Khalaf, D., Hussain, K., Darwish, M. (2025). Enhanced Hill Cipher Encryption Using Chaotic Logistic Maps for Improved Security and Key Randomness. JES. Journal of Engineering Sciences, 53(5), 170-195. doi: 10.21608/jesaun.2025.434995
Doaa Khalaf; Khaled Hussain; Mohamed Darwish. "Enhanced Hill Cipher Encryption Using Chaotic Logistic Maps for Improved Security and Key Randomness". JES. Journal of Engineering Sciences, 53, 5, 2025, 170-195. doi: 10.21608/jesaun.2025.434995
Khalaf, D., Hussain, K., Darwish, M. (2025). 'Enhanced Hill Cipher Encryption Using Chaotic Logistic Maps for Improved Security and Key Randomness', JES. Journal of Engineering Sciences, 53(5), pp. 170-195. doi: 10.21608/jesaun.2025.434995
Khalaf, D., Hussain, K., Darwish, M. Enhanced Hill Cipher Encryption Using Chaotic Logistic Maps for Improved Security and Key Randomness. JES. Journal of Engineering Sciences, 2025; 53(5): 170-195. doi: 10.21608/jesaun.2025.434995
Enhanced Hill Cipher Encryption Using Chaotic Logistic Maps for Improved Security and Key Randomness
1Independent researcher, Faculty of Computers and Information, Computer Science Department, Assuit University, Egypt
2Department of Computer Science, Faculty of Computers and Information, Computer Science Department, Assuit University, Egypt
Abstract
In cryptography, maintaining data confidentiality and ensuring resilience against various attacks are of utmost significance. A popular classical encryption method that is well-known for its effectiveness and simplicity in protecting text data is the Hill cipher. The Hill Cipher algorithm is improved as a polygraphic substitution cipher based on linear algebra. This algorithm uses a square matrix key, and its key matrix must be invertible. However, its susceptibility to known-plaintext and chosen-plaintext attacks, along with key matrix constraints, limits its effectiveness. This paper presents an enhanced Hill cipher algorithm that integrates chaotic logistic maps to improve security, key randomness, and resistance to cryptanalytic attacks. Using the unpredictable nature of chaotic sequences, a dynamic key matrix is generated, ensuring stronger diffusion and confusion properties in encryption. The proposed method eliminates weaknesses associated with traditional hill cipher and enhances resistance to statistical and brute-force attacks. The results of experiments and analysis of security show that the chaotic logistic Hill cipher significantly improves the encryption strength. This approach provides a robust and adaptable cryptographic solution for securing textual data in modern applications.
[1] J. Yin, M. Tang, J. Cao, and S. et al., “Knowledge-driven cybersecurity intelligence: Software vul- nerability coexploitation behavior discovery,” IEEE Transactions on Industrial Informatics, vol. 19, no. 4, pp. 5593–5601, 2023.
[2] V. R. F. Signing, G. A. G. Teague, M. Kountchou, Z. T. Njitacke, N. Tsafack, J. D. D. Nkapkop, C. M. L. Etoundi, and J. Kengne, “A cryptosystem based on a chameleon chaotic system and dynamic dna coding,” Chaos Solitons Fractals, vol. 155, p. 111777, 2022.
[3] F. Kahlessenane, A. Khaldi, M. R. Kafi, and S. Euschi, “A color value differentiation scheme for blind digital image watermarking,” Multimedia Tools and Applications, vol. 80, pp. 19 827–19 844, 2021.
[4] A. Khalifa and A. Guzman, “Imperceptible image steganography using symmetry-adapted deep learning techniques,” Symmetry, vol. 14, p. 1325, 2022.
[5] A. Abdelwahab, (2006). Cryptography scheme based on transparent feedforward neural network and ordered lookup table. JES. Journal of Engineering Sciences, 34(1), 189-197, 2006.
[6] W. Stallings, Cryptography and Network Security: Principles and Practice (7th Edition). Pearson, 2020.
[7] Fauzyah, Zahrah Asri Nur, Aceng Sambas, Prajanto Wahyu Adi, and De Rosal Ignatius Moses Setiadi. "Quantum Key Distribution-Assisted Image Encryption Using 7D and 2D Hyperchaotic Systems." Journal of Future Artificial Intelligence and Technologies 2, no. 1 (2025): 47-62.
[8] R. Flores-Carapia, V. M. Silva-Garc´ıa, M. A. Cardona-L´opez, et al., “A chaotic digital signature algorithm based on a dynamic substitution box,” Scientific Reports, vol. 15, p. 2435, 2025. [Online]. Available: https://doi.org/10.1038/s41598-024-83943-x
[9] P. Radanliev, “Artificial intelligence and quantum cryptography,” Journal of Analytical Science and Technology, vol. 15, p. 4, 2024.
[10] F. Varghese and P. Sasikala, “A detailed review based on secure data transmission using cryptog- raphy and steganography,” Wireless Personal Communications, vol. 129, pp. 2291–2318, 2023.
[11] A. Ostad-Sharif, H. Arshad, M. Nikooghadam, and D. Abbasinezhad-Mood, “Three-party secure data transmission in iot networks through the design of a lightweight authenticated key agreement scheme,” Future Generation Computer Systems, vol. 100, pp. 882–892, 2019.
[12] A. Vambol, “Polynomial-time plaintext-recovery attack on the matrix-based knapsack cipher,” In- ternational Journal of Computing, vol. 19, pp. 474–479, 2020.
[13] S. Dhall, S. Pal, and K. Sharma, “A chaos-based probabilistic block cipher for image encryption,” Journal of King Saud University - Computer and Information Sciences, vol. 34, pp. 1533–1543, 2022.
[14] J. Bezerra, V. de Almeida Camargo, and A. Molter, “A new efficient permutation-diffusion encryp- tion algorithm based on a chaotic map,” Chaos, Solitons Fractals, vol. 151, p. 111235, 2021.
[15] K. Prasad and H. Mahato, “Cryptography using generalized fibonacci matrices with affine-hill ci- pher,” Journal of Discrete Mathematics, Science and Cryptography, vol. 25, pp. 2341–2352, 2022.
[16] H. Wen, Y. Lin, L. Yang, and R. Chen, “Cryptanalysis of an image encryption scheme using variant hill cipher and chaos,” Expert Systems with Applications, vol. 250, p. 123748, 2024.
[17] L. Hill, “Cryptography in an algebraic alphabet,” American Mathematical Monthly, vol. 36, no. 6, pp. 306–312, 1929.
[18] L. S. Hill, “Concerning certain linear transformation apparatus of cryptography,” The American Mathematical Monthly, vol. 38, no. 3, pp. 135–154, 1931.
[19] L. Chen, G. Guo, and Z. Peng, “A hill cipher-based remote data possession checking in cloud storage,” Security and Communication Networks, vol. 7, no. 3, pp. 511–518, 2014.
[20] S. Sahoo, “A cancelable retinal biometric method based on maximum bin computation and his- togram bin encryption using modified hill cipher,” in 2022 IEEE Delhi Section Conference (DEL- CON), 2022, pp. 1–5.
[21] M. Lone and S. Qureshi, “Rgb image encryption based on symmetric keys using arnold transform, 3d chaotic map and affine hill cipher,” Optik, vol. 260, p. 168880, 2022.
[22] Z. Dawahdeh, S. Yaakob, and R. bin Othman, “A new image encryption technique combining elliptic curve cryptosystem with hill cipher,” J. King Saud Univ. Comput. Inf. Sci., vol. 30, pp. 349–355, 2018.
[23] M. Essaid, I. Akharraz, and A. Saaidi, “Image encryption scheme based on a new secure variant of hill cipher and 1d chaotic maps,” J. Inf. Secure. Appl., vol. 47, pp. 173–187, 2019.
[24] Y. Zheng, Q. Huang, S. Cai, X. Xiong, and L. Huang, “Image encryption based on novel hill cipher variant and 2d-igscm hyper-chaotic map,” Nonlinear Dynamics, pp. 1–19, 2024.
[25] S. Mohammed, A. Abbas, M. Ali, and et al., “Design and simulation of secure fiber optic commu- nication system utilizing hill cipher algorithm,” J. Opt., pp. 1–9, 2023.
[26] J. Overbey, W. Traves, and J. Wojdylo, “On the keyspace of the hill cipher,” Cryptologia, vol. 29, no. 1, pp. 59–72, 2005.
[27] X. Chen, K. Makki, K. Yen, and N. Pissinou, “Sensor network security: a survey,” IEEE Commun. Surv. Tutor., vol. 11, no. 2, pp. 52–73, 2009.
[28] Z. Hua, Y. Zhou, and H. Huang, “Cosine-transform-based chaotic system for image encryption,” Inf. Sci. (Ny), vol. 480, pp. 403–419, 2019.
[29] F. Toktas, U. Erkan, and Z. Yetgin, “Cross-channel color image encryption through the 2d hy- perchaotic hybrid map of optimization test functions,” Expert Syst. Appl., vol. 249, p. Sep. 2024, 2024.
[30] U. Erkan, A. Toktas, and Q. Lai, “2d hyperchaotic system based on schaffer function for image encryption,” Expert Syst. Appl., vol. 213, p. Mar. 2023, 2023.
[31] Winarno, E.; Nugroho, K.; Adi, P.W.; Setiadi, D.R.I.M. Combined interleaved pattern to improve confusion-diffusion image encryption based on the hyperchaotic system. IEEE Access 2023, 11, 69005–69021, 10.1109/ACCESS.2023.3285481.
[32] Y. Chen, H. Huang, K. Huang, M. Roohi, and C. Tang, ‘‘A selective chaos driven encryption technique for protecting medical images,’’ Phys. Scripta, vol. 100, no. 1, Jan. 2025, Art. no. 0152a3.
[33] B. Charya, G. S. Rath, S. K. Patra, and S. K. Panigrahy, “Novel methods of generating self-invertible matrix for hill cipher algorithm,” International Journal of Computer Science and Applications, vol. 4, no. 2, pp. 365–378, 2007.
[34] M. Rahman, A. Abidin, M. Yusof, and N. Usop, “Cryptography: a new approach of classical hill cipher,” Int. J. Secur. App., vol. 7, no. 2, pp. 179–190, 2013.
[35] K. Agrawal and A. Gera, “Elliptic curve cryptography with hill cipher generation for secure text cryptosystem,” Int. J. Comput. App., vol. 106, no. 1, 2014.
[36] A. Agarwal, “Secret key encryption algorithm using genetic algorithm,” International Journal of Advanced Research in Computer Science and Software Engineering, vol. 2, no. 4, pp. 216–218, 2012.
[37] N. Sharma and S. Chirgaiya, “A novel approach to hill cipher,” Int. J. Comput. Appl., vol. 108, no. 11, 2014.
[38] A. Siahaan, “Genetic algorithm in hill cipher encryption,” American International Journal of Re-search in Science, Technology, Engineering, and Mathematics, vol. 15, no. 1, pp. 84–89, 2016.
[39] F. H. Khan, R. Shams, F. Qazi, and D. Agha, “Hill cipher key generation algorithm by using an orthogonal matrix,” International Journal of Innovative Science and Modern Engineering, vol. 3, no. 3, pp. 5–7, 2015.
[40] Y. Chen, R. Xie, H. Zhang, et al., “Generation of the high-order random key matrix for hill cipher encryption using the modular multiplicative inverse of triangular matrices,” Wireless Networks, vol. 30, pp. 5697–5707, 2024.
[41] B. Acharya, S. K. Patra, and G. Panda, “Involutory, permuted and reiterative key matrix generation methods for hill cipher system,” Journal Name, vol. Volume, no. Issue, p. Pages, 2009.
[42] S. Saeednia, “How to make the hill cipher secure,” Cryptologia, vol. 24, no. 4, pp. 353–360, 2000.
[43] A. Y. Mahmoud and A. G. Chefranov, “Secure hill cipher modifications and key exchange protocol,” in 2010 IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR), vol. 2. IEEE, 2010, pp. 1–6.
[44] A. Mahmoud and A. Chefranov, “Hill cipher modification based on pseudo-random eigenvalues,” Applied Mathematics Information Science, vol. 8, no. 2, p. 505, 2014.
[45] M. Essaid, I. Akharraz, A. Saaidi, and et al., “Image encryption scheme based on a new secure variant of hill cipher and 1d chaotic maps,” Journal of Information Security and Applications, vol. 47, pp. 173–187, 2019.
[46] A. Krishna and K. Madhuravani, “A modified hill cipher using the randomized approach,” International Journal of Computer Networks and Information Security, vol. 5, no. 5, pp. 56–62, 2012.
[47] P. Lone and D. Singh, “Application of algebra and chaos theory in the security of color images,” Optik, vol. 218, p. 165155, 2020.
[48] L. Ahmad and Q. Shaima, “Encryption scheme for rgb images using chaos and affine hill cipher technique,” Nonlinear Dynamics, vol. 111, pp. 5919–5939, 2023.
[49] R. Hasoun, S. Khlebus, and H. Tayyeh, “A new approach of classical hill cipher in public key cryptography,” International Journal of Nonlinear Analyses and Applications, vol. 12, no. 2, pp. 1071–1082, 2021.
[50] J. Jin, X. Lei, C. Chen, M. Lu, L. Wu, and Z. Li, “A fuzzy zeroing neural network and its application on dynamic hill cipher,” Neural Computing and Applications, pp. 1–15, 2024.
[51] Y. Xi, Y. Ning, J. Jin, and F. Yu, “A dynamic hill cipher with arnold scrambling technique for medical images encryption,” Mathematics, vol. 12, no. 24, p. 3948, 2024.
[52] Pareek, N. K., Patidar, V., & Sud, K. K. (2006). Image encryption using the chaotic logistic map. Image and Vision Computing, 24(9), 926–934. https://doi.org/10.1016/j.imavis.2006.02.021
[53] Rukhin, A., Soto, J., & Nechvatal, J. (2010). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications Special Publication800-22R1a. (April)
[54] Paragas, Jessie. (2020). An Enhanced Cryptographic Algorithm in Securing Healthcare Medical Records. 1-6. 10.1109/ICVEE50212.2020.9243228.
[55] R. G. Barrieta, A. S. Canlas, D. M. A. Cortez, and K. E. Mata, “Modified Hill Cipher Algorithm using Myszkowski Transposition to address Known‑Plaintext attack,” International Journal for Research in Applied Science & Engineering Technology (IJRASET), vol. 10, no. IV, pp. 3242–3249, Apr. 202
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