Abstract
Combining optical image encryption with digital image encryption, we propose a composed optical image hybrid encryption scheme in this paper. The scheme consists of two main parts. In the first part, the original image is encrypted in 4f optical system in the pattern of double random phase encoding. In the second stage, the result of optical encryption is divided into the real part image and the imaginary one. Then, pixels diffusion and confusion are successively carried out on the two images in parallel. Fractional Fourier transform and a generalized chaos, as well as nonlinear transform of matrices are composited to brace the core computation of the algorithm. Plaintext related cipher technology is fully applied to cryptosystem. Moreover, other tools including cumulative sum and modular operation, random matrices, dot operation of matrices, sequence rearrangement, etc., are employed to support the algorithm. Cipher statistical analysis according to SP800 R1a shows that the cryptosystem is secure. Encryption simulations and performance analysis show that the algorithm performs well in effectiveness, feasibility, safety and robustness. The innovation of this work includes two aspects: firstly, the high-dimensional chaotic digital image encryption method is integrated into 4f optical image encryption system, and a new idea of optical image encryption is proposed; Secondly, a separate encryption paradigm of real and imaginary images in frequency domain is proposed, which greatly improves the security of image encryption and transmission. Other contributions of this paper consist in: a novel chaos with multiple free parameters is introduced to sustain the cryptosystem; the algorithm has a super large scale key space to ensure the security of the algorithm. Compared with other known schemes, the proposed algorithm shows relatively overall advantages. So, it is a nice candidate for image protection.
Article PDF
Similar content being viewed by others
Data Availability
The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- RPM:
-
Random Phase Mask
- FT:
-
Fourier Transformation
- FRFT:
-
Fractional Fourier transformation
- CHM:
-
Cosine-sine Henon Map
- NTFM:
-
The Nonlinear Transform about the Matrix
- NTFM− 1 :
-
The Inverse of NTFM
- DCRP:
-
Diffusion cipher related to the plaintext
- PSNR:
-
Peak Signal to Noise Ratio
- SSIM:
-
Structural Similarity
- CORR:
-
The Correlation Coefficient
- NPCR:
-
The Number of Pixels Change Rate
- UACI:
-
The Unified Average Changing Intensity
- BACI:
-
Block Average Changing Intensity
References
Zhang, Y.: Chaotic Digital Image Cryptosystem. Tsinghua University Press, Beijing (2016)
Guo, F.M., Tu, L.: Application of Chaos Theory in Cryptography. Beijing Institute of Technology Press, Beijing (2015)
Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995)
Ben Farah, M.A., Guesmi, R., Kachouri, A., et al.: A novel chaos based optical image encryption using fractional Fouriertransform and DNA sequence operation. Opt. Laser Technol. 121, 105777 (2020)
Sui, L., Xin, M., Tian, A., Jin, H.: Single-channel color imageencryption using phase retrieve algorithm in fractional fourier domain. Opt. Lasers Eng. 51(12), 1297–1309 (2013)
Liu, Z., Li, S., Liu, W., Liu, S.: Opto-digital image encryption by usingbaker mapping and 1-d fractional fourier transform. Opt. Lasers Eng. 51(3), 224–229 (2013)
Liu, Z., Li, S., Liu, W., Wang, Y., Liu, S.: Image encryption algorithmby using fractional fourier transform and pixel scrambling operation basedon double random phase encoding. Opt. Lasers Eng. 51(1), 8–14 (2013)
Singh, N., Sinha, A.: Optical image encryption using fractional Touriertransform and chaos. Opt. Lasers Eng. 46(2), 117–123 (2008)
Singh, N., Sinha, A.: Gyrator transform-based optical image encryptionusing chaos. Opt. Lasers Eng. 47(5), 539–546 (2009)
Li, H., Wang, Y.: Double-image encryption based on discrete fractionalrandom transform and chaotic maps. Opt. Lasers Eng. 49(7), 753–757 (2011)
Liu, Z., Gong, M., Dou, Y., et al.: Double image encryption by using Arnoldtransform and discrete fractional angular transform. Opt. Lasers Eng. 50(2), 248–255 (2012)
Chai, X., Chen, Y., Broyde, L.: A novel chaos-based image encryption algorithm using DNA sequence operations. Opt. Lasers Eng. 88, 197–213 (2017)
Xue, H., Du, J., Li, S., et al.: Region of interest encryption for color images based on a hyper chaotic system with three positive Lyapunov exponents. Opt. Laser Technol. 106, 506–516 (2018)
Wang, S., Wang, C., Xu, C.: An image encryption algorithm based on a hidden attractor chaos system and the Knuth-Durstenfeld algorithm. Opt. Lasers Eng. 128, 105995 (2019)
Huang, Z., Cheng, S., Gong, L., et al.: Nonlinear optical multi-image encryption scheme with two-dimensional linear canonical transform. Opt. Lasers Eng. 124, 105821 (2019)
Liu, Y., Jiang, Z., Xu, X., et al.: Optical image encryption algorithm based on hyper-chaos and public-key cryptography. Opt. Laser Technol. 127, 106171 (2020)
Su, Y., Xu, W., Zhao, J.: Optical image encryption based on chaotic fingerprint phase mask and pattern-illuminated Fourier ptychography. Opt. Lasers Eng. 128, 106020 (2020)
Zhang, Y.: The unified image encryption algorithm based on chaos and cubic S-Box. Inf. Sci. 450, 361–377 (2018)
Hua, Z., Zhou, Y., Huang, H.: Cosinetransformbased chaotic system for image encryption. Inf Sci 480, 403–419 (2019)
Chai, X., Fu, X., Gan, Z., et al.: A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process. 155, 44–62 (2019)
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)
Zhou, W.: A novel image encryption scheme based on conservative hyper chaotic system and closed-loop diffusion between blocks. Signal Process. 171, 107484 (2020)
Zhang, Y., Chen, A., Tang, Y., et al.: Plaintext-related image encryption algorithm based on perceptron-like network. Inf. Sci. 526, 180–202 (2020)
Liang, X., Tan, X., Tao, L.: Plaintext related image hybrid encryption scheme using algebraic interpolation and generalized chaotic map. Multimed. Tools Appl. 79, 2719–2743 (2020)
Abdollahi, Z., MohseniMoghadam, M., Saeedi, H., Ebadi, M.J.: A computational approach for solving fractional Volterra integral equations based on two-dimensional Haar wavelet method. Int. J. Comput. Math. 99(7), P1488-1504, 0020-716 (2022)
Radmanesh, M., Ebadi, M.J.: A local mesh-less collocation method for solving a class of time-dependent fractional integral equations: 2D fractional evolution equation. Eng. Anal. Bound. Elem. 113, 372–381, 0955-7997 (2020)
Nazari, K., Ebadi, M.J., Berahmand, K.: Diagnosis of Alternaria disease and leaf miner pest on tomato leaves using image processing techniques. J. Sci. Food Agric. P1, 0022–5142 (2022)
Alimohammadirokni, M., Emadlou, A., Yuan, J.J.: The Strategic Resources of a Gastronomy Creative City: The Case of San Antonio, Texas. J. Gastronom. Tour. 5(4), P237-252, 2169–2971 (2021)
Preishuber, M., Hütter, T., Katzenbeisser, S.: Depreciating Motivation and Empirical Security Analysis of Chaos-Based Image and Video Encryption. IEEE Trans. Inf. Forensics Secur. 13(9), 2137–2150 (2018)
Kamalakkannan, R., Roopkumar, R., Zayed, A.: On the extension of the coupled fractional Fourier transform and its properties. Integral Transforms and Special Functions 33(1), 65–80 (2022)
Zhao, B., Chen, M., Zou, F.S., et al.: Proficiency in MATLAB-Science computation and the application of data statitics. Posts and Telecommunications Press, Beijing (2018)
Contour Detection and Image Segmentation Resources. https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/resources.html, March, 2023.
Ranzato, M.A., Li, F.-F., Andreetto, M.: Caltech101 image dataset. https://academictorrents.com/details/410206b2624ab243b0fa-87058f73927fc44a5b7c, March, 2023.
Rukhin, A., Nechvatal, J., Smid, M. et al.: A statistical test suite for random and pseudorandom number generator for cryptographic applications. https://xueshu.baidu.com/usercenter/paper/show?paperid=7fd4e905ff21d31c99cd52c1f61f9a26, March, 2023.
Zhen, P., Zhao, G., Min, L., Jin, X.: Chaos-Based Image Encryption Scheme Combining DNA Coding and Entropy. Multimed Tools Appl 75(11), 6303–6319 (2016)
Jin, X., Yin, S., Liu, N., Li, X., Zhao, G., Ge, S.: Color Image Encryption in Non-RGB Color Spaces. Multimed Tools Appl 77(12), 15851–15873 (2018)
Zhou, K., Fan, J., Fan, H., et al.: Secure image encryption scheme using double random-phase encoding and compressed sensing. Opt. Laser Technol. 121, 105769 (2020)
Zhou, Q., Wang, X., Jin, M., Zhang, L., Xu, B.: Optical image encryption based on two-channel detection and deep. Opt. Lasers Eng. 162, P107415, 0143–8166 (2023)
Acknowledgements
This work was supported by National Natural Science Foundation of China [No. 61702153]. We express our sincere gratitude to those who have provided helps for our work.
Funding
National Natural Science Foundation of China [No. 61702153].
Author information
Authors and Affiliations
Contributions
Limin Tao: Conceived overall structure of the paper and performed the experiment.
Xikun Liang: Performed design and analysis of algorithms and wrote the paper.
Zhijing Wu: Performed the data analyses.
Lidong Han: Collected the data.
Jiangping Zhu: Helped perform the analysis with constructive discussions.
Corresponding author
Ethics declarations
Ethics Approval and Consent to Participate
Not applicable.
Consent for Publication
Not applicable.
Competing Interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tao, L., Liang, X., Wu, Z. et al. Plaintext Related Optical Image Hybrid Encryption Based on Fractional Fourier Transform and Generalized Chaos of Multiple Controlling Parameters. J Grid Computing 21, 17 (2023). https://doi.org/10.1007/s10723-023-09655-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10723-023-09655-0