Cover
Vol. 24 No. 2 (2024)

Published: August 31, 2024

Pages: 68-73

Original Article

S-Box Design Utilizing 3D Chaotic Maps for Cryptographic Application

Jenan Ayad Namuq 1
1 Department of Electro-Mechanical Engineering, University of Technology, Baghdad, Iraq
History
  • Received: June 30, 2024
  • Revised: July 26, 2024
  • Accepted: August 1, 2024
  • Available Online: August 17, 2024
DOI

https://doi.org/10.33971/bjes.24.2.9

Abstract

In the realm of cryptography, the Substitution-box (S-box) is a critical component for enhancing the security of encryption algorithms. The inherent characteristics of Chaos, such as sensitivity to beginning conditions and unpredictability, make it a highly suitable choice for encryption applications. In this paper, proposed a method for generating S-Boxes using 3D chaotic maps algorithms including (Cat map, Henon map, Sine map, and Cosine map). The primary focus is on enhancing the security and efficiency of cryptographic systems by leveraging the inherent complexity and unpredictability of chaotic maps. The design methodology focuses on achieving high non-linearity, optimal avalanche effect, and Strict Avalanche Criterion ( SAC ), ensuring that minor changes in plaintext result in significant alterations in the ciphertext. Our study presents a detailed analysis of the generated S-Boxes, demonstrating their robustness against common cryptographic attacks. Key findings include significant improvements in nonlinearity, differential uniformity, and bijectivity compared to traditional methods. The test findings and performance analysis indicate that our proposed S-Box exhibits much lower values of Linear Probability ( LP ) and Differential Probability ( DP ), while maintaining a suitable average value of nonlinearity. Additionally, discussed the broader implications of our findings, emphasizing how the proposed method can be employed to produce high-quality analytical results that enhance the security measures of cryptographic applications. This work adds valuable context to existing research and highlights the potential for our model to outperform conventional S-Box generation techniques.

Keywords

References

  1. Z. Chen, and G. Ye, “An asymmetric image encryption scheme based on hash SHA-3, RSA, and Compressive Sensing,” Optik, Vol. 267, 2022.
  2. S. T. Kamal, K. M. Hosny, T. M. Elgindy, M. M. Darwish and M. M. Fouda, “A new image encryption algorithm for Grey and color medical images,” IEEE Access, Vol. 9, pp. 37855-37865, 2021.
  3. H. I. Mhaibes, M. H. Abood, and A. Farhan, “Simple lightweight cryptographic algorithm to secure imbedded IOT devices,” International Journal of Interactive Mobile Technologies (iJIM), Vol. 16, Issue 20, pp. 98-113, 2022.
  4. 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, Vol. 22, Issue 21, 2022. https://doi.org/10.3390/s22218527
  5. J. Ayad, F. S. Hasan and A. H. Ali, “Image encryption using One Dimensional Chaotic Map and transmission Through OFDM system”, 14th International Conference on Computing Communication and Networking Technologies (ICCCNT), Delhi, India, pp. 1-7, 2023.
  6. J. Ayad, F. S. Hasan and A. H. Ali, “OFDM Transmission for encrypted Images based on 3D Chaotic Map and S-Box through Fading Channel”, International Conference on Smart Systems for applications in Electrical Sciences (ICSSES), Tumakuru, India, pp. 1-6, 2023.
  7. Z. Hua, Y. Zhou, and H. Huang, “Cosine-transform-based chaotic system for image encryption,” Information Sciences, Vol. 480, pp. 403-419, 2019.
  8. J. Ayad, F. S. Hasan and A. H. Ali, “Efficient Transmission of Secure Images with OFDM using Chaotic Encryption”, 4th International Conference on Circuits, Control, Communication and Computing (I4C), Bangalore, India, pp. 391-396, 2022.
  9. R. B. Naik, and U. Singh, “A review on applications of chaotic maps in pseudo-random number generators and encryption,” Annals of Data Science, Vol. 11, pp. 25-50, 2022. https://doi.org/10.1007/s40745-021-00364-7
  10. C. Zhu, Z. Gan, Y. Lu, and X. Chai, “An image encryption algorithm based on 3-D DNA level permutation and substitution scheme,” Multimedia Tools and Applications, Vol. 79, pp. 7227-7258, 2020.
  11. D. S. Laiphrakpam, R. Thingbaijam, K. M. Singh and M. Al Awida, “Encrypting multiple images with an enhanced chaotic map,” IEEE Access, Vol. 10, pp. 87844-87859, 2022. https://doi.org/10.1109/access.2022.3199738
  12. B. Ge, X. Chen, G. Chen and Z. Shen, “Secure and fast image encryption algorithm using hyper-chaos-based key generator and vector operation,” IEEE Access, Vol. 9, pp. 137635-137654, 2021.
  13. A. S. Saljoughi, and H. Mirvaziri, “A new method for image encryption by 3D chaotic map,” Pattern Analysis and Applications, Vol. 22, Issue 1, pp. 243-257, 2018.
  14. Q. Lai, G. Hu, U. Erkan, and A. Toktas, “High-efficiency medical image encryption method based on 2D logisticgaussian hyperchaotic map,” Applied Mathematics and Computation, Vol. 442, 2023.
  15. P. Parida, C. Pradhan, X. -Z. Gao, D. S. Roy and R. K. Barik, “Image encryption and authentication with elliptic curve cryptography and multidimensional chaotic maps,” IEEE Access, Vol. 9, pp. 76191-76204, 2021.
  16. S. Benaissi, N. Chikouche, and R. Hamza, “A novel image encryption algorithm based on hybrid chaotic maps using a key image,” Optik, Vol. 272, 2023.
  17. S. Gao, R. Wu, X. Wang, J. Wang, Q. Li, C. Wang, and X. Tang, “A 3D model encryption scheme based on a cascaded chaotic system,” Signal Processing, Vol. 202, 2023. https://doi.org/10.1016/j.sigpro.2022.108745
  18. D. Wei, M. Jiang, and Y. Deng, “A secure image encryption algorithm based on hyper-chaotic and bit-level permutation,” Expert Systems with Applications, Vol. 213, Part B, 2023. https://doi.org/10.1016/j.eswa.2022.119074
  19. W. Song, C. Fu, Y. Zheng, M. Tie, J. Liu and J. Chen, “A parallel image encryption algorithm using intra bitplane scrambling,” Mathematics and Computers in Simulation, Vol. 204, pp. 71-88, 2023.
  20. S. Yan, L. Li, B. Gu, Y. Cui, J. Wang and J. Song, “Design of hyperchaotic system based on multi-scroll and its encryption algorithm in color image,” Integration, Vol. 88, pp. 203-221, 2023.
  21. L. Zhu, D. Jiang, J. Ni, X. Wang, X. Rong and M. Ahmad “A visually secure image encryption scheme using adaptive-thresholding sparsification compression sensing model and newly-designed memristive chaotic map,” Information Sciences, Vol. 607, pp. 1001-1022, 2022.
  22. A. Javeed, T. Shah and A. Attaullah, “Lightweight secure image encryption scheme based on chaotic differential equation,” Chinese Journal of Physics, Vol. 66, pp. 645659, 2020. https://doi.org/10.1016/j.cjph.2020.04.008
  23. S. Bhowmik and S. Acharyya, “Image encryption approach using improved chaotic system incorporated with differential evolution and genetic algorithm,” Journal of Information Security and Applications, Vol. 72, 2023.
  24. L. Liu, and J. Wang, “A cluster of 1D quadratic chaotic map and its applications in image encryption,” Mathematics and Computers in Simulation, Vol. 204, pp. 89-114, 2023.
  25. S. Zhou, X. Wang and Y. Zhang, “Novel image encryption scheme based on chaotic signals with finiteprecision error,” Information Sciences, Vol. 621, pp. 782798, 2023. https://doi.org/10.1016/j.ins.2022.11.104
  26. E. Setyaningsih, R. Wardoyo, and A. K. Sari, “Securing color image transmission using compression-encryption model with dynamic key generator and efficient symmetric key distribution,” Digital Communications and Networks, Vol. 6, Issue 4, pp. 486-503, 2020.
  27. A. S. Alanazi, “A dual layer secure data encryption and hiding scheme for color images using the threedimensional chaotic map and Lah Transformation,” IEEE Access, Vol. 9, pp. 26583-26592, 2021.
  28. W. J. Jun, and T. S. Fun, “A new image encryption algorithm based on single S-box and dynamic encryption step,” IEEE Access, Vol. 9, pp. 120596-120612, 2021.
  29. M. Tanveer, T. Shah, A. Rehman, A. Ali, G. F. Siddiqui, T. Saba, and U. Tariq, “Multi-images encryption scheme based on 3D chaotic map and Substitution Box,” IEEE Access, Vol. 9, pp. 73924-73937, 2021.
  30. Z. A. Abduljabbar, I. Q. Abduljaleel, J. Ma, M. A. Al Sibahee, V. O. Nyangaresi, D. G. Honi, A. I. Abdulsada, and X. Jiao, “Provably secure and fast color image encryption algorithm based on S-boxes and hyperchaotic map,” IEEE Access, Vol. 10, pp. 26257-26270, 2022.
  31. S. Deb, and P. K. Behera, “Design of key-dependent bijective S-boxes for color image cryptosystem,” Optik, Vol. 253, 2022.
  32. Y. Naseer, D. Shah, and T. Shah, “A novel approach to improve multimedia security utilizing 3D mixed chaotic map,” Microprocessors and Microsystems, Vol. 65, pp. 16, 2019. https://doi.org/10.1016/j.micpro.2018.12.003
  33. X. Qian, Q. Yang, Q. Li, Q. Liu, Y. Wu and W. Wang, “A novel color image encryption algorithm based on threedimensional chaotic maps and reconstruction techniques,” IEEE Access, Vol. 9, pp. 61334-61345, 2021.
  34. J. A. Namuq, F. S. Hasan, and A. H. Ali, “Image encryption based on S-box and 3D-chaotic maps and secure image transmission through OFDM in Rayleigh Fading Channel,” Engineering and Technology Journal, Vol. 42, Issue 2, pp. 288-297, 2024.
  35. J. Wang, J. Chen, F. Wang, and R. Ni, “Optical Image Encryption scheme based on quantum S-box and meaningful ciphertext generation algorithm,” Optics Communications, Vol. 525, 2022.
  36. A. Zahid, and M. Arshad, “An innovative design of substitution-boxes using cubic polynomial mapping,” Symmetry, Vol. 11, Issue 3, 2019.
  37. M. Aslam, S. Beg, A. Anjum, Z. Qadir, S. Khan, S. U. R. Malik, M. A. P. Mahmud, “A strong construction of S-box using Mandelbrot set an image encryption scheme,” PeerJ Computer Science, Vol. 8, 2022.
  38. R. H. Sani, S. Behnia, and A. Akhshani, “Creation of Sbox based on a hierarchy of julia sets: Image encryption approach,” Multidimensional Systems and Signal Processing, Vol. 33, Issue 1, pp. 39-62, 2021.
  39. S. Ibrahim, and A. Alharbi, “Efficient Image Encryption scheme using Henon map, dynamic S-boxes and elliptic curve cryptography,” IEEE Access, Vol. 8, pp. 194289194302, 2020.
  40. B. B. Cassal-Quiroga, and E. Campos-Cantón, “Generation of dynamical S-boxes for block ciphers via extended logistic map,” Mathematical Problems in Engineering, Vol. 2020, pp. 1-12, 2020.
  41. S. Zhou, Y. Qiu, X. Wang, and Y. Zhang, “Novel image Cryptosystem based on new 2D hyperchaotic map and dynamical chaotic S-box,” Nonlinear Dynamics, Vol. 111, pp. 9571-9589, 2023.
  42. X.-Y. Wang, H.-H. Sun, and H. Gao, “An image encryption algorithm based on improved Baker transformation and chaotic S-box,” Chinese Physics B, Vol. 30, Issue 6, 2021.
  43. B. Idrees, S. Zafar, T. Rashid, and W. Gao, “Image encryption algorithm using S-box and dynamic Hénon bit level permutation,” Multimedia Tools and Applications, Vol. 79, Issue 9-10, pp. 6135-6162, 2019.
  44. X. Wang, and J. Yang, “A novel image encryption scheme of dynamic S-boxes and random blocks based on spatiotemporal chaotic system,” Optik, Vol. 217, 2020.
  45. L. Liu, and J. Wang, “A cluster of 1D quadratic chaotic map and its applications in image encryption,” Mathematics and Computers in Simulation, Vol. 204, pp. 89-114, 2023.
  46. S. Bhowmik, and S. Acharyya, “Image encryption approach using improved chaotic system incorporated with differential evolution and genetic algorithm,” Journal of Information Security and Applications, Vol. 72, 2023.
  47. C. Chen, K. Sun, and S. He, “An improved image encryption algorithm with finite computing precision,” Signal Processing, Vol. 168, 2020.
  48. X. Wang, Y. Su, M. Xu, H. Zhang, and Y. Zhang, “A new image encryption algorithm based on Latin square matrix,” Nonlinear Dynamics, Vol. 107, Issue 1, pp. 1277-1293, 2021. https://doi.org/10.1007/s11071-021-07017-7
  49. L. Teng, X. Wang, and Y. Xian, “Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusion,” Information Sciences, Vol. 605, pp. 71-85, 2022.