Skip to main content
SpringerLink
Log in

A hybrid chaotic map with coefficient improved whale optimization-based parameter tuning for enhanced image encryption

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The security of the data becomes the main concern due to the quick rise in the exchange of data over the open networks and the Internet. The cryptographic techniques based on chaos theory reveal some novel and effectual orders to develop secure image encryption approaches. Images are the most attractive kinds of data in the encryption domain. In current years, the chaos-based cryptographic techniques have provided an efficient way to expand secure image encryption frameworks. This proposal temps to develop an optimized HCM for promoting novel image encryption. The proposed image encryption model involves 4 steps, such as image pre-processing, key generation, image encryption using optimized HCM, and image decryption. In the pre-processing, the RGB image is converted into a grayscale image, and the key is generated by the SHA-256 cryptographic hash algorithm. Further, the encryption of the image is performed by HCM with the integration of 2DLCM, and PWLCM. While hybridizing the two chaotic maps for image encryption, parameter tuning or optimization is performed for improving its performance. Moreover, Information entropy is considered as the objective model that has to be maximized while tuning the parameters, and the maximum value of information entropy will mean the best performance. An improvement in the well-known optimization algorithms termed as CI-WOA is adopted for performing the parameter optimization of HCM. Hence, the optimized HCM-based image encryption can be confirmed as an efficient and secure way for all types of image transmissions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

AES:

Advanced encryption standard

PSNR:

Peak signal-to-noise ratio

3DES:

Triple DES

DES:

Data encryption standard

NPCR:

Number of pixel change rate

1D:

One-dimensional

UACI:

Unified average changing intensity

HD:

High-dimensional

2D-SCL:

Two-dimensional chaotic map sine map Chebyshev map and the linear function

DNA:

Deoxyribonucleic acid

BST:

Binary search tree

DWT:

Discrete wavelet transformation

LSMCL:

Logistics-modulated-sine-coupling-logistic chaotic map

KPA:

Known plain text attacks

GWO:

Grey wolf optimization

3D:

Three-dimensional

SHA-3:

Stable Hash algorithm 3

MSE:

Mean square error

CPA:

Cipher plain text attacks

SAGWO:

Self-adaptive grey wolf optimization

Deep CNN:

Deep convolutional neural network

DNN:

Deep neural network

SSIM:

Structural similarity index measure

FSIM:

Feature similarity index measure

DSSIM:

Dissimilarity structural similarity index measure

CSSIM:

Complex wavelet structural similarity index measure

HCM:

Hybrid chaotic map

2DLCM:

2D-logistic chaotic map

PWLCM:

Piecewise linear chaotic map

CI-WOA:

Coefficient improved whale optimization algorithm

References

  • Abhishek S, George N, Deepthi PP (2013) PWLCM based image encryption through compressive sensing. In: IEEE recent advances in intelligent computational systems (RAICS), Trivandrum, pp 48–52

  • Algredo-Badillo I, Feregrino-Uribe C, Cumplido R, Morales-Sandoval M (2013) FPGA-based implementation alternatives for the inner loop of the Secure Hash Algorithm SHA-256. Microprocess Microsyst 37(6–7):750–757

    Article  Google Scholar 

  • Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurc Chaos 16(8):21292151

    Article  MathSciNet  MATH  Google Scholar 

  • Ben Farah MA, Guesmi R, Kachouri A, Samet M (2020) A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation. Opt Laser Technol 121:1

    MATH  Google Scholar 

  • Cao W, Mao Y, Zhou Y (2020) Designing a 2D infinite collapse map for image encryption. Sig Process 171:1

    Article  Google Scholar 

  • Chen LF, Chang GJ, He BY (2017) Optical image conversion and encryption by diffraction, phase retrieval algorithm and incoherent superposition. Opt Lasers Eng 88:221–232

    Article  Google Scholar 

  • Chen C, Sun K, He S (2019) An improved image encryption algorithm with finite computing precision. Signal Processing

  • Chen J, Li XW, Wang Q-H (2019b) Deep learning for improving the robustness of image encryption. IEEE Access 7:181083–181091

    Article  Google Scholar 

  • Darwish SM, Noori ZH (2019) Secure image compression approach based on fusion of 3D chaotic maps and arithmetic coding. IET Signal Proc 13(3):286–295

    Article  Google Scholar 

  • Etem T, Kaya T (2019) A novel true random bit generator design for image encryption. Phys A: Stat Mech Appl

  • Frauel Y, Castro A, Naughton T, Javidi B (2007) Resistance of the double random phase encryption against various attacks. Opt Express 15:10253–10265

    Article  Google Scholar 

  • Gupta A, Singh D, Kaur M (2020) An efficient image encryption using non-dominated sorting genetic algorithm-III based 4-D chaotic maps. J Ambient Intell Hum Comput 11:1309–1324

    Article  Google Scholar 

  • Hu Y, Zhu C, Wang Z (2014) An improved piecewise linear chaotic map based image encryption algorithm. Sci World J

  • Hua Z, Zhou B, Zhou Y (2018) Sine-transform-based Chaotic system with FPGA implementation. IEEE Multimedia 65(3):1

    Google Scholar 

  • John FB, Alejandro MA, Roberto T (2014) Experimental QR code optical encryption: noise-free data recovering. Opt Lett 39(10):3074–3077

    Article  Google Scholar 

  • Kang Y, Zhang LH, Zhang DW (2018) Optical encryption based on ghost imaging and public key cryptography. Opt Lasers Eng 111:58–64

    Article  Google Scholar 

  • Kaur M, Kumar V (2018a) Beta Chaotic map based image encryption using genetic algorithm. Int J Bifurc Chaos 28(11):1

    Article  MathSciNet  MATH  Google Scholar 

  • Kaur M, Kumar V (2018b) Parallel non-dominated sorting genetic algorithm-II-based image encryption technique. Imaging Sci J 66(8):453–462

    Article  Google Scholar 

  • Kaur M, Kumar M (2020) A comprehensive review on image encryption techniques. Comput Methods Eng 27:15–43

    Article  MathSciNet  Google Scholar 

  • Kaur M, Kumar V, Li L (2019) Color image encryption approach based on memetic differential evolution. Neural Comput Appl 31:7975–7987

    Article  Google Scholar 

  • Kaur M, Singh D, Sun K, Rawat U (2020) Color image encryption using non-dominated sorting genetic algorithm with local chaotic search based 5D chaotic map. Fut Gen Comput Syst 107:333–350

    Article  Google Scholar 

  • Khan J, Khan M, Ahmad J, Hwang S, Ahmed W (2017) An improved image encryption scheme based on a non-linear Chaotic algorithm and substitution boxes. Informatica 28:629–649

    Article  Google Scholar 

  • Koppu S, Madhu Viswanatham V (2018) Medical image security enhancement using two dimensional chaotic mapping optimized by self-adaptive grey wolf algorithm. Evol Intel 11(1–2):53–71

    Article  Google Scholar 

  • Kumar P, Fatima A, Nishchal NK (2019) Image encryption using phase-encoded exclusive-OR operations with incoherent illumination. J Opt 21:065701

    Article  Google Scholar 

  • Li X, Mou Y, Cai Z Ji, Zhang J (2003) On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision. Comput Phys Commun 153(1):52–58

    Article  MathSciNet  MATH  Google Scholar 

  • Lin L, Shen M, So H, Chang C (2012) Convergence analysis for initial condition estimation in coupled map lattice systems. IEEE Trans Signal Process 60(8):4426–4432

    Article  MathSciNet  MATH  Google Scholar 

  • Maniyath SR, Thanikaiselvan V (2020) An efficient image encryption using deep neural network and chaotic Map. Microprocess Microsyst 77:1

    Article  Google Scholar 

  • Mirjalili S, Lewis A (2016) The Whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  • Muniraj I, Guo CL, Malallah R (2017) Low photon count based digital holography for quadratic phase cryptography. Opt Lett 42(14):2774–2777

    Article  Google Scholar 

  • Nematzadeh H, Enayatifar R, Yadollahi M, Lee M, Jeong G (2019) Binary Search Tree Image encryption with DNA. Optik

  • Oteko Tresor L, Sumbwanyambe M (2019) A selective image encryption scheme based on 2D DWT, Henon map and 4D Qi hyper-Chaos. IEEE Access 7:103463–103472

    Article  Google Scholar 

  • Patro AK, Acharya B (2019) An efficient colour image encryption scheme based on 1-D chaotic maps. J Inf Secur Appl 46:23–41

    Google Scholar 

  • Qin W, Peng X (2010) Asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt Lett 35(2):118–120

    Article  Google Scholar 

  • Singh N, Sinha A (2009) Gyrator transform-based optical image encryption using chaos. Opt Lett 47:539–546

    Google Scholar 

  • Wang X-Y, Yang L, Liu R, Kadir A (2010) A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn 62(3):615621

    Article  MathSciNet  MATH  Google Scholar 

  • Wang Y, Quan C, Tay CJ (2014) Nonlinear multiple-image encryption based on mixture retrieval algorithm in Fresnel domain. Opt Commun 330(1):9198

    Google Scholar 

  • Wu Y, Noonan JP, Yang G, Jin H (2012) Image encryption using the two-dimensional logistic chaotic map. J Electron Imaging 21(1):1

    Article  Google Scholar 

  • Xiao B, Luo J, Bi X, Li W, Chen B (2020) Fractional discrete Tchebyshev moments and their applications in image encryption and watermarking. Inf Sci 516:545–559

    Article  MathSciNet  Google Scholar 

  • Yao S, Chen L, Zhong Y (2019) An encryption system for color image based on compressive sensing. Opt Laser Technol 120:1

    Article  Google Scholar 

  • Zhang X, Wang L, Zhou Z, Niu Y (2019) A Chaos-based image encryption technique utilizing Hilbert curves and H-fractals. IEEE Access 7:74734–74746

    Article  Google Scholar 

  • Zhou Y, Bao L, Chen C (2014) A new 1D chaotic system for image encryption. Signal Process 97:172–182

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Zhu C, Liao C, Deng X (2013) Breaking and improving an image encryption scheme based on total shufing scheme. Nonlinear Dyn 71(12):2534

    Google Scholar 

  • Zhu C, Wang G, Sun K (2018) Improved cryptanalysis and enhancements of an image encryption scheme using combined 1D Chaotic maps. Entropy 20(11):843

    Article  Google Scholar 

  • Zhu H, Zhao Y, Song Y (2019) 2D logistic-modulated-sine-coupling-logistic chaotic map for image encryption. IEEE Access 7:14081–14098

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing Science and Engineering, Vellore Institute of Technology Chennai, Chennai, India

    S. Saravanan & M. Sivabalakrishnan

Authors
  1. S. Saravanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Sivabalakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Saravanan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This paper does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saravanan, S., Sivabalakrishnan, M. A hybrid chaotic map with coefficient improved whale optimization-based parameter tuning for enhanced image encryption. Soft Comput 25, 5299–5322 (2021). https://doi.org/10.1007/s00500-020-05528-w

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05528-w

Keywords

Search

Navigation