Three Level Image Encryption Using a Modulo-based Chaotic Map
DOI:
https://doi.org/10.5890/JVTSD.2024.12.002Abstract
This paper investigates the issue of chaos-based image encryption. Based on the $z$-shaped fuzzy number, the exponential function, and the modulo operator, a 1-D chaotic map is constructed and studied. This map contains areas with constant chaotic behavior and high Lyapunov exponent values. A statistically secure pseudorandom bit generator is designed based on the new map, and it is used in the encryption process. A three level color image encryption technique is introduced that is based on a shuffling process to the rows and columns of an image, followed by a modulation process in each pixel, and finally by an XOR operation. The resulting ciphertext image is then shown to be resistant to a variety of attacks, including histogram, correlation, and entropy analysis, NPCR and UACI measures, cropping and tampering attacks, and transmission noise. This is demonstrated by applying the encryption to a set of images.References
[1] Sharma, M., Ranjan, R.K., and Bharti, V. (2022), A pseudo-random bit generator based on chaotic maps enhanced with a bit-xor operation, Journal of Information Security and Applications, 64, 103299.
[2] Tang, X. and Mandal, S. (2021), Encrypted physical layer communications using synchronized hyperchaotic maps, IEEE Access, 9, 13286-13303.
[3] Teh, J.S., Tan, K., and Alawida, M. (2019), A chaos-based keyed hash function based on fixed point representation, Cluster Computing, 22, 649-660.
[4] Artiles, J.A., Chaves, D.P., and Pimentel, C. (2022), Robust image watermarking algorithm using chaotic sequences, Journal of Information Security and Applications, 68, 103219.
[5] Kumar, M., Saxena, A., and Vuppala, S.S. (2020), A survey on chaos based image encryption techniques, Multimedia Security Using Chaotic Maps: Principles and Methodologies, 1-26.
[6] Hua, Z., Zhou, B., and Zhou, Y. (2018), Sine chaotification model for enhancing chaos and its hardware implementation, IEEE Transactions on Industrial Electronics, 66(2), 1273-1284.
[7] Talhaoui, M.Z., Wang, X., and Midoun, M.A. (2021), A new one-dimensional cosine polynomial chaotic map and its use in image encryption, The Visual Computer, 37, 541-551.
[8] Zhang, Z., Zhu, H., Ban, P., Wang, Y., and Zhang, L.Y. (2022), Buffeting chaotification model for enhancing chaos and its hardware implementation, IEEE Transactions on Industrial Electronics, 70(3), 2916-2926.
[9] Barman, M. and Chaudhury, J.P. (2013), A framework for selection of membership function using fuzzy rule base system for the diagnosis of heart disease, International Journal of Information Technology and Computer Science, 5(11), 62-70.
[10] Ayubi, P., Setayeshi, S., and Rahmani, A.M. (2020), Deterministic chaos game: a new fractal based pseudo-random number generator and its cryptographic application, Journal of Information Security and Applications, 52, 102472.
[11] Liu, L., Miao, S., Cheng, M., and Gao, X. (2016), A pseudorandom bit generator based on new multi-delayed chebyshev map, Information Processing Letters, 116(11), 674-681.
[12] Alawida, M., Samsudin, A., and Teh, J.S. (2020), Enhanced digital chaotic maps based on bit reversal with applications in random bit generators, Information Sciences, 512, 1155-1169.
[13] Tutueva, A.V., Nepomuceno, E.G., Karimov, A.I., Andreev, V.S., and Butusov, D.N. (2020), Adaptive chaotic maps and their application to pseudo-random numbers generation, Chaos, Solitons & Fractals, 133, 109615
[14] Moysis, L., Volos, C., Jafari, S., Munoz-Pacheco, J.M., Kengne, J., Rajagopal, K., and Stouboulos, I. (2020), Modification of the logistic map using fuzzy numbers with application to pseudorandom number generation and image encryption, Entropy, 22(4).
[15] Klir, G. and Yuan, B. (1995), Fuzzy Sets and Fuzzy Logic, 4, Prentice hall New Jersey.
[16] Akraam, M., Rashid, T., and Zafar, S. (2022), An image encryption scheme proposed by modifying chaotic tent map using fuzzy numbers, Multimedia Tools and Applications, 82(11), 16861-16879.
[17] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., and Barker, E. (2001), A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Technical report, Booz-allen and hamilton inc mclean va.
[18] Marton, K. and Suciu, A. (2015), On the interpretation of results from the nist statistical test suite, Science and Technology, 18(1), 18-32.
[19] Tsafack, N., Iliyasu, A.M., De~Dieu, N.J., Zeric, N.T., Kengne, J., Abd-El-Atty, B., Belazi, A., and Abd EL-Latif, A.A. (2021), A memristive rlc oscillator dynamics applied to image encryption, Journal of Information Security and Applications, 61, 102944.
[20] Abdelfatah, R.I. (2019), Secure image transmission using chaotic-enhanced elliptic curve cryptography, IEEE Access, 8, 3875-3890.
[21] El-Latif, A.A.A., Abd-El-Atty, B., Belazi, A., and Iliyasu, A.M. (2021), Efficient chaos-based substitution-box and its application to image encryption, Electronics, 10(12), 1392.
[22] De, S., Bhaumik, J., and Giri, D. (2022), A secure image encryption scheme based on three different chaotic maps, Multimedia Tools and Applications, 81(4), 5485-5514.
[23] Yosefnezhad Irani, B., Ayubi, P., Amani Jabalkandi, F., Yousefi Valandar, M., and Jafari Barani, M. (2019), Digital image scrambling based on a new one-dimensional coupled sine map, Nonlinear Dynamics, 97(4), 2693-2721.
[24] Pourjabbar Kari, A., Habibizad~Navin, A., Bidgoli, A.M., and Mirnia, M. (2021), A new image encryption scheme based on hybrid chaotic maps Multimedia Tools and Applications, 80, 2753-2772.
[25] Wu, Y., Noonan, J.P., and Agaian, S. (2011), Npcr and uaci randomness tests for image encryption, Cyber journals: multidisciplinary journals in science and technology, Journal of Selected Areas in Telecommunications (JSAT), 1(2), 31-38.
[26] Alvarez, G. and Li, S. (2006), Some basic cryptographic requirements for chaos-based cryptosystems, International Journal of Bifurcation and Chaos, 16(08), 2129-2151.
[27] Moysis, L., Kafetzis, I., Tutueva, A., Butusov, D., and Volos, C. (2022), Chaos-based image encryption based on bit level cubic shuffling, Cybersecurity: A New Approach Using Chaotic Systems, Springer, 157-191.
[28] Wang, X., Xu, M., and Li, Y. (2019), Fast encryption scheme for 3d models based on chaos system, Multimedia Tools and Applications, 78(23), 33865-33884.
[29] Teh, J.S., Alawida, M., and Sii, Y.C. (2020), Implementation and practical problems of chaos-based cryptography revisited, Journal of Information Security and Applications, 50, 102421.
[30] Sayed, W.S., Radwan, A.G., Fahmy, H.A., and El-Sedeek, A. (2020), Software and hardware implementation sensitivity of chaotic systems and impact on encryption applications, Circuits, Systems, and Signal Processing, 39, 5638-5655.
[31] Montero-Canela, R., Zambrano-Serrano, E., Tamariz-Flores, E.I., Muñoz-Pacheco, J.M., and Torrealba-Meléndez, R. (2020), Fractional chaos based-cryptosystem for generating encryption keys in ad hoc networks, Ad Hoc Networks, 97, 102005.
Article Metrics
Usage tracking begins September 1, 2026.