# Optimizing Security and Cost Efficiency in N-Level Cascaded Chaotic-Based Secure Communication System

^{*}

## Abstract

**:**

## 1. Introduction

- 1.
- Introduce a novel N-level cascaded chaotic-based secure communication system for voice encryption using the 4D unified hyperchaotic system.
- 2.
- Investigate the effect of increasing the number of cascaded levels on encryption quality.
- 3.
- Implement the proposed system on FPGA and analyze its performance using various parameters.
- 4.
- Analyze the effect of increasing the number of cascaded levels from N = 1 to N = 20 to reach the best performance by measuring various of metrics.
- 5.
- Introduce VBPM as a new performance metric for evaluating the system’s overall performance.
- 6.
- Demonstrate the superiority of the proposed system compared to other related works in terms of security and efficiency.

## 2. Model Description of the N-Levels Cascaded Chaotic-Based Secure Communication System for Voice Encryption

- 1.
- When ${a}_{4}=13$, the output hyperchaotic attractor is similar to Lorenz attractor.
- 2.
- When ${a}_{4}=27$, the output hyperchaotic attractor is similar to Lu attractor.
- 3.
- When ${a}_{4}=36$, the attractor is similar to Chen attractor.

**Assumption 1.**

**Assumption 2.**

## 3. Hardware Implementation

**Cyclon V**platform. We use the 32-bits fixed-point arithmetic representation for all the variables and constants for the FPGA implementation. This representation has 1-bit for the sign, 7-bits for the integer part, and 24-bits for the fractional part.

## 4. Numerical Simulation

#### 4.1. Signal-to-Noise Ratio (SNR)

#### 4.2. Peak Signal-to-Noise Ratio (PSNR)

#### 4.3. Percent Residual Deviation (PRD)

#### 4.4. Correlation Coefficient (CC) Analysis

#### 4.5. Timing Analysis

## 5. Experimental Results

#### Comparison with Existing Work

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lorenz, E.N. Deterministic nonperiodic flow. J. Atmos. Sci.
**1963**, 20, 130–141. [Google Scholar] [CrossRef] - Rössler, O.E. Continuous chaos—Four prototype equations. Ann. N. Y. Acad. Sci.
**1979**, 316, 376–392. [Google Scholar] [CrossRef] - Rajagopal, K.; Jahanshahi, H.; Varan, M.; Bayır, I.; Pham, V.T.; Jafari, S.; Karthikeyan, A. A hyperchaotic memristor oscillator with fuzzy based chaos control and LQR based chaos synchronization. AEU-Int. J. Electron. Commun.
**2018**, 94, 55–68. [Google Scholar] [CrossRef] - Matsumoto, T.; Chua, L.; Komuro, M. The double scroll. IEEE Trans. Circuits Syst.
**1985**, 32, 797–818. [Google Scholar] [CrossRef] - Holmes, P. A nonlinear oscillator with a strange attractor. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1979**, 292, 419–448. [Google Scholar] - Hénon, M. A two-dimensional mapping with a strange attractor. In The Theory of Chaotic Attractors; Springer: Berlin/Heidelberg, Germany, 1976; pp. 94–102. [Google Scholar]
- Sprott, J.C.; Sprott, J.C. Chaos and Time-Series Analysis; Oxford University Press: Oxford, UK, 2003; Volume 69, Available online: https://test-sprott.physics.wisc.edu/chaostsa/answers/SOLUTIONS.pdf (accessed on 25 July 2024).
- Beyene, G.A.; Rahma, F.; Rajagopal, K.; Al-Hussein, A.B.A.; Boulaaras, S. Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation. J. Nonlinear Math. Phys.
**2023**, 30, 1375–1391. [Google Scholar] [CrossRef] - Fa-Qiang, W.; Chong-Xin, L. Hyperchaos evolved from the Liu chaotic system. Chin. Phys.
**2006**, 15, 963. [Google Scholar] [CrossRef] - Bonny, T.; Al Debsi, R.; Majzoub, S.; Elwakil, A.S. Hardware optimized fpga implementations of high-speed true random bit generators based on switching-type chaotic oscillators. Circuits Syst. Signal Process.
**2019**, 38, 1342–1359. [Google Scholar] [CrossRef] - Muthuswamy, B. Implementing memristor based chaotic circuits. Int. J. Bifurc. Chaos
**2010**, 20, 1335–1350. [Google Scholar] [CrossRef] - Sambas, A.; Miroslav, M.; Vaidyanathan, S.; Ovilla-Martínez, B.; Tlelo-Cuautle, E.; Abd El-Latif, A.A.; Abd-El-Atty, B.; Benkouider, K.; Bonny, T. A New Hyperjerk System with a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design and an Application to Image Encryption. IEEE Access
**2024**, 12, 9177–9194. [Google Scholar] [CrossRef] - Bernstein, D.J.; Lange, T. Post-quantum cryptography. Nature
**2017**, 549, 188–194. [Google Scholar] [CrossRef] [PubMed] - Pan, D.; Lin, Z.; Wu, J.; Zhang, H.; Sun, Z.; Ruan, D.; Yin, L.; Long, G.L. Experimental free-space quantum secure direct communication and its security analysis. Photonics Res.
**2020**, 8, 1522–1531. [Google Scholar] [CrossRef] - Zhang, J.; Rajendran, S.; Sun, Z.; Woods, R.; Hanzo, L. Physical layer security for the Internet of Things: Authentication and key generation. IEEE Wirel. Commun.
**2019**, 26, 92–98. [Google Scholar] [CrossRef] - Nakamura, Y.; Sekiguchi, A. The chaotic mobile robot. IEEE Trans. Robot. Autom.
**2001**, 17, 898–904. [Google Scholar] [CrossRef] - Li, C.H.; Song, Y.; Wang, F.Y.; Wang, Z.Q.; Li, Y.B. A chaotic coverage path planner for the mobile robot based on the Chebyshev map for special missions. Front. Inf. Technol. Electron. Eng.
**2017**, 18, 1305–1319. [Google Scholar] [CrossRef] - AlMutairi, F.; Bonny, T. New Image Encryption Algorithm Based on Switching-type Chaotic Oscillator. In Proceedings of the 2019 International Conference on Electrical and Computing Technologies and Applications (ICECTA), Ras Al Khaimah, United Arab Emirates, 19–21 November 2019; pp. 1–5. [Google Scholar]
- Chen, G.; Zhou, J.; Liu, Z. Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. Int. J. Bifurc. Chaos
**2004**, 14, 2229–2240. [Google Scholar] [CrossRef] - Bonny, T.; Nasir, Q. Clock glitch fault injection attack on an FPGA-based non-autonomous chaotic oscillator. Nonlinear Dyn.
**2019**, 96, 2087–2101. [Google Scholar] [CrossRef] - Manhil, M.M.; Jamal, R.K. A novel secure communication system using Duffing’s chaotic model. Multimed. Tools Appl.
**2024**, 1–14. [Google Scholar] [CrossRef] - Karawanich, K.; Chimnoy, J.; Khateb, F.; Marwan, M.; Prommee, P. Image cryptography communication using FPAA-based multi-scroll chaotic system. Nonlinear Dyn.
**2024**, 112, 4951–4976. [Google Scholar] [CrossRef] - Cuomo, K.M.; Oppenheim, A.V.; Strogatz, S.H. Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process.
**1993**, 40, 626–633. [Google Scholar] [CrossRef] - Cuomo, K.M.; Oppenheim, A.V. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett.
**1993**, 71, 65. [Google Scholar] [CrossRef] [PubMed] - Abd, M.H.; Tahir, F.R.; Al-Suhail, G.A.; Pham, V.T. An adaptive observer synchronization using chaotic time-delay system for secure communication. Nonlinear Dyn.
**2017**, 90, 2583–2598. [Google Scholar] [CrossRef] - Hussein, E.A.; Khashan, M.K.; Jawad, A.K. A high security and noise immunity of speech based on double chaotic masking. Int. J. Electr. Comput. Eng.
**2020**, 10, 4270. [Google Scholar] [CrossRef] - Busawon, K.; Canyelles-Pericas, P.; Binns, R.; Elliot, I.; Ghassemlooy, Z. A brief survey and some discussions on chaos-based communication schemes. In Proceedings of the 2018 11th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP), Budapest, Hungary, 18–20 July 2018; pp. 1–5. [Google Scholar]
- Short, K.M. Steps toward unmasking secure communications. Int. J. Bifurc. Chaos
**1994**, 4, 959–977. [Google Scholar] [CrossRef] - Yuan, F.; Bai, C.J.; Li, Y.X. Cascade discrete memristive maps for enhancing chaos. Chin. Phys. B
**2021**, 30, 120514. [Google Scholar] [CrossRef] - Yuan, F.; Li, Y.; Wang, G. A universal method of chaos cascade and its applications. Chaos Interdiscip. J. Nonlinear Sci.
**2021**, 31, 021102. [Google Scholar] [CrossRef] - Kharel, R. Design and Implementation of Secure Chaotic Communication Systems. Ph.D. Thesis, Northumbria University, Newcastle upon Tyne, UK, 2011. [Google Scholar]
- Zhang, G.; Ding, W.; Li, L. Image encryption algorithm based on tent delay-sine cascade with logistic map. Symmetry
**2020**, 12, 355. [Google Scholar] [CrossRef] - Liu, Y.; Xie, Y.; Ye, Y.; Zhang, J.; Wang, S.; Liu, Y.; Pan, G.; Zhang, J. Exploiting Optical Chaos With Time-Delay Signature Suppression for Long-Distance Secure Communication. IEEE Photonics J.
**2017**, 9, 1–12. [Google Scholar] [CrossRef] - Pan, J.; Ding, Q.; Du, B. A new improved scheme of chaotic masking secure communication based on Lorenz system. Int. J. Bifurc. Chaos
**2012**, 22, 1250125. [Google Scholar] [CrossRef] - Zhou, Y.; Hua, Z.; Pun, C.M.; Chen, C.P. Cascade chaotic system with applications. IEEE Trans. Cybern.
**2014**, 45, 2001–2012. [Google Scholar] [CrossRef] - Waried, H.H. Synchronization of quantum cascade lasers with mutual optoelectronic coupling. Chin. J. Phys.
**2018**, 56, 1113–1120. [Google Scholar] [CrossRef] - Yu, Z.; Du, B.; Kong, D.; Chai, Z. A 4D conservative chaotic system: Dynamics and realization. Phys. Scr.
**2024**, 99, 085263. [Google Scholar] [CrossRef] - Wang, X.Y.; Zhao, G.B. Hyperchaos generated from the unified chaotic system and its control. Int. J. Mod. Phys. B
**2010**, 24, 4619–4637. [Google Scholar] [CrossRef] - Bonny, T.; Nassan, W.A.; Baba, A. Voice encryption using a unified hyper-chaotic system. Multimed. Tools Appl.
**2022**, 1–19. [Google Scholar] [CrossRef] - Al Nassan, W.; Bonny, T.; Baba, A. A New Chaos-Based Cryptoystem for Voice Encryption. In Proceedings of the 2020 3rd International Conference on Signal Processing and Information Security (ICSPIS), Dubai, United Arab Emirates, 25–26 November 2020; pp. 1–4. [Google Scholar]
- Mohamed, M.A.; Bonny, T.; Sambas, A.; Vaidyanathan, S.; Nassan, W.A.; Zhang, S.; Obaideen, K.; Mamat, M.; Nawawi, M.; Kamal, M. A Speech Cryptosystem Using the New Chaotic System with a Capsule-Shaped Equilibrium Curve. Comput. Mater. Contin.
**2023**, 75. Available online: https://www.techscience.com/cmc/v75n3/52569 (accessed on 25 July 2024). - Bashier, E. Speech scrambling based on chaotic maps and one-time pad, Computing, Electrical and Electronics Engineering (ICCEEE). In Proceedings of the International Conference on Computing, Electrical and Electronic Engineering (ICCEEE), Khartoum, Sudan, 26–28 August 2013; pp. 128–133. [Google Scholar]
- Sheela, S.; Suresh, K.; Tandur, D. Chaos based speech encryption using modified Henon map. In Proceedings of the 2017 Second International Conference on Electrical, Computer and Communication Technologies (ICECCT), Coimbatore, India, 22–24 February 2017; pp. 1–7. [Google Scholar]
- Sathiyamurthi, P.; Ramakrishnan, S. Speech encryption using chaotic shift keying for secured speech communication. EURASIP J. Audio Speech Music Process.
**2017**, 2017, 1–11. [Google Scholar] [CrossRef] - Yousif, S.F. Speech Encryption Based on Zaslavsky Map. J. Eng. Appl. Sci.
**2019**, 14, 6392–6399. [Google Scholar] [CrossRef] - Kordov, K. A novel audio encryption algorithm with permutation-substitution architecture. Electronics
**2019**, 8, 530. [Google Scholar] [CrossRef] - Gebereselassie, S.A.; Roy, B.K. A new Secure Speech Communication Scheme Based on Hyperchaotic Masking and Modulation. IFAC-PapersOnLine
**2022**, 55, 914–919. [Google Scholar] [CrossRef] - Paul, B.; Trivedi, G. Post quantum cryptography algorithms: A review and applications. In Proceedings of the 7th ASRES International Conference on Intelligent Technologies, Jakarta, Indonesia, 16–18 December 2022; Springer: Singapore, 2022; pp. 3–17. [Google Scholar]

Ref. | Used Chaotic Systems | Levels of Masking |
---|---|---|

[34] 2012 | Lorenz System | 1, 2 |

[35] 2014 | Seed map | 2 |

[33] 2017 | Optical chaos with TD signature suppression | 3 |

[25] 2017 | Lur’e system | 1, 2 |

[36] 2018 | Quantum cascade lasers | 2 |

[32] 2020 | Tent Delay-Sine cascade with Logistic Map | 2 |

[26] 2020 | Rossler chaotic flow system | 1, 2 |

[29] 2021 | discrete memristive maps | 2, 3 |

**Table 2.**FPGA resource utilization and maximum operating frequency for the N-level chaotic-based secure communication system using different values of N.

FPGA Resources | Number of Levels | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 15 | 20 | |

Logic Utilization (in ALMs) % | 14 | 27 | 41 | 55 | 69 | 79 | 93 | 105 | 120 | 132 | 184 | 263 |

Maximum Frequency(MHz) | 31.08 | 30.19 | 30.97 | 31.29 | 30.42 | 30.58 | 29.69 | - | - | - | - | - |

Number of Levels (N) | SNR | PSNR | PRD | Correlation Coefficient CC | Encryption Time (te) $\mathsf{\mu}$s | Decryption Time (td) $\mathsf{\mu}$s |
---|---|---|---|---|---|---|

1 | −60.10 | 11.15 | $1.0124\times {10}^{+5}$ | 0.0027 | 0.32 | 0.23 |

2 | −65.41 | 12.39 | $1.8650\times {10}^{+5}$ | 0.0011 | 0.47 | 0.30 |

3 | −69.02 | 12.56 | $2.8242\times {10}^{+5}$ | 0.0006 | 0.74 | 0.46 |

4 | −71.68 | 12.47 | $3.8411\times {10}^{+5}$ | 0.0004 | 0.81 | 0.47 |

5 | −73.99 | 11.95 | $5.0087\times {10}^{+5}$ | 0.0005 | 1.1 | 0.6 |

6 | −75.98 | 11.37 | $6.3008\times {10}^{+5}$ | 0.0006 | 1.2 | 0.7 |

7 | −77.76 | 10.73 | $7.7353\times {10}^{+5}$ | 0.0008 | 1.3 | 0.7 |

8 | −79.34 | 10.18 | $9.2707\times {10}^{+5}$ | 0.0011 | 1.8 | 0.8 |

9 | −79.34 | 10.18 | $1.1057\times {10}^{+6}$ | 0.0014 | 1.8 | 0.9 |

10 | −80.87 | 9.56 | $1.3088\times {10}^{+6}$ | 0.0017 | 1.9 | 1 |

15 | −82.33 | 8.95 | $2.5864\times {10}^{+6}$ | 0.0020 | 3 | 1.6 |

20 | −92.02 | 7.44 | $3.9904\times {10}^{+6}$ | 0.0018 | 4 | 2 |

Number of Levels (N) | SNR | PSNR | PRD | Correlation Coefficient (CC) | Encryption Time (te) | Decryption Time (td) | Logic Utilization | Maximum Frequency | VBPM |
---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0.7246 | 0 | 1 | 0 | 0 | 0 | 0.8687 | 1.5748 |

2 | 0.1664 | 0.9668 | 0.0219 | 0.3043 | 0.0408 | 0.0395 | 0.0522 | 0.3125 | 3.6938 |

3 | 0.2794 | 1 | 0.0466 | 0.0870 | 0.1141 | 0.1299 | 0.1084 | 0.8 | 5.2676 |

4 | 0.3628 | 0.9824 | 0.0727 | 0 | 0.1332 | 0.1356 | 0.1647 | 1 | 6.0775 |

5 | 0.4352 | 0.8809 | 0.1028 | 0.0435 | 0.2120 | 0.2090 | 0.2209 | 0.4563 | 2.8723 |

6 | 0.4975 | 0.7676 | 0.1360 | 0.0870 | 0.2391 | 0.2566 | 0.2610 | 0.5562 | 2.3800 |

7 | 0.5533 | 0.6426 | 0.1729 | 0.1739 | 0.2663 | 0.2655 | 0.3173 | 0 | 1.3786 |

8 | 0.6028 | 0.5352 | 0.2123 | 0.3043 | 0.4022 | 0.3220 | 0.3655 | - | 0.9884 |

9 | 0.6028 | 0.5352 | 0.2583 | 0.4348 | 0.4022 | 0.3785 | 0.4257 | - | 0.8642 |

10 | 0.6507 | 0.4141 | 0.3150 | 0.5652 | 0.4293 | 0.4350 | 0.4739 | - | 0.7314 |

15 | 0.6964 | 0.2949 | 0.6390 | 0.6957 | 0.7283 | 0.7740 | 0.6827 | - | 0.5678 |

20 | 1 | 0 | 1 | 0.6087 | 1 | 1 | 1 | - | 0.5542 |

Author | Ref. | Chaotic Oscillators | Correlation Coefficient | SNR in dB |
---|---|---|---|---|

Alwahbani and Bashier 2013 | [42] | circle map and logistic map | 0.0017 | −14.0065 |

Sheela et al., 2017 | [43] | Henon map (2D-MHM) and standard map | −0.0037 | - |

Sathiyamurthi and Ramakrishnan 2017 | [44] | logistic map, tent map, quadratic map, and Bernoulli’s map | 0.0119 | - |

Yousif 2019 | [45] | Zaslavsky map | −0.00092 | −56.8661 |

Kordov 2019 | [46] | chaotic circle map and modified rotation equations | −0.0011166 | −16.0483 |

Gebereselassie et al., 2022 | [47] | Chen’s hyperchaotic system | −0.0007 | - |

Proposed System | Unified hyperchaotic system | 0.0004 | −71.68 |

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**MDPI and ACS Style**

Bonny, T.; Al Nassan, W.
Optimizing Security and Cost Efficiency in N-Level Cascaded Chaotic-Based Secure Communication System. *Appl. Syst. Innov.* **2024**, *7*, 107.
https://doi.org/10.3390/asi7060107

**AMA Style**

Bonny T, Al Nassan W.
Optimizing Security and Cost Efficiency in N-Level Cascaded Chaotic-Based Secure Communication System. *Applied System Innovation*. 2024; 7(6):107.
https://doi.org/10.3390/asi7060107

**Chicago/Turabian Style**

Bonny, Talal, and Wafaa Al Nassan.
2024. "Optimizing Security and Cost Efficiency in N-Level Cascaded Chaotic-Based Secure Communication System" *Applied System Innovation* 7, no. 6: 107.
https://doi.org/10.3390/asi7060107