An efficient confidentiality scheme based on quadratic chaotic map and Fibonacci sequence

Majid Khan; Hafiz Muhammad Waseem; Majid Khan; Hafiz Muhammad Waseem

doi:10.3934/math.20241323

AIMS Mathematics

2024, Volume 9, Issue 10: 27220-27246. doi: 10.3934/math.20241323

Previous Article Next Article

Research article Special Issues

An efficient confidentiality scheme based on quadratic chaotic map and Fibonacci sequence

Majid Khan ^{1
,
,},
Hafiz Muhammad Waseem ²

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Warwick Manufacturing Group (WMG), Warwick University, United Kingdom

Received: 06 May 2024 Revised: 27 August 2024 Accepted: 29 August 2024 Published: 20 September 2024
MSC : 94A60, 68P25

In today's rapidly evolving digital landscape, secure data transmission and exchange are crucial for protecting sensitive information across personal, financial, and global infrastructures. Traditional cryptographic algorithms like RSA and AES face increasing challenges due to the rise of quantum computing and enhanced computational power, necessitating innovative approaches for data security. We explored a novel encryption scheme leveraging the quadratic chaotic map (QCM) integrated with the Fibonacci sequence, addressing key sensitivity, periodicity, and computational efficiency. By employing chaotic systems' inherent unpredictability and sensitivity to initial conditions, the proposed method generates highly secure and unpredictable ciphers suitable for text and image encryption. We incorporated a combined sequence from the Fibonacci sequence and QCM, providing enhanced complexity and security. Comprehensive experimental analyses, including noise and occlusion attack simulations, demonstrate the scheme's robustness, resilience, and practicality. The results indicated that the proposed encryption framework offers a secure, efficient, and adaptable solution for digital data protection against modern computational threats.
- chaotic map,
- Fibonacci sequence,
- image encryption,
- information security
Citation: Majid Khan, Hafiz Muhammad Waseem. An efficient confidentiality scheme based on quadratic chaotic map and Fibonacci sequence[J]. AIMS Mathematics, 2024, 9(10): 27220-27246. doi: 10.3934/math.20241323

Related Papers:

Abstract

In today's rapidly evolving digital landscape, secure data transmission and exchange are crucial for protecting sensitive information across personal, financial, and global infrastructures. Traditional cryptographic algorithms like RSA and AES face increasing challenges due to the rise of quantum computing and enhanced computational power, necessitating innovative approaches for data security. We explored a novel encryption scheme leveraging the quadratic chaotic map (QCM) integrated with the Fibonacci sequence, addressing key sensitivity, periodicity, and computational efficiency. By employing chaotic systems' inherent unpredictability and sensitivity to initial conditions, the proposed method generates highly secure and unpredictable ciphers suitable for text and image encryption. We incorporated a combined sequence from the Fibonacci sequence and QCM, providing enhanced complexity and security. Comprehensive experimental analyses, including noise and occlusion attack simulations, demonstrate the scheme's robustness, resilience, and practicality. The results indicated that the proposed encryption framework offers a secure, efficient, and adaptable solution for digital data protection against modern computational threats.

References

[1]	B. S. Kumar, R. Revathi, An efficient image encryption algorithm using a discrete memory-based logistic map with deep neural network, J. Eng. Appl. Sci., 71 (2024), 41. https://doi.org/10.1186/s44147-023-00349-8 doi: 10.1186/s44147-023-00349-8
[2]	C. Wang, Y. Zhang, A novel image encryption algorithm with deep neural network, Signal Process., 196 (2022), 108536. https://doi.org/10.1016/j.sigpro.2022.108536 doi: 10.1016/j.sigpro.2022.108536
[3]	A. Ampavathi, G. Pradeepini, T. V. Saradhi, Optimized deep learning-enabled hybrid logistic piece-wise chaotic map for secured medical data storage system, Int. J. Inf. Technol. Decis. Mak., 22 (2023), 1743–1775. https://doi.org/10.1142/S0219622022500869 doi: 10.1142/S0219622022500869
[4]	H. Lee, Y. Lee, Optimizations of privacy-preserving DNN for low-latency inference on encrypted data, IEEE Access, 11 (2023), 104775–104788. https://doi.org/10.1109/ACCESS.2023.3318433 doi: 10.1109/ACCESS.2023.3318433
[5]	U. Sirisha, B. S. Chandana, Privacy preserving image encryption with optimal deep transfer learning-based accident severity classification model, Sensors, 23 (2023), 519. https://doi.org/10.3390/s23010519 doi: 10.3390/s23010519
[6]	W. S. Admass, Y. Y. Munaye, A. Diro, Cyber security: State of the art, challenges and future directions, Cyber Security Appl., 2 (2023), 100031. https://doi.org/10.1016/j.csa.2023.100031 doi: 10.1016/j.csa.2023.100031
[7]	P. Singh, S. Dutta, P. Pranav, Optimizing GANs for cryptography: The role and impact of activation functions in neural layers assessing the cryptographic strength, Appl. Sci., 14 (2024), 2379. https://doi.org/10.3390/app14062379 doi: 10.3390/app14062379
[8]	Y. Chen, S. Xie, J. Zhang, A hybrid domain image encryption algorithm based on improved henon map, Entropy, 24 (2022), 287. https://doi.org/10.3390/e24020287 doi: 10.3390/e24020287
[9]	M. Devipriya, M. Sreenivasan, M. Brindha, Reconfigurable architecture for image encryption using a three-layer artificial neural network, IETE J. Res., 70 (2024), 473–86. https://doi.org/10.1080/03772063.2022.2127940 doi: 10.1080/03772063.2022.2127940
[10]	R. B. Naik, U. Singh, A review on applications of chaotic maps in pseudo-random number generators and encryption, Ann. Data Sci., 11 (2024), 25–50. https://doi.org/10.1007/s40745-021-00364-7 doi: 10.1007/s40745-021-00364-7
[11]	A. Chattopadhyay, P. Hassanzadeh, D. Subramanian, Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network, Nonlinear Process. Geophys., 27 (2020), 373–389. https://doi.org/10.5194/npg-27-373-2020 doi: 10.5194/npg-27-373-2020
[12]	K. Yang, Q. Duan, Y. Wang, T. Zhang, Y. Yang, R. Huang, Transiently chaotic simulated annealing based on intrinsic nonlinearity of memristors for efficient solution of optimization problems, Sci. Adv., 6 (2020), eaba9901. https://doi.org/10.1126/sciadv.aba9901 doi: 10.1126/sciadv.aba9901
[13]	F. Masood, W. Boulila, A. Alsaeedi, J. S. Khan, J. Ahmad, M. A. Khan, et al., A novel image encryption scheme based on Arnold cat map, Newton-Leipnik system and Logistic Gaussian map, Multimedia Tools Appl., 81 (2022), 30931–30959. https://doi.org/10.1007/s11042-022-12844-w doi: 10.1007/s11042-022-12844-w
[14]	S. I. Batool, H. M. Waseem, A novel image encryption scheme based on Arnold scrambling and Lucas series, Multimedia Tools Appl., 78 (2019), 27611–27637. https://doi.org/10.1007/s11042-019-07881-x doi: 10.1007/s11042-019-07881-x
[15]	J. Ye, X. Deng, A. Zhang, H. Yu, A novel image encryption algorithm based on improved Arnold transform and chaotic pulse-coupled neural network, Entropy., 24 (2022), 1103. https://doi.org/10.3390/e24081103 doi: 10.3390/e24081103
[16]	B. Zhang, L. Liu, Chaos-based image encryption: Review, application, and challenges, Mathematics., 11 (2023), 2585. https://doi.org/10.3390/math11112585 doi: 10.3390/math11112585
[17]	C. Qin, J. Hu, F. Li, Z. Qian, X. Zhang, JPEG image encryption with adaptive DC coefficient prediction and RS pair permutation, IEEE Trans. Multimedia, 25 (2022), 2528–2542. https://doi.org/10.1109/TMM.2022.3148591 doi: 10.1109/TMM.2022.3148591
[18]	Y. Peng, C. Fu, G. Cao, W. Song, J. Chen, C. W. Sham, JPEG-compatible joint image compression and encryption algorithm with file size preservation, ACM T. Multim. Comput., 20 (2024), 1–20. https://doi.org/10.1145/363345 doi: 10.1145/363345
[19]	M. A. Cardona-López, R. O. Flores-Carapia, V. M. Silva-García, E. D. Vega-Alvarado, M. D. González-Ramírez, A comparison between EtC and SPN systems: The security cost of compatibility in JPEG images, IEEE Access., 36 (2024), 1–14. https://doi.org/10.1109/ACCESS.2024.3458808 doi: 10.1109/ACCESS.2024.3458808
[20]	Q. Wang, X. Zhang, X. Zhao, Image encryption algorithm based on improved Zigzag transformation and quaternary DNA coding, J. Inf. Secur. Appl., 70 (2022), 103340. https://doi.org/10.1016/j.jisa.2022.103340 doi: 10.1016/j.jisa.2022.103340
[21]	Z. Guo, P. Sun, Improved reverse zigzag transform and DNA diffusion chaotic image encryption method, Multimedia Tools Appl., 81 (2022), 11301–11323. https://doi.org/10.1007/s11042-022-12269-5 doi: 10.1007/s11042-022-12269-5
[22]	H. Wen, Z. Xie, Z. Wu, Y. Lin, W. Feng, Exploring the future application of UAVs: Face image privacy protection scheme based on chaos and DNA cryptography, J. King Saud Univ. Comput. Inf. Sci., 36 (2024), 101871. https://doi.org/10.1016/j.jksuci.2023.101871 doi: 10.1016/j.jksuci.2023.101871
[23]	Y. Yang, L. Huang, N. V. Kuznetsov, B. Chai, Q. Guo, Generating multiwing hidden chaotic attractors with only stable node-foci: Analysis, implementation, and application, IEEE Trans. Ind. Electron., 71 (2023), 3986–3995. https://doi.org/10.1109/TIE.2023.3273242 doi: 10.1109/TIE.2023.3273242
[24]	L. Xu, J. Zhang, A novel four-wing chaotic system with multiple attractors based on hyperbolic sine: Application to image encryption, Integration., 87 (2022), 313–331. https://doi.org/10.1016/j.vlsi.2022.07.012 doi: 10.1016/j.vlsi.2022.07.012
[25]	J. Zhang, J. Yang, L. Xu, X. Zhu, The circuit realization of a fifth-order multi-wing chaotic system and its application in image encryption, Int. J. Circ. Theory Appl., 51 (2023), 1168–1186. https://doi.org/10.1002/cta.3490 doi: 10.1002/cta.3490
[26]	M. W. Hafiz, S. O. Hwang, A probabilistic model of quantum states for classical data security, Front. Phys., 18 (2023), 51304. https://doi.org/10.1007/s11467-023-1293-3 doi: 10.1007/s11467-023-1293-3
[27]	A. G. Weber, The USC-SIPI image database: Version 5, 2006. http://sipi.usc.edu/database/
[28]	S. I. Batool, M. Amin, H. M. Waseem, Public key digital contents confidentiality scheme based on quantum spin and finite state automation, Phys. A Stat. Mech. Appl., 537 (2020), 122677. https://doi.org/10.1016/j.physa.2019.122677 doi: 10.1016/j.physa.2019.122677
[29]	S. Patel, A. Vaish, Block based visually secure image encryption algorithm using 2D-compressive sensing and nonlinearity, Optik., 272 (2023), 170341. https://doi.org/10.1016/j.ijleo.2022.170341 doi: 10.1016/j.ijleo.2022.170341
[30]	Y. Peng, Z. Lan, K. Sun, W. Xu, A simple color image encryption algorithm based on a discrete memristive hyperchaotic map and time-controllable operation, Opt. Laser Technol., 165 (2023), 109543. https://doi.org/10.1016/j.optlastec.2023.109543 doi: 10.1016/j.optlastec.2023.109543
[31]	H. M. Waseem, A. Alghafis, M. Khan, An efficient public key cryptosystem based on dihedral group and quantum spin states, IEEE Access, 8 (2020), 71821–71832. https://doi.org/10.1109/ACCESS.2020.2987097 doi: 10.1109/ACCESS.2020.2987097
[32]	A. Nabilah, L. Said, M. Khan, Construction of optimum multivalued cryptographic Boolean function using artificial bee colony optimization and multi-criterion decision-making, Soft Comput., 28 (2024), 5213–5223. https://doi.org/10.1007/s00500-023-09267-6 doi: 10.1007/s00500-023-09267-6
[33]	N. Rani, S. R. Sharma, V. Mishra, Grayscale and colored image encryption model using a novel fused magic cube, Nonlinear Dyn., 108 (2022), 1773–1796. https://doi.org/10.1007/s11071-022-07276-y doi: 10.1007/s11071-022-07276-y
[34]	Q. Lai, G. Hu, U. Erkan, A. Toktas, A novel pixel-split image encryption scheme based on 2D Salomon map, Expert Syst. Appl., 213 (2023), 118845. https://doi.org/10.1016/j.eswa.2022.118845 doi: 10.1016/j.eswa.2022.118845
[35]	H. M. Waseem, S. S. Jamal, I. Hussain, M. Khan, A novel hybrid secure confidentiality mechanism for medical environment based on Kramer's spin principle, Int. J. Theor. Phys., 60 (2021), 314–330. https://doi.org/10.1007/s10773-020-04694-9 doi: 10.1007/s10773-020-04694-9
[36]	X. Liu, X. Tong, Z. Wang, M. Zhang, Uniform non-degeneracy discrete chaotic system and its application in image encryption, Nonlinear Dyn., 108 (2022), 653–682. https://doi.org/10.1007/s11071-021-07198-1 doi: 10.1007/s11071-021-07198-1
[37]	N. R. Zhou, L. J. Tong, W. P. Zou, Multi-image encryption scheme with quaternion discrete fractional Tchebyshev moment transform and cross-coupling operation, Signal Process., 211 (2023), 109107. https://doi.org/10.1016/j.sigpro.2023.109107 doi: 10.1016/j.sigpro.2023.109107
[38]	A. Alghafis, H. M. Waseem, M. Khan, S. S. Jamal, A hybrid cryptosystem for digital contents confidentiality based on rotation of quantum spin states, Phys. A Stat. Mech. Appl., 554 (2020), 123908. https://doi.org/10.1016/j.physa.2019.123908 doi: 10.1016/j.physa.2019.123908
[39]	M. W. Hafiz, W. K. Lee, S. O. Hwang, M. Khan, A. Latif, Discrete logarithmic factorial problem and Einstein crystal model based public-key cryptosystem for digital content confidentiality, IEEE Access., 10 (2022), 102119–102134. https://doi.org/10.1109/ACCESS.2022.3207781 doi: 10.1109/ACCESS.2022.3207781
[40]	N. Abughazalah, A. Latif, M. W. Hafiz, M. Khan, A. S. Alanazi, I. Hussain, Construction of multivalued cryptographic Boolean function using recurrent neural network and its application in image encryption scheme, Artif. Intell. Rev., 56 (2023), 5403–5443. https://doi.org/10.1007/s10462-022-10295-1 doi: 10.1007/s10462-022-10295-1
[41]	K. S. Krishnan, B. Jaison, S. P. Raja, Secured color image compression based on compressive sampling and Lü system, Inf. Technol. Control., 49 (2020), 346–369. https://doi.org/10.5755/j01.itc.49.3.25901 doi: 10.5755/j01.itc.49.3.25901
[42]	S. O. Hwang, H. M. Waseem, N. Munir, Billiard quantum chaos: A pioneering image encryption scheme in the post-quantum era, IEEE Access., 12 (2024), 39840–39853. https://doi.org/10.1109/ACCESS.2024.3415083 doi: 10.1109/ACCESS.2024.3415083
[43]	M. Ahmad, S. Agarwal, A. Alkhayyat, A. Alhudhaif, F. Alenezi, A. H. Zahid, et al., An image encryption algorithm based on new generalized fusion fractal structure, Inf. Sci., 592 (2022), 1–20. https://doi.org/10.1016/j.ins.2022.01.042 doi: 10.1016/j.ins.2022.01.042
[44]	W. Alexan, Y. L. Chen, L. Y. Por, M. Gabr, Hyperchaotic maps and the single neuron model: A novel framework for chaos-based image encryption, Symmetry., 15 (2023), 1081. https://doi.org/10.3390/sym15051081 doi: 10.3390/sym15051081
[45]	M. Khan, H. M. Waseem, A novel digital contents privacy scheme based on Kramer's arbitrary spin, Int. J. Theor. Phys., 58 (2019), 2720–2743 https://doi.org/10.1007/s10773-019-04162-z doi: 10.1007/s10773-019-04162-z
[46]	A. H. Ismail, H. M. Waseem, M. Ishtiaq, S. S. Jamal, M. Khan, Quantum spin half algebra and generalized Megrelishvili protocol for confidentiality of digital images, Int. J. Theor. Phys., 60 (2021), 1720–1741. https://doi.org/10.1007/s10773-021-04794-0 doi: 10.1007/s10773-021-04794-0
[47]	Y. Wang, Y. Shang, Z. Shao, Y. Zhang, G. Coatrieux, H. Ding, et al., Multiple color image encryption based on cascaded quaternion gyrator transforms, Signal Process. Image Commun., 107 (2022), 116793. https://doi.org/10.1016/j.image.2022.116793 doi: 10.1016/j.image.2022.116793
[48]	H. M. Waseem, S. O. Hwang, Design of highly nonlinear confusion component based on entangled points of quantum spin states, Sci. Rep., 13 (2023), 1099. https://doi.org/10.1038/s41598-023-28002-7 doi: 10.1038/s41598-023-28002-7

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)