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Index-based simultaneous permutation-diffusion in image encryption using two-dimensional price map

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Abstract

This paper proposes an index-based simultaneous permutation-diffusion image encryption algorithm (ISPD-IEA) based on chaos theory and a permutation-diffusion coupled encryption mechanism. The proposed method introduces a novel two-dimensional (2D) Price map derived from the Price function and classical maps, exhibiting superior chaotic dynamical properties compared to existing alternatives. By integrating the permutation-diffusion process, ISPD-IEA effectively diffuses minor changes in pixel values while altering their positions, enhancing both encryption efficiency and resistance against differential analysis attacks. Experimental results and thorough security analysis confirm the outstanding security and high encryption efficiency of ISPD-IEA. The algorithm not only achieves excellent encryption performance but also demonstrates its ability to resist various attacks commonly encountered in image encryption scenarios.

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References

  1. Liu H, Liu J, Ma C (2023) Constructing dynamic strong S-Box using 3D chaotic map and application to image encryption. Multimed Tools Appl 82:23899–23914

    Google Scholar 

  2. Nazari K, Ebadi MJ, Berahmand K (2022) Diagnosis of alternaria disease and leafminer pest on tomato leaves using image processing techniques. J Sci Food Agric 102(15):6907–6920

    CAS  PubMed  Google Scholar 

  3. Rostami M, Berahmand K, Nasiri E, Forouzandeh S (2021) Review of swarm intelligence-based feature selection methods. Eng Appl Artif Intel 100:104210

    Google Scholar 

  4. Enayatifar R, AH Abdullah, Isnin IF (2014) Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt Lasers Eng 56:83–93

    Google Scholar 

  5. Li S, Zheng X (2002) On the security of an image encryption method. Proceedings of the 2002 IEEE Int Conference Image Process 2:925–928

    Google Scholar 

  6. Li B, Liao X, Jiang Y (2019) A novel image encryption scheme based on improved random number generator and its implementation. Nonlinear Dyn 95(3):1781–1805

    Google Scholar 

  7. Wang X, Wang Y, Zhu X, Luo C (2020) A novel chaotic algorithm for image encryption utilizing one-time pad based on pixel level and DNA level. Opt Lasers Eng 125:105851

    Google Scholar 

  8. Ali TS, Ali R (2022) A novel color image encryption scheme based on a new dynamic compound chaotic map and S-box. Multimed Tools Appl 81:20585–20609

    PubMed  PubMed Central  Google Scholar 

  9. Lai Q, Zhang H, Kuate PDK, Xu GH, Zhao XW (2022) Analysis and implementation of no-equilibrium chaotic system with application in image encryption. Appl Intell 52:11448–11471

    Google Scholar 

  10. Wang XY, Gao S, Ye XL, Zhou S, Wang MX (2021) A new image encryption algorithm with cantor diagonal scrambling based on the PUMCML system. Int J Bifur Chaos 31(01):2150003

    MathSciNet  Google Scholar 

  11. Sui LS, Gao B (2013) Color image encryption based on gyrator transform and Arnold transform. Optics & Laser Tech 48:530–538

    ADS  Google Scholar 

  12. Chen L, Zhao D (2005) Optical image encryption based on fractional wavelet transform. Optics Commun 254(4–6):361–367

    ADS  CAS  Google Scholar 

  13. Wang XY, Sun HH (2020) A chaotic image encryption algorithm based on improved Joseph traversal and cyclic shift function. Opt Laser Eng 122:105854

    Google Scholar 

  14. Yin Q, Wang CH (2018) A new chaotic image encryption scheme using breadth-first search and dynamic diffusion. Int J Bifur Chaos 28(04):1850047

    MathSciNet  Google Scholar 

  15. Firdous A, Rehman A, Saad Missen MM (2019) A highly efficient color image encryption based on linear transformation using chaos theory and SHA-2. Multimed Tools Appl 78:24809–24835

    Google Scholar 

  16. Nosrati K, Volos C, Azemi A (2017) Cubature Kalman filter-based chaotic synchronization and image encryption. Signal Process: Image Commun 58:35–48

    Google Scholar 

  17. Cao WJ, Mao YJ, Zhou YC (2020) Designing a 2D infinite collapse map for image encryption. Signal Process 171:107457

    Google Scholar 

  18. Hua ZY, Zhu ZH, Chen YY, Li YM (2021) Color image encryption using orthogonal Latin squares and a new 2D chaotic system. Nonlinear Dyn 104:4505–4522

    Google Scholar 

  19. Gao X (2021) Image encryption algorithm based on 2D hyperchaotic map. Optics & Laser Tech 142:107252

    Google Scholar 

  20. Teng L, Wang XY, Yang FF, Xian YJ (2021) Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion. Nonlinear Dyn 105(2):1859–1876

    Google Scholar 

  21. Hua ZY, Zhu ZH, Yi S, Zhang Z, Huang HJ (2021) Cross-plane colour image encryption using a two-dimensional logistic tent modular map. Inf Sci 546:1063–1083

    MathSciNet  Google Scholar 

  22. Sun JL (2021) 2D-SCMCI hyperchaotic map for image encryption algorithm. IEEE Access 9:59313–59327

    Google Scholar 

  23. Zhu LY, Jiang DH, Ni JQ, Wang XY, Rong XW, Ahmad M, Chen YP (2022) A stable meaningful image encryption scheme using the newly-designed 2D discrete fractional-order chaotic map and Bayesian compressive sensing. Signal Process 195:108489

    Google Scholar 

  24. Nan SX, Feng XF, Wu YF, Zhang H (2022) Remote sensing image compression and encryption based on block compressive sensing and 2D-LCCCM. Nonlinear Dyn 108(3):2705–2729

    Google Scholar 

  25. Lai Q, Yang L, Liu Y (2022) Design and realization of discrete memristive hyperchaotic map with application in image encryption. Chaos, Solitons & Fractals 165:112781

    Google Scholar 

  26. Lai Q, Wan ZQ, Zhang H, Chen GR (2022) Design and analysis of multiscroll memristive hopfield neural network with adjustable memductance and application to image encryption. IEEE Trans Neural Net Learn Syst. https://doi.org/10.1109/TNNLS.2022.3146570

    Article  Google Scholar 

  27. Zhang Y (2021) A new unified image encryption algorithm based on a lifting transformation and chaos. Inf Sci 547:307–327

    MathSciNet  Google Scholar 

  28. Lai Q, Chen Z (2023) Grid-scroll memristive chaotic system with application to image encryption. Chaos, Solitons & Fractals 170:113341

    MathSciNet  Google Scholar 

  29. Enayatifar R, Abdullah AH, Isnin IF, Altameem A, Lee M (2017) Image encryption using a synchronous permutation-diffusion technique. Optics Lasers Eng 90:146–154

    ADS  Google Scholar 

  30. Ye RS (2011) A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism. Optics Commun 284(22):5290–5298

    ADS  CAS  Google Scholar 

  31. Liu LD, Lei YH, Wang D (2020) A fast chaotic image encryption scheme with simultaneous permutation-diffusion operation. IEEE Access 8:27361–27374

    Google Scholar 

  32. Ge B, Chen G, Chen X, Shen ZH (2022) Efficient Hyperchaotic Image Encryption Algorithm Based on a Fast Key Generation Method and Simultaneous Permutation-Diffusion Structure. Security Commun Net 2237525

  33. Ye GD, Wu HS, Liu M, Shi Y (2022) Image encryption scheme based on blind signature and an improved Lorenz system. Expert Syst Appl 117709

  34. Pourasad Y, Ranjbarzadeh R, Mardani A (2021) A new algorithm for digital image encryption based on chaos theory. Entropy 23(3):341

    ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  35. Yang J, Wu H (2018) Color image encryption algorithm based on chaotic system and dynamic DNA coding and operation. Comput Eng 44(2):151–157

    Google Scholar 

  36. Shahna KU, Mohamed A (2020) A novel image encryption scheme using both pixel level and bit level permutation with chaotic map. Appl Soft Comput 90:106162

    Google Scholar 

  37. Wang Y, Lei P, Yang HQ, Cao HY (2015) Security analysis on a color image encryption based on DNA encoding and chaos map. Comput Electric Eng 46:433–446

    Google Scholar 

  38. Price WL (1977) A controlled random search procedure for global optimisation. The Computer Journal 20(4):367–370

    Google Scholar 

  39. Rosenstein MT, Collins JJ, De Luca CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena 65(1–2):117–134

    ADS  MathSciNet  Google Scholar 

  40. Richman JS, Moorman JR (2000) Physiological time-series analysis using approximate entropy and sample entropy. Americ J Physiology-Heart Circul Phys 278(6):H2039–H2049

    CAS  Google Scholar 

  41. Theiler J (1987) Efficient algorithm for estimating the correlation dimension from a set of discrete points. Physical review A 36(9):4456

    ADS  MathSciNet  CAS  Google Scholar 

  42. Grassberger P, Procaccia I (1983) Estimation of the Kolmogorov entropy from a chaotic signal. Physical review A 28(4):2591

    ADS  Google Scholar 

  43. Liu H, Xu Y, Ma C (2020) Chaos-based image hybrid encryption algorithm using key stretching and hash feedback. Optik 216:164925

    ADS  Google Scholar 

  44. Liu H, Kadir A, Xu C (2020) Color image encryption with cipher feedback and coupling chaotic map. Int J Bifuract Chaos 30(12):2050173

    MathSciNet  Google Scholar 

  45. Zhang Y (2015) The image encryption algorithm with plaintext-related shuffling. IETE Tech Rev 33(3):310–322

    Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China under Grant 61961019, and the Youth Key Project of Natural Science Foundation of Jiangxi Province of China under Grant 20202ACBL212003, and the Jiangxi Provincial Natural Science Foundation under Grant 20232BAB202008.

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Authors and Affiliations

  1. School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, 330013, China

    Qiang Lai & Hui Zhang

  2. Department of Computer Engineering, Engineering Faculty, Tarsus University, Mersin, 33400, Turkey

    Deniz Ustun

  3. Department of Computer Engineering, Engineering Faculty, Karamanoglu Mehmetbey University, Karaman, 70200, Turkey

    Ugur Erkan

  4. Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University, Ankara, 06830, Turkey

    Abdurrahim Toktas

Authors
  1. Qiang Lai
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  2. Hui Zhang
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  3. Deniz Ustun
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  4. Ugur Erkan
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  5. Abdurrahim Toktas
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All authors contributed to the study of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Qiang Lai.

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Lai, Q., Zhang, H., Ustun, D. et al. Index-based simultaneous permutation-diffusion in image encryption using two-dimensional price map. Multimed Tools Appl 83, 28827–28847 (2024). https://doi.org/10.1007/s11042-023-16663-5

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  • DOI: https://doi.org/10.1007/s11042-023-16663-5

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