Lett. A
**1999**, 263, 373–375. [Google Scholar] [CrossRef] - Baptista, M. Cryptography with chaos. Phys. Lett. A
**1998**, 240, 50–54. [Google Scholar] [CrossRef] - Wong, K. A fast chaotic cryptographic scheme with dynamic look-up table. Phys. Lett. A
**2002**, 298, 238–242. [Google Scholar] [CrossRef] - Zhao, G.; Wang, J.; Lu, F. Analysis of Some Recently Proposed Chaos-based Public Key Encryption Algorithms. In Proceedings of the 2006 International Conference on Communications, Circuits and Systems, Guilin, China, 25–28 June 2006. [Google Scholar]
- Xiao, D.; Liao, X.; Deng, S. A novel key agreement protocol based on chaotic maps. Inf. Sci.
**2007**, 177, 1136–1142. [Google Scholar] [CrossRef] - Zhu, H.; Hao, X. A provable authenticated key agreement protocol with privacy protection using smart card based on chaotic maps. Nonlinear Dyn.
**2015**, 81, 311–321. [Google Scholar] [CrossRef] - Srinivas, J.; Das, A.K.; Wazid, M.; Kumar, N. Anonymous Lightweight Chaotic Map-Based Authenticated Key Agreement Protocol for Industrial Internet of Things. IEEE Trans. Dependable Secur. Comput.
**2020**, 17, 1133–1146. [Google Scholar] [CrossRef] - Mood, D.A.; Nikooghadam, M. Efficient Anonymous Password-Authenticated Key Exchange Protocol to Read Isolated Smart Meters by Utilization of Extended Chebyshev Chaotic Maps. IEEE Trans. Ind. Inform.
**2018**, 14, 1. [Google Scholar] [CrossRef] - Irshad, A.; Sher, M.; Chaudhry, S.A.; Xie, Q.; Kumari, S.; Wu, F. An improved and secure chaotic map based authenticated key agreement in multi-server architecture. Multimed. Tools Appl.
**2018**, 77, 1167–1204. [Google Scholar] [CrossRef] - Wang, X.; Zhao, J. An improved key agreement protocol based on chaos. Commun. Nonlinear Sci. Numer. Simul.
**2010**, 15, 4052–4057. [Google Scholar] [CrossRef] - Irshad, A.; Ahmad, H.F.; Alzahrani, B.A.; Sher, M.; Chaudhry, S.A. An efficient and anonymous Chaotic Map based authenticated key agreement for multi-server architecture. KSII Trans. Internet Inf. Syst.
**2016**, 10, 5572–5595. [Google Scholar] [CrossRef] - Tan, Z. A privacy-preserving multi-server authenticated key-agreement scheme based on Chebyshev chaotic maps. Secur. Commun. Networks
**2016**, 9, 1384–1397. [Google Scholar] [CrossRef] [Green Version] - Li, J.L. Wireless Power Transmission: State-of-the-Arts in Technologies and Potential Applications. In Proceedings of the Asia-Pacific Microwave Conference 2011, Melbourne, VIC, Australia, 5–8 December 2011. [Google Scholar]
- Wu, K.; Choudhury, D.; Matsumoto, H. Wireless Power Transmission, Technology, and Applications [Scanning the Issue]. Proc. IEEE
**2013**, 101, 1271–1275. [Google Scholar] [CrossRef] - Mou, X.; Sun, H. Wireless Power Transfer: Survey and Roadmap. In Proceedings of the 2015 IEEE 81st Vehicular Technology Conference (VTC Spring), Glasgow, UK, 11–14 May 2015. [Google Scholar]
- Mohammed, S.S.; Ramasamy, K.; Shanmuganantham, T. Wireless Power Transmission—A Next Generation Power Transmission System. Int. J. Comput. Appl.
**2010**, 1, 102–105. [Google Scholar] [CrossRef] - Geiser, J. Coupled Systems: Theory, Models, and Applications in Engineering; Chapman and Hall/CRC: Boca Raton, FL, USA, 2014. [Google Scholar]
- Kocarev, L.; Tasev, Z. Public-key encryption based on Chebyshev maps. In Proceedings of the 2003 International Symposium on Circuits and Systems, Bangkok, Thailand, 25–28 May 2003; pp. 28–31. [Google Scholar]
- Zhang, L. Cryptanalysis of the public key encryption based on multiple chaotic systems. Chaos Solitons Fractals
**2008**, 37, 669–674. [Google Scholar] [CrossRef] - Shoup, V.A. Computational Introduction to Number Theory and Algebra; Cambridge University Press: Cambridge, UK, 2015. [Google Scholar]
- Lima, J.; De Souza, R.M.C.; Panario, D. Security of public-key cryptosystems based on Chebyshev polynomials over prime finite fields. In Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, 6–11 July 2008. [Google Scholar]
- Gong, P.; Li, P.; Shi, W. A secure chaotic maps-based key agreement protocol without using smart cards. Nonlinear Dyn.
**2012**, 70, 2401–2406. [Google Scholar] [CrossRef] - Islam, S.K.H. Provably secure dynamic identity-based three-factor password authentication scheme using extended chaotic maps. Nonlinear Dyn.
**2014**, 78, 2261–2276. [Google Scholar] [CrossRef] - Jiang, Q.; Wei, F.; Fu, S.; Ma, J.; Li, G.; Alelaiwi, A. Robust extended chaotic maps-based three-factor authentication scheme preserving biometric template privacy. Nonlinear Dyn.
**2015**, 83, 2085–2101. [Google Scholar] [CrossRef] - Lin, H.-Y. Improved chaotic maps-based password-authenticated key agreement using smart cards. Commun. Nonlinear Sci. Numer. Simul.
**2015**, 20, 482–488. [Google Scholar] [CrossRef] - Zhu, H.; Hao, X.; Liu, H. An Efficient Authenticated Key Agreement Protocol Based on Chaotic Maps with Privacy Protection using Smart Card. J. Inf. Hiding Multimed. Signal Process.
**2015**, 6, 500–510. [Google Scholar] - Cheng, G.; Chin-Chen, C. Chaotic maps-based password-authenticated key agreement using smart cards. Commun. Nonlinear Sci. Numer. Simul.
**2013**, 18, 1433–1440. [Google Scholar] [CrossRef] - Chang, Y.-F.; Tai, W.-L.; Wu, W.-N.; Li, W.-H.; Chen, Y.-C. Comments on Chaotic Maps-Based Password-Authenticated Key Agreement Using Smart Cards. In Proceedings of the 2014 Tenth International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2014, Kitakyushu, Japan, 27–29 August 2014. [Google Scholar]
- Burmester, M.; de Medeiros, B.; Motta, R. Robust, anonymous RFID authentication with constant key-lookup. In Proceedings of the 2008 ACM Symposium on Information, Computer and Communications Security, ASIACCS 2008, Tokyo, Japan, 18–20 March 2008. [Google Scholar]
- Chen, Y.; Chou, J.-S.; Sun, H.-M. A novel mutual authentication scheme based on quadratic residues for RFID systems. Comput. Netw.
**2008**, 52, 2373–2380. [Google Scholar] [CrossRef]

Schemes | Computation Cost | Computation Time in Seconds | F1 | F2 | F3 | F4 |
---|---|---|---|---|---|---|

[35] | 49T_{H} + 10T_{C} + 2T_{S} | 0.25602 | No | Yes | Strong | Yes |

[38] | 43T_{H} + 10T_{C} | 0.23534 | No | Yes | Weak | Yes |

[47] | 18T_{H} + 10T_{C} | 0.22084 | No | No | Weak | Yes |

[48] | 7T_{H} + 4T_{C} | 0.0882 | Yes | No | Weak | Yes |

[49] | 5T_{H} + 6T_{C} + 5T_{S} | 0.17214 | No | No | Weak | Yes |

[50] | 12T_{H} + 4T_{C} | 0.09112 | No | No | Weak | Yes |

[51] | 5T_{H} + 4T_{C} + 5T_{S} | 0.13006 | No | No | Weak | No |

[53] | 21T_{H} + 6T_{C} | 0.13842 | No | Yes | Strong | Yes |

[54] | 9T_{H} + 4T_{C} | 0.08938 | No | Yes | Strong | Yes |

Ours | 13T_{H} + 4T_{C} + T_{SQ} + T_{SR} | 0.20337 | Yes | Yes | Strong | Yes |

Notation | Meaning |
---|---|

F1 | Non-usage of extra device such as smartcard |

F2 | Supports user anonymity |

F3 | Resistance to possible attacks |

F4 | Supports perfect forward secrecy |

TH | Time for executing a hash function |

TC | Time for executing a chaotic map operation |

TS | Time for executing a symmetric encryption or decryption operation |

TSQ | Time for executing a squaring operation |

TSR | Time for executing a square root operation |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ahene, E.; Ofori-Oduro, M.; Twum, F.; Walker, J.; Missah, Y.M.
Efficient Authentication Protocol and Its Application in Resonant Inductive Coupling Wireless Power Transfer Systems. *Sensors* **2021**, *21*, 8245.
https://doi.org/10.3390/s21248245

**AMA Style**

Ahene E, Ofori-Oduro M, Twum F, Walker J, Missah YM.
Efficient Authentication Protocol and Its Application in Resonant Inductive Coupling Wireless Power Transfer Systems. *Sensors*. 2021; 21(24):8245.
https://doi.org/10.3390/s21248245

**Chicago/Turabian Style**

Ahene, Emmanuel, Mark Ofori-Oduro, Frimpong Twum, Joojo Walker, and Yaw Marfo Missah.
2021. "Efficient Authentication Protocol and Its Application in Resonant Inductive Coupling Wireless Power Transfer Systems" *Sensors* 21, no. 24: 8245.
https://doi.org/10.3390/s21248245