Abstract
In this paper, an image encryption algorithm based on Fibonacci Q-matrix and genetic algorithm is proposed. The new four-layer encryption framework of diffusion-scrambling-diffusion-optimization is adopted. Firstly, an improved four-direction diffusion operation is performed on the original image to achieve efficient global diffusion based on row and column vectors and the first-round diffusion matrix is obtained. Secondly, using the Logistic chaotic system to improve the Josephus scrambling, and then use the improved scrambling method to scramble the first-round diffusion matrix, which improves the scrambling effect of the algorithm. Thirdly, the scrambling matrix is divided into blocks, and then the Fibonacci Q-matrix corresponding to each block is dynamically selected by random numbers and the two are rapidly diffused, which further improves the diffusion effect. Finally, in order to make the optimization more targeted, the initial population is generated by the second-round diffusion matrix and the fitness function is selected according to the correlation of the second-round diffusion matrix. In the optimization process, multiple rounds of selection, crossover and fitness calculation are performed on the initial population to obtain the encrypted image. In addition, the initial values of the NHS hyperchaotic system used in the improved four-way diffusion and the Logistic chaotic system used in the improved Josephus scrambling is all generated from the 256-bit hash values of the original image, which makes the proposed algorithm highly sensitive to plaintext image. The experimental results and security analyses show that the algorithm not only has high security but also has certain robustness and real-time performance, which is suitable for practical applications.
Similar content being viewed by others
References
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
Chai X, Gan Z, Yuan K, Chen Y, Liu X (2019) A novel image encryption scheme based on DNA sequence operations and chaotic systems. Neural Comput Appl 31(1):219–237. https://doi.org/10.1007/s00521-017-2993-9
Arshad S, Khan M (2021) New extension of data encryption standard over 128-bit key for digital images. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06023-5
Hedayati R, Mostafavi S (2021) A lightweight image encryption algorithm for secure communications in multimedia Internet of Things. Wirel Pers Commun. https://doi.org/10.1007/s11277-021-09173-w
Wang X, Zhao H (2020) Fast image encryption algorithm based on parallel permutation-and-diffusion strategy. Multimedia Tools Appl 79(27–28):19005–19024
Hafsa A, Sghaier A, Malek J, Machhout M (2021) Image encryption method based on improved ECC and modified AES algorithm. Multimedia Tools Appl 2:1–33. https://doi.org/10.1007/s11042-021-10700-x
Zhou S, Wang X, Zhang Y, Ge B, Wang M, Gao S (2021) A novel image encryption cryptosystem based on true random numbers and chaotic systems. Multimedia Syst. https://doi.org/10.1007/s00530-021-00803-8
Dong W, Li Q, Tang Y, Hu M, Zeng R (2021) A robust and multi chaotic DNA image encryption with pixel-value pseudorandom substitution scheme. Opt Commun 499:127211. https://doi.org/10.1016/j.optcom.2021.127211
Elhoseny M, Shankar K, Lakshmanaprabu S, Maseleno A, Arunkumar N (2020) Hybrid optimization with cryptography encryption for medical image security in Internet of Things. Neural Comput Appl 32(15):10979–10993. https://doi.org/10.1007/s00521-018-3801-x
Iqbal N, Hanif M (2021) An efficient grayscale image encryption scheme based on variable length row-column swapping operations. Multimedia Tools Appl. https://doi.org/10.1007/s11042-021-11386-x
Hanif M, Naqvi RA, Abbas S, Khan MA, Iqbal N (2020) A novel and efficient 3D multiple images encryption scheme based on chaotic systems and swapping operations. IEEE Access 8:123536–123555. https://doi.org/10.1109/ACCESS.2020.3004536
Wang R, Deng G, Duan X (2021) An image encryption scheme based on double chaotic cyclic shift and Josephus problem. J Inf Secur Appl 58:102699. https://doi.org/10.1016/j.jisa.2020.102699
Shengtao G, Tao W, Shida W, Xuncai Z, Ying N (2020) A novel image encryption algorithm based on chaotic sequences and cross-diffusion of bits. IEEE Photonics J 13(1):1–15. https://doi.org/10.1109/JPHOT.2020.3044222
Ge B, Chen G, Fang R, Liao Z (2021) Hyperchaotic image encryption algorithm based on matrix four-way diffusion. Comput Mod 6:113–119
Wang J, Liu W, Zhang S (2020) Adaptive encryption of digital images based on lifting wavelet optimization. Multimedia Tools Appl 79(13):9363–9386
Aouissaoui I, Bakir T, Sakly A (2021) Robustly correlated key-medical image for DNA-chaos based encryption. IET Image Process 15(12):2770–2786
Dai J, Ma Y, Zhou N (2021) Quantum multi-image compression-encryption scheme based on quantum discrete cosine transform and 4D hyper-chaotic Henon map. Quantum Inf Process 20(7):1–24. https://doi.org/10.1007/s11128-021-03187-w
Zhao S, Yan F, Chen K, Yang H (2021) Interpolation-based high capacity quantum image steganography. Int J Theor Phys. https://doi.org/10.1007/s10773-021-04891-0
Zhu H, Chen X, Yang Y (2021) A multimode quantum image representation and its encryption scheme. Quantum Inf Process 20(9):315. https://doi.org/10.1007/s11128-021-03255-1
Gan Z, Chai X, Zhi X, Ding W, Lu Y, Wu X (2021) Image cipher using image filtering with 3D DNA-based confusion and diffusion strategy. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06225-x
Hao J, Li H, Yan H, Mou J (2021) A new fractional chaotic system and its application in image encryption with DNA mutation. IEEE Access 9:52364–52377. https://doi.org/10.1109/ACCESS.2021.3069977
Uddin M, Jahan F, Islam MK, Rakib Hassan M (2021) A novel DNA-based key scrambling technique for image encryption. Complex Intell Syst. https://doi.org/10.1007/s40747-021-00515-6
Zou C, Wei X, Zhang Q, Zhou C, Zhou S (2021) Encryption algorithm based on DNA strand displacement and DNA sequence operation. IEEE Trans NanoBiosci 20(2):223–234
Zhao Y, Liu L (2021) A bit shift image encryption algorithm based on double chaotic systems. Entropy 23(9):1127. https://doi.org/10.3390/e23091127
Zheng J, Liu L (2020) Novel image encryption by combining dynamic DNA sequence encryption and the improved 2D logistic sine map. IET Image Process 14(11):2310–2320
Zhou W, Wang X, Wang M, Li D (2022) A new combination chaotic system and its application in a new Bit-level image encryption scheme. Opt Lasers Eng 149:106782. https://doi.org/10.1016/j.optlaseng.2021.106782
Ghazvini M, Mirzadi M, Parvar N (2020) A modified method for image encryption based on chaotic map and genetic algorithm. Multimedia Tools Appl 79(37):26927–26950
Abdullah A, Enayatifar R, Lee M (2012) A hybrid genetic algorithm and chaotic function model for image encryption. AEU-Int J Electron Commun 66(10):806–816
Wong K, Yap W, Wong DC, Phan RC, Goi B (2020) Cryptanalysis of genetic algorithm-based encryption scheme. Multimedia Tools Appl 79(35):25259–25276. https://doi.org/10.1007/s11042-020-09191-z
Li T, Du B, Liang X (2020) Image encryption algorithm based on logistic and two-dimensional Lorenz. IEEE Access 8:13792–13805. https://doi.org/10.1109/ACCESS.2020.2966264
Méndez-Ramírez RD, Arellano-Delgado A, Murillo-Escobar MA, Cruz-Hernández C (2021) A new 4D hyperchaotic system and its analog and digital implementation. Electronics 10(15):1793. https://doi.org/10.3390/electronics10151793
Méndez-Ramírez RD, Arellano-Delgado A, Cruz-Hernández C, Martínez-Clark R (2017) A new simple chaotic Lorenz-type system and its digital realization using a TFT touch-screen display embedded system. Complexity. https://doi.org/10.1155/2017/6820492
Zhang M, Tong X, Wang Z, Chen P (2021) Joint lossless image compression and encryption scheme based on CALIC and hyperchaotic system. Entropy 23(8):1096. https://doi.org/10.3390/e23081096
Wang X, Sun H (2020) A chaotic image encryption algorithm based on improved Joseph traversal and cyclic shift function. Opt Laser Technol 122:105854. https://doi.org/10.1016/j.optlastec.2019.105854
Hosny KM, Kamal ST, Darwish MM, Papakostas GA (2021) New image encryption algorithm using hyperchaotic system and Fibonacci Q-Matrix. Electronics 10(9):1066. https://doi.org/10.3390/electronics10091066
Kumar S (2021) Image data security using Quasigroup combined with Fibonacci Q-transformation. J Inf Secur Appl 61:102941. https://doi.org/10.1016/j.jisa.2021.102941
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.ins.2018.12.048
Taneja N, Raman B, Gupta I (2011) Selective image encryption in fractional wavelet domain. AEUE-Int J Electron Commun 65(4):338–344
Liang Z, Qin Q, Zhou C, Wang N, Xu Y, Zhou W (2021) Medical image encryption algorithm based on a new five-dimensional three-leaf chaotic system and genetic operation. Plos One. https://doi.org/10.1371/journal.pone.0260014
Hu H, Cao Y, Xu J, Ma C, Yan H (2021) An image compression and encryption algorithm based on the fractional-order simplest chaotic circuit. IEEE Access 9:22141–22155. https://doi.org/10.1109/ACCESS.2021.3054842
Man Z, Li J, Di X, Sheng Y, Liu Z (2021) Double image encryption algorithm based on neural network and chaos. Chaos, Solitons & Fractals 152:111318. https://doi.org/10.1016/j.chaos.2021.111318
Wang X, Gao S (2020) Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory. Inf Sci 507:16–36. https://doi.org/10.1016/j.ins.2019.08.041
Taneja N, Bhatnagar G, Raman B (2013) Joint watermarking and encryption for still visual data. Multimed Tools Appl 67(3):593–606
Goel N, Raman B, Gupta I (2014) Chaos based joint compression and encryption framework for end-to-end communication systems. Adv Multimedia 910106:10. https://doi.org/10.1155/2014/910106
Deb S, Biswas B, Bhuyan B (2019) Secure image encryption scheme using high efficiency word-oriented feedback shift register over finite field. Multimedia Tools Appl 78(24):34901–34925
Gao H, Wang X (2021) Chaotic image encryption algorithm based on Zigzag transform with bidirectional crossover from random position. IEEE Access 9:105627–105640. https://doi.org/10.1109/ACCESS.2021.3099214
Shafique A, Ahmed J, Rehman MU, Hazzazi MM (2021) Noise-resistant image encryption scheme for medical images in the chaos and wavelet domain. IEEE Access 9:59108–59130. https://doi.org/10.1109/ACCESS.2021.3071535
Acknowledgements
This work was supported in part by the National Youth Science Foundation of China under the Grant numbers 62002046, 61802040.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest. Also there are no competing interests among authors.
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
Liang, Z., Qin, Q. & Zhou, C. An image encryption algorithm based on Fibonacci Q-matrix and genetic algorithm. Neural Comput & Applic 34, 19313–19341 (2022). https://doi.org/10.1007/s00521-022-07493-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-022-07493-x