Abstract
Protecting digital images is crucial, and image encryption schemes based on chaotic systems have been extensively studied where image permutation is a critical process. The updating processes of particle swarm optimization algorithm have the ability to change the rules of particles motion, and it can be employed to permutate image. In this work, an image encryption scheme based on the updating processes of particle swarm optimization algorithm and hyperchaotic system is proposed. Specifically, a key generation mechanism combined with secure hash algorithm 256 hash is first introduced to generate the initial values of hyperchaotic complex Lü system. Then, the plain image is confused by the position and velocity updating processes of particle swarm optimization algorithm. In addition, an adaptive diffusion mechanism is designed and applied to the confused image to obtain the final cipher image. Simulation results and security analysis show that the proposed scheme exhibits good performance of sophisticated dynamic behavior, high sensitivity to key, and effectively resisting the typical cryptanalysis attacks, and provides an alternative to real-time image encryption application.
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References
Adrian-Viorel D (2016) Circular inter-intra pixels bit-level permutation and chaos-based image encryption. Inf Sci 355:314–327. https://doi.org/10.1016/j.ins.2015.10.027
Ahmad M, Zaiyan M, Ansari S, Lambi D et al (2018) Cryptanalysis of an image encryption algorithm based on PWLCM and inertial delayed neural network. J Intell Fuzzy Syst 34:1323–1332. https://doi.org/10.3233/JIFS-169428
Asgari-Chenaghlu M, Balafar M-A, Feizi-Derakhshi M-R (2019) A novel image encryption algorithm based on polynomial combination of chaotic maps and dynamic function generation. Signal Process 157:1–13. https://doi.org/10.1016/j.sigpro.2018.11.010
Çavuşoğlu Ü, Kaçar S, Pehlivan I, Zengin A (2017) Secure image encryption algorithm design using a novel chaos based S-box. Chaos Solitons Fractals 95:92–101. https://doi.org/10.1016/j.chaos.2016.12.018
Chai X, Gan Z, Yang K, Chen Y, Liu X (2017) An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and dna sequence operations. Signal Process Image Commun 52:6–19. https://doi.org/10.1016/j.image.2016.12.007
Chai X, Yang K, Gan Z (2017) A new chaos-based image encryption algorithm with dynamic key selection mechanisms. Multimed Tools Appl 76:9907–9927. https://doi.org/10.1007/s11042-016-3585-x
Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213. https://doi.org/10.1016/j.optlaseng.2016.08.009
Chai X, Fu X, Gan Z, Lu Y, Chen Y (2019) A color image cryptosystem based on dynamic dna encryption and chaos. Signal Process 155:44–62. https://doi.org/10.1016/j.sigpro.2018.09.029
Chen J, Zhu Z, Fu C, Yu H, Zhang Y (2015) Reusing the permutation matrix dynamically for efficient image cryptographic algorithm. Signal Process 111:294–307. https://doi.org/10.1016/j.sigpro.2015.01.003
Chen J, Zhu Z, Fu C, Zhang L, Zhang Y (2015) An efficient image encryption scheme using lookup table-based confusion and diffusion. Nonlinear Dyn 81:1151–1166. https://doi.org/10.1007/s11071-015-2057-6
Chen J, Zhu Z, Zhang L, Zhang Y, Yang B (2018) Exploiting self-adaptive permutation-diffusion and dna random encoding for secure and efficient image encryption. Signal Process 142:340–353. https://doi.org/10.1016/j.sigpro.2017.07.034
Diab H (2018) An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access 6:42227–42244. https://doi.org/10.1109/ACCESS.2018.2858839
Dridi M, Hajjaji M, Bouallegue B, Mtibaa A (2016) Cryptography of medical images based on a combination between chaotic and neural network. IET Image Process 10:830–839. https://doi.org/10.1049/iet-ipr.2015.0868
Enayatifar R, Guimar\(\tilde{a}\)es FG, Siarry P, (2019) Index-based permutation-diffusion in multiple-image encryption using dna sequence. Optics Lasers Eng 115:131–140. https://doi.org/10.1016/j.optlaseng.2018.11.017
Hua Z, Zhou Y (2017) Design of image cipher using block-based scrambling and image filtering. Inf Sci 396:97–113. https://doi.org/10.1016/j.ins.2017.02.036
Hua Z, Yi S, Zhou Y (2018) Medical image encryption using high-speed scrambling and pixel adaptive diffusion. Signal Process 144:134–144. https://doi.org/10.1016/j.sigpro.2017.10.004
Hua Z, Jin F, Xu B, Huang H (2018) 2D Logistic-Sine-coupling map for image encryption. Signal Process 149:148–161. https://doi.org/10.1016/j.sigpro.2018.03.010
Hua Z, Zhou Y, Huang H (2019) Cosine-transform-based chaotic system for image encryption. Inf Sci 480:403–419. https://doi.org/10.1016/j.optlaseng.2016.08.009
Jang W, Kang H, Lee B, Kim K, Shin D, Kim SC (2007) Optimized fuzzy clustering by predator prey paericle swarm optimization. IEEE Congr Evolut Comput. https://doi.org/10.1109/cec.2007.4424886
Lakshmanan S, Prakash M, Lim C, Rakkiyappan R (2018) Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Trans Neural Netw Learn Syst 29:195–207. https://doi.org/10.1109/CEC.2001.934377
Lambić D (2017) Cryptanalyzing a novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn 89:2255–2257. https://doi.org/10.1007/s11071-017-3583-1
Li M, Xu M, Luo J, Fan H (2019) Cryptanalysis of an image encryption using 2d hénon-sine map and dna approach. IEEE Access 7:63336–63345. https://doi.org/10.1109/ACCESS.2019.2916402
Liu D, Zhang W, Yu H, Zhu Z (2018) An image encryption scheme using self-adaptive selective permutation and inter-intra-block feedback diffusion. Signal Process 151:130–143. https://doi.org/10.1016/j.sigpro.2018.05.008
Luo Y, Du M (2013) A self-adapting image encryption algorithm based on spatiotemporal chaos and ergodic matrix. Chin Phys B 22:1–9. https://doi.org/10.1088/1674-1056/22/8/080503
Luo Y, Du M, Liu J (2015) A symmetrical image encryption scheme in wavelet and time domain. Commun Nonlinear Sci Numer Simul 20:447–460. https://doi.org/10.1016/j.cnsns.2014.05.022
Luo Y, Tang S, Qin X, Cao L, Jiang F, Liu J (2018) A double-image encryption scheme based on amplitude-phase encoding and discrete complex random transformation. IEEE Access 6:77740–77753. https://doi.org/10.1109/ACCESS.2018.2884013
Luo Y, Ouyang X, Liu J, Cao L (2019) A colour image encryption using genetic operators and generalized henon chaotic mapping. In: 21st IEEE International conference on high performance computing and communications (HPCC) pp. 1720–1725
Luo Y, Zhou R, Liu J, Qiu S, Cao Y (2017) A novel image encryption scheme based on Kepler’s third law and random Hadamard transform. Chin Phys B 26:1–14. https://doi.org/10.1088/1674-1056/26/12/120504
Mahmoud G, Mahmoud E, Ahmed M (2009) On the hyperchaotic complex Lü system. Nonlinear Dyn 58:725–738. https://doi.org/10.1007/s11071-009-9513-0
Mahmoud GM, Mahmoud EE, Arafa AA (2015) On modified time delay hyperchaotic complex Lü system. Nonlinear Dyn 80:855–869. https://doi.org/10.1007/s11071-015-1912-9
Norouzi B, Mirzakuchaki S (2014) A fast color image encryption algorithm based on hyper-chaotic systems. Nonlinear Dyn 78:995–1015. https://doi.org/10.1007/s00530-013-0314-4
Norouzi B, Seyedzadeh S, Mirzakuchaki S, Mosavi M (2014) A novel image encryption based on hash function with only two-round diffusion process. Multimed Syst 20:45–64. https://doi.org/10.1007/s00530-013-0314-4
Noshadian S, Ebrahimzade SJ (2018) Kazemitabar, Optimizing chaos based image encryption. Multimed Tools Appl 77:25569–25590. https://doi.org/10.1007/s11042-018-5807-x
Ouyang X, Luo Y, Liu J, Cao L, Liu Y (2020) A color image encryption method based on memristive hyperchaotic system and DNA encryption. Int J Modern Phys B 34:1–29. https://doi.org/10.1142/S0217979220500149
Ouyang X, Luo Y, Liu J, Liu Y, Bi J, Qiu S (2018) Period analysis of chaotic systems under finite precisions. In: international conference on systems engineering (ICSEng) pp. 1–5
Pak C, Huang L (2017) A new color image encryption using combination of the 1d chaotic map. Signal Process 138:129–137. https://doi.org/10.1016/j.sigpro.2017.03.011
Pan X, Xue L, Lu Y, Sun N (2019) Hybrid particle swarm optimization with simulated annealing. Multimed Tools Appl 78:29921–29936. https://doi.org/10.1007/s11042-018-6602-4
Rukhin A, Soto J, Nechvatal J (2010) A statistical test suite for random and pseudorandom number generators for cryptographic applications, Nist Special Publication pp. 1–131
Saravanan S, Sivabalakrishnan M (2021) A hybrid chaotic map with coefficient improved whale optimizationbased parameter tuning for enhanced image encryption. Soft Comput 25:5299–5322. https://doi.org/10.1007/s00500-020-05528-w
Shahna KU, Mohamed A (2020) A novel image encryption scheme using both pixel level and bit level permutation with chaotic map. Appl Soft Comput 90:1–17. https://doi.org/10.1016/j.asoc.2020.106162
Shreef MA, Hoomod HK (2013) Image encryption using lagrange-least squares interpolation. Int J Adv Comput Sci Inf Technol 2:35–55
Toughi S, Fathi MH, Sekhavat YA (2017) An image encryption scheme based on elliptic curve pseudo random and advanced encryption system. Signal Process 141:217–227. https://doi.org/10.1016/j.sigpro.2017.06.010
Wang X, Xu D (2014) A novel image encryption scheme based on Brownian motion and PWLCM chaotic system. Nonlinear Dyn 75:345–353. https://doi.org/10.1007/s11071-013-1070-x
Wang X, Teng L, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92:1101–1108. https://doi.org/10.1016/j.sigpro.2011.10.023
Wang X, Zhang D, Wei N (2015) Fractal image coding algorithm using particle swarm optimisation and hybrid quadtree partition scheme. IET Image Process 9:153–161. https://doi.org/10.1049/iet-ipr.2014.0001
Wang X, Gu S, Zhang Y (2015) Novel image encryption algorithm based on cycle shift and chaotic system. Opt Lasers Eng 68:126–134. https://doi.org/10.1016/j.optlaseng.2014.12.025
Wang X, Wang S, Zhang Y, Luo C (2018) A one-time pad color image cryptosystem based on sha-3 and multiple chaotic systems. Optics Lasers Eng 103:1–8. https://doi.org/10.1016/j.optlaseng.2017.11.009
Wang X, Wang Y, Wang S, Zhang Y, Wu X (2018) A novel pseudo-random coupled LP spatiotemporal chaos and its application in image encryption. Chin Phys B 27:1–11. https://doi.org/10.1088/1674-1056/27/11/110502
Wang H, Xiao D, Chen X, Huang H (2018) Cryptanalysis and enhancements of image encryption using combination of the 1d chaotic map. Signal Process 144:444–452. https://doi.org/10.1016/j.sigpro.2017.11.005
Wu Y, Zhou Y, Saveriades G, Agaian S, Noonan JP, Natarajan P (2013) Local shannon entropy measure with statistical tests for image randomness. Inf Sci 222:323–342. https://doi.org/10.1016/j.ins.2012.07.049
Wu J, Liao X, Yang B (2018) Image encryption using 2d hénon-sine map and dna approach. Signal Process 153:11–23. https://doi.org/10.1016/j.sigpro.2018.06.008
Wu J, Liao X, Yang B (2018) Cryptanalysis and enhancements of image encryption based on three-dimensional bit matrix permutation. Signal Process 142:292–300. https://doi.org/10.1016/j.sigpro.2017.06.014
Xu L, Li Z, Li J, Hua W (2016) A novel bit-level image encryption algorithm based on chaotic maps. Opt Lasers Eng 78:17–25. https://doi.org/10.1016/j.optlaseng.2015.09.007
Yang Y, Pan Q, Sun S, Xu P (2015) Novel image encryption based on quantum walks. Sci Rep 5:7784. https://doi.org/10.1038/srep07784
Ye G, Huang X, Zhang L, Wang Z (2017) A self-cited pixel summation based image encryption algorithm. Chin Phys B 26:1–8. https://doi.org/10.1088/1674-1056/26/1/010501
Yuan H, Liu Y, Gong L, Wang J (2017) A new image cryptosystem based on 2D hyper-chaotic system. Multimed Tools Appl 76:8087–8108. https://doi.org/10.1007/s11042-016-3454-7
Zeng J, Wang C (2021) A novel hyperchaotic image encryption system based on particle swarm optimization algorithm and cellular automata. Sec Commun Netw 2021:1–15. https://doi.org/10.1155/2021/6675565
Zhang Y, Wang X (2015) A new image encryption algorithm based on non-adjacent coupled map lattices. Appl Soft Comput 26:10–20. https://doi.org/10.1016/j.asoc.2014.09.039
Zhou N, Chen W, Yan X, Wang Y (2018) Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf Process 17:137. https://doi.org/10.1007/s11128-018-1902-1
Zhu C (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285:29–37. https://doi.org/10.1016/j.optcom.2011.08.079
Zhu C, Sun K (2018) Cryptanalyzing and improving a novel color image encryption algorithm using RT-enhanced chaotic tent maps. IEEE Access 6:18759–18770. https://doi.org/10.1109/ACCESS.2018.2817600
Zhu C, Wang G, Sun K (2018) Cryptanalysis and improvement on an image encryption algorithm design using a novel chaos based S-box. Symmetry 10:399. https://doi.org/10.3390/sym10090399
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This research was supported by the National Natural Science Foundation of China under Grants 61801131, the funding of Overseas 100 Talents Program of Guangxi Higher Education, 2018 Guangxi One Thousand Young and Middle-Aged College and University Backbone Teachers Cultivation Program.
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YL contributed to conceptualization, methodology, writing—review & editing. XO contributed to methodology, validation, writing—original draft, writing—review & editing. JL contributed to methodology, writing—review & editing. LC contributed to validation, writing—review & editing. YZ contributed to validation, writing—review & editing.
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Luo, Y., Ouyang, X., Liu, J. et al. An image encryption scheme based on particle swarm optimization algorithm and hyperchaotic system. Soft Comput 26, 5409–5435 (2022). https://doi.org/10.1007/s00500-021-06554-y
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DOI: https://doi.org/10.1007/s00500-021-06554-y