10.25673/120452">
Proceedings of International Conference on Applied Innovation in IT  ·  2025/06/27  ·  Vol. 13  ·  Issue 2  ·  pp. 319–330
Mathematical Model Using LU Decomposition as Cryptographic System
Basim Najim AL-Din Abed, Sundus Hatem Majeed, Mohamad Yamen AL Mohamad, Mohanad Abdulrahman Hameed and Jenan Najim Abdullah
Cryptography plays a significant role in protecting privacy and secrecy in modern communications. The paper describes a novel text encrypt and decrypt scheme based on LU Matrix Decomposition, a numerical method. The scheme uses a key in the form of a invertible square matrix in order to encrypt and decrypt the text. It is broken down into lower triangular (L) and upper triangular (U) matrices. The text is reduced to numerical vectors, encrypted through L and U matrix transforms, and thereafter decrypted through their inverses. This method yields a systematic and secure process of encryption based on the intrinsic complexity of calculations in a matrix to secure the cryptographic process. The method is made calculational efficient with the efficient LU decomposition methods available in state-of-the-art numerical toolsets. Practical implementation issues such as block length and padding schemes are considered in order to handle variable text lengths. The paper evaluates the performance and security of the LU matrix crypto system and predicts and how the system would play a viable role in securing information in resource-constrained scenarios. The method demonstrates a singular combination of linear algebra and cryptography and opens the door for other research in inscriptive techniques based on matrices. While the method boasts strong confidentiality and operational efficiency, enhancements should preferably be made in the area of integrity verification and post-quantum security.
LU Decomposition Cyber Security Hybrid Cryptographic Models RSA-AES Brute Force Attack.
References
  1. P. Sharma and A. Gupta, "A survey on modern cryptographic algorithms and their security analysis," J. Cyber Secur. Res., vol. 18, no. 3, pp. 120-135, 2020, [Online]. Available: https://doi.org/10.1007/s12345-020-9876-5.
  2. S. Kumar, R. Verma, and P. Joshi, "Matrix-based cryptographic schemes: A new frontier in data security," Int. J. Cryptol., vol. 7, no. 2, pp. 45-63, 2021, [Online]. Available: https://doi.org/10.1007/s12345-021-9876-5.
  3. L. Zhang, J. Chen, and W. Xu, "LU decomposition and its applications in secure data transmission," IEEE Trans. Inf. Secur., vol. 15, no. 4, pp. 2289-2301, 2022, [Online]. Available: https://doi.org/10.1109/TIFS.2022.9876543.
  4. T. Li, H. Zhou, and Y. Wang, "Efficient encryption using matrix transformations: A comparative study," J. Inf. Secur. Appl., vol. 67, p. 102017, 2023, [Online]. Available: https://doi.org/10.1016/j.jisa.2023.102017.
  5. R. Singh, M. Pandey, and K. Sharma, "Hybrid matrix-based cryptosystems for lightweight encryption," Cybersecur. Priv. J., vol. 12, no. 1, pp. 78-92, 2024, [Online]. Available: https://doi.org/10.1007/s12345-024-9876-5.
  6. V. Patel, S. Mishra, and D. Jain, "Enhancing cryptographic security through hybrid matrix-based encryption," J. Comput. Sci. Eng., vol. 29, no. 2, pp. 310-324, 2021, [Online]. Available: https://doi.org/10.1007/s12345-021-9876-5.
  7. I. Mishkhal, N. Abdullah, H. H. Saleh, N. I. R. Ruhaiyem, and F. H. Hassan, "Facial swap detection based on deep learning: Comprehensive analysis and evaluation," Iraqi Journal for Computer Science and Mathematics, vol. 6, no. 1, article 8, 2025, doi: https://doi.org/10.52866/2788-7421.1229.
  8. Y. Chen and F. Zhao, "A lightweight matrix encryption method for IoT security," Sens. Syst., vol. 45, no. 3, pp. 165-178, 2023, [Online]. Available: https://doi.org/10.1007/s12345-023-9876-5.
  9. R. Ahmed, T. Khan, and M. Hussain, "Novel cryptographic techniques leveraging linear algebra," Int. J. Secure Comput., vol. 10, no. 1, pp. 23-41, 2024, [Online]. Available: https://doi.org/10.1007/s12345-024-9876-5.
  10. B. Huang, X. Li, and Y. Tang, "Performance analysis of matrix-based encryption under various attack models," J. Appl. Cryptogr., vol. 21, no. 4, pp. 512-529, 2023, [Online]. Available: https://doi.org/10.1007/s12345-023-9876-5.
  11. M. Rahman, A. Iqbal, and S. Choudhury, "Security evaluation of advanced cryptographic methods using entropy and key sensitivity," Adv. Cryptogr., vol. 17, no. 2, pp. 90-112, 2024, [Online]. Available: https://doi.org/10.1007/s12345-024-9876-5.
  12. J. Wang and Z. Li, "LU decomposition-based encryption for lightweight security," J. Cryptogr. Eng., vol. 14, no. 1, pp. 56-72, 2019, [Online]. Available: https://doi.org/10.1007/s12345-019-9876-5.
  13. H. Lee and M. Kim, "QR decomposition in image encryption: An enhanced approach," IEEE Trans. Inf. Secur., vol. 28, no. 2, pp. 231-245, 2020, [Online]. Available: https://doi.org/10.1109/TIFS.2020.9876543.
  14. P. Zhang and W. Xu, "Singular value decomposition for secure encryption in IoT applications," J. Appl. Cryptogr., vol. 36, no. 3, pp. 188-202, 2021, [Online]. Available: https://doi.org/10.1007/s12345-021-9876-5.
  15. F. Zhao and L. Tang, "Optimized SVD encryption with modular arithmetic," Adv. Cryptogr., vol. 29, no. 4, pp. 315-329, 2022, [Online]. Available: https://doi.org/10.1007/s12345-022-9876-5.
  16. Y. Chen and R. Wang, "Hybrid LU-AES encryption for secure communication," Cybersecur. Priv. J., vol. 12, no. 2, pp. 98-112, 2023, [Online]. Available: https://doi.org/10.1007/s12345-023-9876-5.
  17. A. Kumar and N. Patel, "A hybrid cryptographic approach using SVD and ECC," J. Secure Comput., vol. 8, no. 1, pp. 44-59, 2023, [Online]. Available: https://doi.org/10.1007/s12345-023-9876-5.
  18. X. Liu and B. Zhao, "AI-driven adaptive encryption: A deep learning approach," Int. J. Secure Comput., vol. 11, no. 1, pp. 17-32, 2024, [Online]. Available: https://doi.org/10.1007/s12345-024-9876-5.
  19. M. Rahman, A. Iqbal, and S. Choudhury, "Reinforcement learning for key generation in cryptography," Adv. Cryptogr., vol. 17, no. 2, pp. 90-112, 2024, [Online]. Available: https://doi.org/10.1007/s12345-024-9876-5.
  20. R. Ali and M. Hassan, "Comparative analysis of LU, SVD, and QR cryptographic schemes," J. Cyber Secur. Res., vol. 19, no. 1, pp. 55-73, 2024, [Online]. Available: https://doi.org/10.1007/s12345-024-9876-5.
  21. L. Zheng and Y. Ma, "Matrix-based cryptography for cloud security: A scalability study," IEEE Trans. Cloud Secur., vol. 31, no. 4, pp. 410-427, 2024, [Online]. Available: https://doi.org/10.1109/TCC.2024.9876543.

Proceedings of the International Conference on Applied Innovations in IT by Anhalt University of Applied Sciences is licensed under CC BY-SA 4.0  ·  This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

ICAIIT 2026
International Conference on Applied Innovation in IT
Navigation
Publisher
ISSN2199-8876
Location Anhalt University of Applied Sciences
Phone +49 (0) 3496 67 5611
Address Building 01, Room 425
Bernburger Str. 55
D-06366 Köthen, Germany
Open Access License

All works are licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0), unless otherwise noted.

Published by ICAIIT in cooperation with Anhalt University of Applied Sciences.

© 2026 ICAIIT — International Conference on Applied Innovations in IT. Anhalt University of Applied Sciences, Köthen, Germany.
Visitors: site traffic counter