Abstract

In today’s technological age, ensuring the security of data transmitted across unsecured and open channels from one destination to another is an important issue. Strong techniques to protect images during transmission and storage are becoming more and more critical as the digital age advances. The main focus of the presented work is to enhance the protection of digital image data from unapproved sources over these open networks. It is possible that conventional encryption methods may not provide enough protection against contemporary cryptographic attacks. Thus, this study proposes an encryption method that combines the cryptographic properties of S-boxes and Baker’s map together with the chaotic dynamics of the discrete compound chaotic (DCC) map. During encryption, the level of confusion and diffusion is well maintained. The confusion is achieved by employing the chaotic sequence obtained from the DCC map and through the use of Baker’s map. The S-box and a DCC map are utilized for diffusion purposes. Further, to achieve a better scrambling effect, Baker’s map is implemented multiple times (n_b k times). The innovation of the proposed scheme lies in its novel integration of the discrete compound chaotic map (DCC map) with the cryptographic properties of S-boxes and Baker’s map, achieving an enhanced level of diffusion and confusion in encrypted images. Further, the hashSHA−256 utilized to derive initial conditions ensures the dependency of the proposed scheme on the original image, offering a robust defence against differential attacks and providing a more secure framework than traditional encryption techniques. The strong proposed scheme’s capability was demonstrated via the following key results: average entropy value of 7.9971, low correlation coefficients in the encrypted images, high MSE values, average encryption time of 0.2599 seconds, UACI of 33.4765, NPCR of 99.6113, successful decryption without data loss. These statistical and simulation analysis results confirm the scheme’s efficiency, high security, and robustness.

Keywords

S-Box, Discrete Compound Chaotic Map, Baker’s Map, Confusion-Diffusion,

Downloads

Download data is not yet available.

References

  1. M. Kumar, S. Agrawal, Color image encoding in DOST domain using DWT and SVD. Optics and Laser Technology, 75, (2015) 138–145. https://doi.org/10.1016/j.optlastec.2015.06.022
  2. C. Fu, Z.-K. Wen, Z.-L. Zhu, H. Yu, A security improved image encryption scheme based on chaotic baker map and hyperchaotic Lorenz system. International Journal of Computational Science and Engineering, 12(2–3), (2016) 113–123. https://doi.org/10.1504/IJCSE.2016.076212
  3. M.B. Farah, A. Farah, T. Farah, An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dynamics, 99(4), (2020) 3041–3064. https://doi.org/10.1007/s11071-019-05413-8
  4. A.A.A. El-Latif, B. Abd-El-Atty, A. Belazi, A.M. Iliyasu, Efficient chaos-based substitution-box and its application to image encryption. Electronics, 10(12), (2021) 1392. https://doi.org/10.3390/electronics10121392
  5. H. Shi, M. Ji’e, C. Li, D. Yan, S. Duan, L. Wang, A novel image encryption algorithm based on 2D self-coupling sine map. International Journal of Bifurcation and Chaos, 32(15), (2022) 2250233. https://doi.org/10.1142/S0218127422502339
  6. D. Singh, S. Kumar, A multiphase encryption scheme using RSS, modified RMAC and Chen’s hyperchaotic map. Multimedia Tools and Applications, 83(19), (2024) 57059–5708.
  7. Q. He, P. Li, Y. Wang, A color image encryption algorithm based on compressive sensing and block-based DNA coding. IEEE Access, IEEE, 12 (2024) 77621-77638. https://doi.org/10.1109/ACCESS.2024.3406766
  8. Y.M. Afify, N.H. Sharkawy, W. Gad, N. Badr, A new dynamic DNA-coding model for gray-scale image encryption. Complex & Intelligent Systems, 10(1), (2024) 745–761. https://doi.org/10.1007/s40747-023-01187-0
  9. X. Yan, Q. Hu, L. Teng, A novel color image encryption method based on new three-dimensional chaotic mapping and DNA coding. Nonlinear Dynamics, 113 (2024) 1799-1826. https://doi.org/10.1007/s11071-024-10277-8
  10. S. Kumar, D. Sharma, A chaotic based image encryption scheme using elliptic curve cryptography and genetic algorithm. Artificial Intelligece Review, 57(4), (2024) 87. https://doi.org/10.1007/s10462-024-10719-0
  11. M.M. Deep, M.N.D. Praveen, P.S. Deekshith, P.V. Teja, S.K. Kannaiah, K. Prasad, (2024) A survey on image encryption using elliptic curve cryptography. Proceedings of the International Conference on Inventive Computation Technologies (ICICT), IEEE, Lalitpur, Nepal, 1460–1464. https://doi.org/10.1109/ICICT60155.2024.10544776
  12. X. Tong, M. Cui, Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator. Signal Processing, 89(4), (2009) 480–491. https://doi.org/10.1016/j.sigpro.2008.09.011
  13. M. Usama, O. Rehman, I. Memon, S. Rizvi, An efficient construction of key-dependent substitution box based on chaotic sine map. International Journal of Distributed Sensor Networks, 15(12), (2019) 1550147719895957. https://doi.org/10.1177/1550147719895957
  14. L.S. Khan, M.M. Hazzazi, M. Khan, S.S. Jamal, A novel image encryption based on Rossler map diffusion and particle swarm optimization generated highly non-linear substitution boxes. Chinese Journal of Physics, 72, (2021) 558–574. https://doi.org/10.1016/j.cjph.2021.03.029
  15. D. Lambić, A novel method of S-box design based on discrete chaotic map. Nonlinear Dynamics, 87, (2017) 2407–2413. https://doi.org/10.1007/s11071-016-3199-x
  16. C.E. Shannon, Communication theory of secrecy systems. The Bell System Technical Journal, Nokia Bell Labs, 28(4), (1949) 656–715. https://doi.org/10.1002/j.1538-7305.1949.tb00928.x
  17. A. Vaish, An error free and key sensitive color image encryption-using sine powered map and Arnold transform in Stockwell domain. Multimedia Tools and Applications, 83 (2023) 1–19. https://doi.org/10.1007/s11042-023-16277-x
  18. S. Kumar, S. Srivastava, Image encryption using simplified data encryption standard (S-DES). International Journal of Computer Applications, 104(2), (2014) 38-42. https://doi.org/10.5120/18178-9070
  19. A. Kumar, M. Dua, A novel exponent–sine–cosine chaos map-based multiple-image encryption technique. Multimedia Systems, 30(3), (2024) 141. https://doi.org/10.1007/s00530-024-01334-8
  20. Y. Luo, J. Yu, W. Lai, L. Liu, A novel chaotic image encryption algorithm based on improved baker map and logistic map. Multimedia Tools and Applications, 78, (2019) 22023–22043. https://doi.org/10.1007/s11042-019-7453-3
  21. M. Salleh, S. Ibrahim, I.F. Isnin, (2003) Enhanced chaotic image encryption algorithm based on baker’s map. Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03, IEEE, Bangkok, Thailand. https://doi.org/10.1109/ISCAS.2003.1206022
  22. T. Xiang, X. Liao, G. Tang, Y. Chen, K.-W. Wong, A novel block cryptosystem based on iterating a chaotic map. Physics Letters A, 349(1–4), (2006) 109–115. https://doi.org/10.1016/j.physleta.2005.02.083
  23. M. François, T. Grosges, D. Barchiesi, R. Erra, A new image encryption scheme based on a chaotic function. Signal Processing: Image Communication, 27(3), (2012) 249–259. https://doi.org/10.1016/j.image.2011.11.003
  24. X. Wang, L. Teng, X. Qin, A novel colour image encryption algorithm based on chaos. Signal Processing, 92(4), (2012) 1101–1108. https://doi.org/10.1016/j.sigpro.2011.10.023
  25. M. Kumar, A. Vaish, Encryption of color images using mSVD in DCST domain. Optics and Lasers in Engineering, 88, (2017) 51–59. https://doi.org/10.1016/j.optlaseng.2016.07.009
  26. F. Masood, J. Masood, L. Zhang, S.S. Jamal, W. Boulila, S.U. Rehman, F.A. Khan, J. Ahmad, A new color image encryption technique using DNA computing and Chaos-based substitution box. Soft Computing, 26(16), (2022) 7461-7477.
  27. D. Chatterjee, B.G. Banik, A. Banik, Attack resistant chaos-based cryptosystem by modified baker map and logistic map. International Journal of Information and Computer Security, 20(1–2), (2023) 48–83.
  28. .Z. Hussain, M.A.A.A. Khodher, Medical image encryption using multi chaotic maps. TELKOMNIKA (Telecommunication Computing Electronics and Control), 21(3), (2023) 556–565. http://doi.org/10.12928/telkomnika.v21i3.24324
  29. S. Sudevan, K. Jain, (2023) A lightweight medical image encryption scheme using chaotic maps and image scrambling. Proceedings of the International Symposium on Digital Forensics and Security (ISDFS), IEEE, Chattanooga, USA
  30. E.A. Naeem, A.B. Joshi, D. Kumar, F.E.A. El-Samie, Few-detail image encryption algorithm based on diffusion and confusion using Henon and Baker chaotic maps. Soft Computing, 28(4), (2024) 2851–2861. https://doi.org/10.1007/s00500-023-09333-z
  31. L. Yi, X. Tong, Z. Wang, M. Zhang, H. Zhu, J. Liu, A novel block encryption algorithm based on chaotic S-box for wireless sensor network. IEEE Access, IEEE, 7, (2019) 53079–53090. https://doi.org/10.1109/ACCESS.2019.2911395
  32. L. Liu, Y. Zhang, X. Wang, A novel method for constructing the S-box based on spatiotemporal chaotic dynamics. Applied Sciences, 8(12), (2018) 2650. https://doi.org/10.3390/app8122650
  33. A. Ullah, S.S. Jamal, T. Shah, A novel construction of substitution box using a combination of chaotic maps with improved chaotic range. Nonlinear Dynamics, 88, (2017) 2757–2769. https://doi.org/10.1007/s11071-017-3409-1
  34. V. Patidar, N. Pareek, K. Sud, A new substitution–diffusion based image cipher using chaotic standard and logistic maps. Communications in Nonlinear Science and Numerical Simulation, 14(7), (2009) 3056–3075. https://doi.org/10.1016/j.cnsns.2008.11.005
  35. S. Yang, X. Tong, Z. Wang, M. Zhang, Efficient color image encryption algorithm based on 2D coupled chaos and multi-objective optimized S-box. Physica Scripta, 97(4), (2022) 045204. https://doi.org/10.1088/1402-4896/ac59fa
  36. R. Ali, J. Ali, P. Ping, M.K. Jamil, A novel S-box generator using Frobenius automorphism and its applications in image encryption. Nonlinear Dynamics, 112(21), (2024) 19463–19486. https://doi.org/10.1007/s11071-024-10003-4
  37. D. Ustun, S. Sahinkaya, N. Atli, Developing a secure image encryption technique using a novel S-box constructed through real-coded genetic algorithm’s crossover and mutation operators. Expert Systems with Applications, 256, (2024) 124904. https://doi.org/10.1016/j.eswa.2024.124904
  38. R.S. Ali, O.Z. Akif, S.A. Jassim, A.K. Farhan, E.-S.M. El-Kenawy, A. Ibrahim, M.E. Ghoneim, A.A. Abdelhamid, Enhancement of the CAST block algorithm based on novel S-box for image encryption. Sensors, 22(21), (2022) 8527. https://doi.org/10.3390/s22218527
  39. J. Zheng, Q. Zeng, An image encryption algorithm using a dynamic S-box and chaotic maps. Applied Intelligence, 52(13), (2022) 15703–15717. https://doi.org/10.1007/s10489-022-03174-3
  40. L. Wang, Q. Ran, J. Ding, Quantum color image encryption scheme based on 3D non-equilateral Arnold transform and 3D logistic chaotic map. International Journal of Theoretical Physics, 62(2), (2023) 36. https://doi.org/10.1007/s10773-023-05295-y
  41. D. Singh, S. Kumar, Image authentication and encryption algorithm based on RSA cryptosystem and chaotic maps. Expert Systems with Applications, 274, (2025) 126883. https://doi.org/10.1016/j.eswa.2025.126883
  42. L. Li, A novel chaotic map application in image encryption algorithm. Expert Systems with Applications, 252, (2024) 124316. https://doi.org/10.1016/j.eswa.2024.124316
  43. D. Singh, S. Kumar, C. Verma, Z. Illes, N. Kumar, Visually meaningful image encryption for secure and authenticated data transmission using chaotic maps. Journal of King Saud University – Computer and Information Sciences, 36(10), (2024) 102235. https://doi.org/10.1016/j.jksuci.2024.102235
  44. L.L. Hu, M.X. Chen, M.M. Wang, N.R. Zhou, A multi-image encryption scheme based on block compressive sensing and nonlinear bifurcation diffusion. Chaos, Solitons & Fractals, 188, (2024) 115521. https://doi.org/10.1016/j.chaos.2024.115521
  45. Q. Lu, C. Zhu, X. Deng, An efficient image encryption scheme based on the LSS chaotic map and single S-box. IEEE Access, IEEE, 8, (2020) 25664–25678. https://doi.org/10.1109/ACCESS.2020.2970806
  46. U.H. Mir, P.N. Lone, D. Singh, D. Mishra, A public and private key image encryption by modified approach of Vigenère cipher and the chaotic maps. The Imaging Science Journal, 71(1), (2023) 82–96. https://doi.org/10.1080/13682199.2023.2175436
  47. A. Mahboob, M. Asif, I. Siddique, A. Saleem, M. Nadeem, D. Grzelczyk, J. Awrejcewicz, A novel construction of substitution box based on polynomial mapped and finite field with image encryption application. IEEE Access, 10, (2022) 119244–119258. https://doi.org/10.1109/ACCESS.2022.3218643
  48. P. Ayubi, S. Setayeshi, A.M. Rahmani, Deterministic chaos game: A new fractal based pseudo-random number generator and its cryptographic application. Journal of Information Security and Applications, 52, (2020) 102472. https://doi.org/10.1016/j.jisa.2020.102472
  49. D. Ravichandran, P. Praveenkumar, J.B.B. Rayappan, R. Amirtharajan, DNA chaos blend to secure medical privacy. IEEE Transactions on Nanobioscience, IEEE, 16(8), (2017) 850–858. https://doi.org/10.1109/TNB.2017.2780881
  50. U.H. Mir, D. Singh, D. Mishra, P.N. Lone, Multilayer security of RGB image in discrete Hartley domain. Applications and Applied Mathematics: An International Journal, 15(2), (2020) 29.
  51. M. Diwakar, M. Kumar, CT image denoising using NLM and correlation-based wavelet packet thresholding. IET Image Processing, 12(5), (2018) 708–715. https://doi.org/10.1049/iet-ipr.2017.0639
  52. S. Agrawal, M. Kumar, Mean value based reversible data hiding in encrypted images. Optik, 130 (2017) 922–934. https://doi.org/10.1016/j.ijleo.2016.11.059
  53. X.Y. Wang, P. Li, Y.Q. Zhang, L.Y. Liu, H. Zhang, X. Wang, A novel color image encryption scheme using DNA permutation based on the Lorenz system. Multimedia Tools and Applications, 77, (2018) 6243–6265. https://doi.org/10.1007/s11042-017-4534-z
  54. Y. Wu, J.P. Noonan, S. Agaian, NPCR and UACI randomness tests for image encryption. Cyber Journals: Multidisciplinary Journals in Science and Technology – Journal of Selected Areas in Telecommunications, (2011) 31–38.
  55. P.N. Lone, D. Singh, U.H. Mir, Image encryption using DNA coding and three-dimensional chaotic systems. Multimedia Tools and Applications, 81(4), (2022) 5669–5693. https://doi.org/10.1007/s11042-021-11802-2
  56. P.N. Lone, D. Singh, U.H. Mir, A novel image encryption using random matrix affine cipher and the chaotic maps. Journal of Modern Optics, 68(10), (2021) 507–521. https://doi.org/10.1080/09500340.2021.1924885
  57. W. Alexan, M. Elkandoz, M. Mashaly, E. Azab, A. Aboshousha, Color image encryption through chaos and KAA map. IEEE Access, 11, (2023) 11541–11554. https://doi.org/10.1109/ACCESS.2023.3242311
  58. W. Alexan, M. ElBeltagy, A. Aboshousha, RGB image encryption through cellular automata, S-box and the Lorenz system. Symmetry, 14(3), (2022) 443. https://doi.org/10.3390/sym14030443
  59. M.T. Elkandoz, W. Alexan, Image encryption based on a combination of multiple chaotic maps. Multimedia Tools and Applications, 81(18), (2022) 25497–25518. https://doi.org/10.1007/s11042-022-12595-8
  60. S. Sheela, K. Suresh, D. Tandur, Image encryption based on modified Henon map using hybrid chaotic shift transform. Multimedia Tools and Applications, 77, (2018) 25223–25251. https://doi.org/10.1007/s11042-018-5782-2
  61. L. Teng, X. Wang, Y. Xian, Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusion. Information Sciences, 605, (2022) 71–85. https://doi.org/10.1016/j.ins.2022.05.032
  62. G. Ye, K. Jiao, X. Huang, Quantum logistic image encryption algorithm based on SHA-3 and RSA. Nonlinear Dynamics, 104, (2021) 2807–2827. https://doi.org/10.1007/s11071-021-06422-2