Abstract
This paper proposes a new chaotic system based on sine map, i.e., the coupled piecewise sine map (CPSM), which utilizes piecewise mechanism to obtain more uniform probability density distribution of state values, and enhances the complexity of chaotic system by coupling parameters between sub-systems. Then, from the view of resisting the chosen ciphertext attack, a ciphertext sensitive diffusion structure is presented. Based on the CPSM and the ciphertext sensitive diffusion structure, this paper proposes a new image encryption algorithm. Since the CPSM can generate chaotic sequences with good cryptographic properties and the diffusion structure has good diffusion performance in both the encryption process and the decryption process, the proposed encryption algorithm is extremely sensitive to the ciphertext tampering. Thus, it can effectively resist the chosen ciphertext attacks. Experimental results and security analysis also confirmed that the proposed algorithm has good security and can ensure the secure transmission of image in the Internet.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11071-021-06576-z/MediaObjects/11071_2021_6576_Fig13_HTML.png)
Similar content being viewed by others
Data availability statements
All data generated or analyzed during this study are included in this published article.
References
Aboughalia, R.A., Osama, A.A.: Color image encryption based on chaotic block permutation and xor operation. In: Libyan International Conference on Electrical Engineering and Technologies (LICEET2018) (2018)
Alawida, M., The, J.S., Samsudin, A., Alshoura, W.H.: An image encryption scheme based on hybridizing digital chaos and finite state machine. Signal Process. 164, 249–266 (2019)
Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcation Chaos 16(08), 2129–2151 (2006)
Belazi, A., Talha, M., Kharbech, S., Xiang, W.: Novel medical image encryption scheme based on chaos and dna encoding. IEEE Access 7, 36667–36681 (2019)
Broumandnia, A.: The 3d modular chaotic map to digital color image encryption. Futur. Gener. Comp. Syst. 99, 489–499 (2019)
Chen, Z., Yuan, X., Yuan, Y., Iu, H., Fernando, T.: Parameter identification of chaotic and hyper-chaotic systems using synchronization-based parameter observer. IEEE Trans. Circuits Syst. I-Regul. Pap. 63(9), 1464–1475 (2016)
Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcation Chaos 8(6), 1259–1284 (1998)
hua Gan, Z., li Chai, X., jun Han, D., ran Chen, Y.: A chaotic image encryption algorithm based on 3-d bit-plane permutation. Neural Comput. Appl 31, 7111–7130 (2019)
Geetha, P., Jayanthi, V.S., Jayanthi, A.N.: Multiple share creation based visual cryptographic scheme using diffusion method with a combination of chaotic maps for multimedia applications. Multimed. Tools Appl. 78, 18503–18530 (2019)
Girdhar, A., Kapur, H., Kumar, V.A.: A novel grayscale image encryption approach based on chaotic maps and image blocks. Appl. Phys. B 127, 39 (2021)
Herbadji, D., Derouiche, N., Belmeguenai, A., Herbadji, A., Boumerdassi, S.: A tweakable image encryption algorithm using an improved logistic chaotic map. Traitement du Signal 36(5), 407–417 (2019)
Hua, Z., Zhou, B., Zhou, Y.: Sine-transform-based chaotic system with fpga implementation. IEEE Trans. Ind. Electron. 65(3), 2557–2566 (2018)
Hua, Z., Zhou, Y.: Image encryption using 2d logistic-adjusted-sine map. Inf. Sci. 339, 237–253 (2016)
Hua, Z., Zhou, Y., Pun, C.M., Chen, C.P.: 2d sine logistic modulation map for image encryption. Inf. Sci. 297, 80–94 (2015)
Hussein, W.A., Al-Saidi, N.M.G., Natiq, H.: A new 2d hénon-logistic map for producing hyperchaotic behavior. In: 2018 Third Scientific Conference of Electrical Engineering, p. 265–269 (2018)
Kang, X., Guo, Z.: A new color image encryption scheme based on dna encoding and spatiotemporal chaotic system. Signal Process. Image Commun 80, 115670 (2020)
Kaur, M., Singh, D., Sun, K., Rawat, U.: Color image encryption using non-dominated sorting genetic algorithm with local chaotic search based 5d chaotic map. Futur. Gener. Comp. Syst. 107, 333–350 (2020)
Khan, J.S., Ahmad, J., Ahmed, S.S., Siddiqa, H.A., Abbasi, S.F., Kayhan, S.K.: Dna key based visual chaotic image encryption. J. Intell. Fuzzy Syst. 37, 2549–2561 (2019)
Khedmati, Y., Parvaz, R., Behroo, Y.: 2d hybrid chaos map for image security transform based on framelet and cellular automata. Inf. Sci. 512, 855–879 (2020)
K.U., S., Mohamed, A.: A novel image encryption scheme using both pixel level and bit level permutation with chaotic map. Appl. Soft. Comput. 90, 106162 (2020)
Lahdir, M., Hamiche, H., Kassim, S., Tahanout, M., Kemih, K., Addouche, S.A.: A novel robust compression-encryption of images based on spiht coding and fractional-order discrete-time chaotic system. Opt. Laser Technol. 109, 534–546 (2019)
Li, C., Tan, K., Feng, B., Lü, J.: The graph structure of the generalized discrete arnold’s cat map. IEEE Trans. Comput. (2021). https://doi.org/10.1109/TC.2021.3051387
Li, C., Zhang, Y., Xie, E.Y.: When an attacker meets a cipher-image in 2018: A year in review. J. Inf. Secur. Appl. 48, 102361 (2019)
Liu, H., Wang, X.: Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt. Commun. 284, 3895–3903 (2011)
Liu, Z., Wang, Y., Zhao, Y., Zhang, L.Y.: A stream cipher algorithm based on 2d coupled map lattice and partitioned cellular automata. Nonlinear Dyn. 101(2), 1383–1396 (2020)
Mansouri, A., Wang, X.: A novel one-dimensional sine powered chaotic map and its application in a new image encryption scheme. Inf. Sci. 520, 46–62 (2020)
Naseer, Y., Shah, D., Shah, T.: A novel approach to improve multimedia security utilizing 3d mixed chaotic map. Microprocess. Microsyst. 65, 1–6 (2019)
Parvaz, R., Zarebnia, M.: A combination chaotic system and application in color image encryption. Opt. Laser Technol. 101, 30–41 (2018)
Patro, K.A.K., Acharya, B., Nath, V.: Secure multilevel permutation-diffusion based image encryption using chaotic and hyper-chaotic maps. Microsyst. Technol. 25, 4593–4607 (2019)
ur Rehman, A., Liao, X.F.: A novel robust dual diffusion/ confusion encryption technique for color image based on chaos, dna and sha-2. Multimed. Tools Appl. 78, 2105–2133 (2019)
Slimane, N.B., Aouf, N., Bouallegue, K., Machhout, M.: A novel chaotic image cryptosystem based on dna sequence operations and single neuron model. Multimed. Tools Appl. 77, 30993–31019 (2018)
Sui, L., Duan, K., Liang, J., Zhang, Z., Meng, H.: Asymmetric multiple-image encryption based on coupled logistic maps in fractional fourier transform domain. Opt. Lasers Eng. 62, 139–152 (2014)
Teh, J.S., Tan, K., Alawida, M.: A chaos-based keyed hash function based on fixed point representation. Cluster Comput. 22(2), 649–660 (2019)
Valandar, M.Y., Barani, M.J., Ayubi, P.: A fast color image encryption technique based on three dimensional chaotic map. Optik 193, 162921 (2019)
Wang, X., Sun, H.: A chaotic image encryption algorithm based on improved joseph traversal and cyclic shift function. Opt. Laser Technol. 122, 105854 (2020)
Wang, X., Wang, Y., Zhu, X., Luo, C.: A novel chaotic algorithm for image encryption utilizing one-time pad based on pixel level and dna level. Opt. Lasers Eng. 125, 105851 (2020)
Wang, X., Zhang, J., Cao, G.: An image encryption algorithm based on zigzag transform and ll compound chaotic system. Opt. Laser Technol. 119, 105581 (2019)
Wu, X., Wang, D., Kurths, J., Kan, H.: A novel lossless color image encryption scheme using 2d dwt and 6d hyperchaotic system. Inf. Sci. 349–350, 137–153 (2016)
Xiang, H., Liu, L.: A new perturbation-feedback hybrid control method for reducing the dynamic degradation of digital chaotic systems and its application in image encryption. Multimed. Tools Appl. (2021). https://doi.org/10.1007/s11042-021-10680-y
Ye, G., Jiao, K., Wu, H., Pan, C., Huang, X.: An asymmetric image encryption algorithm based on a fractional-order chaotic system and the rsa public-key cryptosystem. Int. J. Bifurcation Chaos 30(15), 2050233 (2020)
Ye, G., Zhao, H., Chai, H.: Chaotic image encryption algorithm using wave-line permutation and block diffusion. Nonlinear Dyn. 83, 2067–2077 (2016)
Zhang, Y.: The unified image encryption algorithm based on chaos and cubic s-box. Inf. Sci. 450, 361–377 (2018)
Zhou, L., Tan, F., Yu, F.: A robust synchronization-based chaotic secure communication scheme with double-layered and multiple hybrid networks. IEEE Syst. J. 14(2), 2508–2519 (2020)
Zhu, H., Dai, L., Liu, Y., Wu, L.: A three-dimensional bit-level image encryption algorithm with rubik’s cube method. Math. Comput. Simul. 185, 754–770 (2021)
Zhu, H., Zhang, X., Yu, H., Zhao, C., Zhu, Z.: An image encryption algorithm based on compound homogeneous hyper-chaotic system. Nonlinear Dyn. 89, 61–79 (2017)
Zuras, D., Cowlishaw, M., Aiken, A., et al.: Ieee standard for floating-point arithmetic. IEEE Std 754–2008, 1–70 (2008)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 61772215), the MOE Layout Foundation of Humanities and Social Sciences (No. 20YJAZH102), the Foundation of Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS201908), and the Doctoral Talent Training Project of Chongqing University of Posts and Telecommunications (No. BYJS202008).
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
Liu, J., Wang, Y., Liu, Z. et al. A chaotic image encryption algorithm based on coupled piecewise sine map and sensitive diffusion structure. Nonlinear Dyn 104, 4615–4633 (2021). https://doi.org/10.1007/s11071-021-06576-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-021-06576-z