Abstract
The fractional-order functions show better performance than their corresponding integer-order functions in various image processing applications. In this paper, the authors propose a novel utilization of fractional-order chaotic systems in color image encryption. The 4D hyperchaotic Chen system of fractional-order combined with the Fibonacci Q-matrix. The proposed encryption algorithm consists of three steps: in step#1, the input image decomposed into the primary color channels, R, G, & B. The confusion and diffusion operations are performed for each channel independently. In step#2, the 4D hyperchaotic Chen system of fractional orders generates random numbers to permit pixel positions. In step#3, we split the permitted image into \(2\times 2\) blocks where the Fibonacci Q-matrix diffused each of them. Experiments performed where the obtained results ensure the efficiency of the proposed encryption algorithm and its ability to resist attacks.








Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abd Elaziz MA, Hosny KM, Salah A, Darwish MM, Lu S, Sahlol AT (2020) New machine learning method for image-based diagnosis of COVID-19. PLoS One 15(6):e0235187. https://doi.org/10.1371/journal.pone.0235187
Abro WA, Qi G, Ali Z, Feng Y, Aamir M (2020) Multi-turn intent determination and slot filling with neural networks and regular expressions. Knowl Based Syst 208:106428
Ali Z, Qi G, Muhammad K, Ali B, Abro WA (2020) Paper recommendation based on heterogeneous network embedding. Knowl Based Syst 210:106438
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
Chen B, Yu M, Su Q, Shim HJ, Shi YQ (2018) Fractional quaternion Zernike moments for robust color image copy-move forgery detection. IEEE Access 6:56637–56646
Chen J, Li XW, Wang QH (2019) Deep learning for improving the robustness of image encryption. IEEE Access 7:181083–181091
Ding Y, Wu G, Chen D, Zhang N, Gong L, Cao M, Qin Z (2020) A deep learning-based image encryption and decryption network for internet of medical things. IEEE Internet Things 8:1504–1518
Ding Y, Tan F, Qin Z, Cao M, Choo KKR, Qin Z (2021) DeepKeyGen: a deep learning-based stream cipher generator for medical image encryption and decryption. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3062754 (Online first)
Essaid M, Akharraz I, Saaidi A (2019) Image encryption scheme based on a new secure variant of Hill cipher and 1D chaotic maps. J Inform Secur Appl 47:173–187
Hegazi AS, Matouk AE (2011) Dynamical behaviors and synchronization in the fractional-order hyperchaotic Chen system. Appl Math Lett 24(11):1938–1944
Hosny KM, Darwish MM (2019) Resilient color image watermarking using quaternion radial substituted chebychev moments. ACM Trans Multimed Comput Commun Appl 15(2):46
Hosny KM, Darwish MM, Li K, Salah A (2018) Parallel multi-core CPU and GPU for fast and robust medical image watermarking. IEEE Access 6:77212–77225
Hosny KM, Darwish MM, Aboelenen T (2020a) Novel fractional-order generic Jacobi–Fourier moments for image analysis. Signal Processing 172:107545
Hosny KM, Darwish MM, Aboelenen T (2020b) New fractional-order legendre-fourier moments for pattern recognition applications. Pattern Recogn 103:1–19
Hosny KM, Darwish MM, Fouda MM (2021a) Robust color images watermarking using new fractional-order exponent moments. IEEE Access 9:47425–47435
Hosny KM, Kamal ST, Darwish MM (2021b) A color image encryption technique using block scrambling and chaos. Multimed Tools Appl. https://doi.org/10.1007/s11042-021-11384-z (Online first)
Irani BY, Ayubi P, Jabalkandi FA, Valandar MY, Barani MJ (2019) Digital image scrambling based on a new one-dimensional coupled Sine map. Nonlinear Dyn 97(4):2693–2721
Jithin KC, Sankar S (2020) Colour image encryption algorithm combining Arnold map, DNA sequence operation, and a Mandelbrot set. J Inf Secur Appl. 50:102428
Kadhim IJ, Premaratne P, Vial PJ (2020) Improved image steganography based on super-pixel and coefficient-plane-selection. Signal Process 171:107481
Kamal ST, Hosny KM, Elgindy TM, Darwish MM, Fouda MM (2021) A new image encryption algorithm for grey and color medical images. IEEE Access 9:37855–37865
Kaur P, Pannu HS, Malhi AK (2019) Plant disease recognition using fractional-order Zernike moments and SVM classifier. Neural Comput Appl 31:8749–8768
Kaur M, Singh D, Kumar V (2020) Color image encryption using minimax differential evolution-based 7d hyper-chaotic map. Appl Phys B 126(9):1–19
Li Y, Tang WK, Chen G (2005) Generating hyperchaos via state feedback control. Int J Bifurcat Chaos 15(10):3367–3375
Li M, Lu D, Wen W, Ren H, Zhang Y (2018) Cryptanalyzing a color image encryption scheme based on hybrid hyper-chaotic system and cellular automata. IEEE Access 6:47102–47111
Li M, Wang P, Liu Y, Fan H (2019a) Cryptanalysis of a novel bit-level color image encryption using improved 1D chaotic map. IEEE Access 7:145798–145806
Li P, Xu J, Mou J, Yang F (2019b) Fractional-order 4D hyperchaotic memristive system and application in color image encryption. EURASIP J Image Video Process 2019(1):22
Liu H, Kadir A, Liu J (2019a) Color pathological image encryption algorithm using arithmetic over Galois field and coupled hyperchaotic system. Opt Lasers Eng 122:123–133
Liu Z, Wu C, Wang J, Hu Y (2019b) A color image encryption using dynamic DNA and 4-D memristive hyper-chaos. IEEE Access 7:78367–78378
Naskar PK, Bhattacharyya S, Nandy D, Chaudhuri A (2020) A robust image encryption scheme using chaotic tent map and cellular automata. Nonlinear Dyn 100:2877–2898
Nematzadeh H, Enayatifar R, Yadollahi M, Lee M, Jeong G (2020) Binary search tree image encryption with DNA. Optik 202:163505
Pak C, Huang L (2017) A new color image encryption using combination of the 1D chaotic map. Signal Process 138:129–137
Parvaz R, Zarebnia M (2018) A combination chaotic system and application in color image encryption. Opt Laser Technol 101:30–41
Rehman A, Liao X, Ashraf R, Ullah S, Wang H (2018) A color image encryption technique using exclusive-OR with DNA complementary rules based on chaos theory and SHA-2. Optik 159:348–367
Sahari ML, Boukemara I (2018) A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption. Nonlinear Dyn 94(1):723–744
Teng L, Wang X, Meng J (2018) A chaotic color image encryption using integrated bit-level permutation. Multimed Tools Appl 77(6):6883–6896
Wang X, Feng L, Li R, Zhang F (2019a) A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model. Nonlinear Dyn 95:2797–2824
Wang X, Qin X, Liu C (2019b) Color image encryption algorithm based on customized globally coupled map lattices. Multimed Tools Appl 78(5):6191–6209
Wu X, Kan H, Kurths J (2015) A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl Soft Comput 37:24–39
Wu X, Wang D, Kurths J, Kan H (2016) A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system. Inf Sci 349:137–153
Wu X, Wang K, Wang X, Kan H, Kurths J (2018) Color image DNA encryption using NCA map-based CML and one-time keys. Signal Process 148:272–287
Xian Y, Wang X, Yan X, Li Q, Wang X (2020) Image encryption based on chaotic sub-block scrambling and chaotic digit selection diffusion. Opt Lasers Eng 134:106202
Xuejing K, Zihui G (2020) A new color image encryption scheme based on DNA encoding and spatiotemporal chaotic system. Signal Process Image Commun 80:115670
Yang B, Liao X (2018) A new color image encryption scheme based on logistic map over the finite field Z N. Multimed Tools Appl 77(16):21803–21821
Yang YG, Guan BW, Li J, Li D, Zhou YH, Shi WM (2019) Image compression-encryption scheme based on fractional-order hyperchaotic systems combined with 2D compressed sensing and DNA encoding. Opt Laser Technol. https://doi.org/10.1016/j.optlastec.2019.105661
Yang F, Mou J, Liu J, Ma C, Yan H (2020a) Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application. Signal Process. https://doi.org/10.1016/j.sigpro.2019.107373
Yang F, Mou J, Ma C, Cao Y (2020b) Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application. Opt Lasers Eng. https://doi.org/10.1016/j.optlaseng.2020.106031
Yao S, Chen L, Zhong Y (2019) An encryption system for color image based on compressive sensing. Opt Laser Technol. https://doi.org/10.1016/j.optlastec.2019.105703
Zhang Q, Han J (2021) A novel color image encryption algorithm based on image hashing, 6D hyperchaotic and DNA coding. Multimed Tools Appl 80(9):13841–13864
Zhang YQ, He Y, Li P, Wang XY (2020) A new color image encryption scheme based on 2DNLCML system and genetic operations. Opt Lasers Eng. https://doi.org/10.1016/j.optlaseng.2020.106040
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(6):1–24
Zhou Z, Mu Y, Wu QJ (2019) Coverless image steganography using partial-duplicate image retrieval. Soft Comput 23(13):4927–4938
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hosny, K.M., Kamal, S.T. & Darwish, M.M. Novel encryption for color images using fractional-order hyperchaotic system. J Ambient Intell Human Comput 13, 973–988 (2022). https://doi.org/10.1007/s12652-021-03675-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-021-03675-y