This study presents an innovative image encryption algorithm anchored on the two-dimensional Logistic chaotic system, designed to address the limitations of traditional methods in terms of speed and security. The algorithm employs pixel shifting and scrambling, coupled with a segmented grayscale value substitution, to achieve a high level of security with strong key sensitivity and robust resistance to both differential and statistical attacks. Experimental validation demonstrates its superiority with fast encryption speeds, as evidenced by an encryption time of 0.2136 seconds for a 256×256 color image, and an entropy close to its ideal value, indicating excellent randomness. This method also exhibits high performance in resisting differential attacks, with Number of Pixels Change Rate (NPCR) and the Unified Average Changing Intensity (UACI) values nearing their optimal expected values. The integration of Quantum Key Distribution (QKD) is suggested for future work to enhance security against quantum computing threats, solidifying the algorithm’s potential as a leading solution for the image encryption.

[1] Alrubaie A., Khodher M., and Abdulameer A., “Image Encryption Based on 2DNA Encoding and Chaotic 2D Logistic Map,” Journal of Engineering and Applied Science, vol. 70, no. 1, pp. 60, 2023. https://jeas.springeropen.com/articles/10.1186/s4 4147-023-00228-2

[2] Antunes J., Gupta R., Mukherjee Z., and Wanke P., “Information Entropy, Continuous Improvement, and US Energy Performance: A Novel Stochastic-Entropic Analysis for Ideal Solutions (SEA-IS),” Annals of Operations Research, vol. 313, no. 1, pp. 289-318, 2022. https://ideas.repec.org/a/spr/annopr/v313y2022i1 d10.1007_s10479-021-04428-y.html

[3] Chen C., Sun K., and Xu Q., “A Color Image Encryption Algorithm Based on 2D-CIMM Chaotic Map,” China Communications, vol. 17, no. 5, pp. 12-20, 2020. https://ieeexplore.ieee.org/document/9103913

[4] Darani A., Yengejeh Y., Pakmanesh H., and Navarro G., “Image encryption Algorithm Based on a New 3D Chaotic System Using Cellular Automata,” Chaos, Solitons and Fractals, vol. 179, pp. 114396, 2024. https://doi.org/10.1016/j.chaos.2023.114396

[5] Demirtas M., “A New RGB Color Image Encryption Scheme Based on Cross-Channel 922 The International Arab Journal of Information Technology, Vol. 21, No. 5, September 2024 Pixel and Bit Scrambling Using Chaos,” Optik, vol. 265, pp. 169430, 2022. https://doi.org/10.1016/j.ijleo.2022.169430

[6] Elazzaby F., Elakkad N., and Sabour K., “The Coupling of a Multiplicative Group and the Theory of Chaos in the Encryptions of Images,” The International Arab Journal of Information Technology, vol. 21, no. 1, pp. 1-16, 2024. DOI:10.34028/iajit/21/1/1

[7] Elkandoz M. and Alexan W., “Image Encryption Based on a Combination of Multiple Chaotic Maps,” Multimedia Tools and Applications, vol. 81, no. 18, pp. 25497-25518, 2022. https://doi.org/10.1007/s11042-022-12595-8

[8] Elkandoz M., Alexan W., and Hussein H., “3D Image Steganography Using Sine Logistic Map and 2D Hyperchaotic Map,” in Proceedings of the International Conference on Electrical and Computing Technologies and Applications, Ras Al Khaimah, pp. 1-6, 2019. https://ieeexplore.ieee.org/document/8959700

[9] Farah M., Guesmi R., Kachouri A., and Samet M., “A Novel Chaos Based Optical Image Encryption Using Fractional Fourier Transform and DNA Sequence Operation,” Optics and Laser Technology, vol. 121, pp. 105777, 2020. https://doi.org/10.1016/j.optlastec.2019.105777

[10] Fotsing J., Moukam Kakmeni J., Tiedeu A., and Fotsin H., “Image Encryption Algorithm Based on 2D Logistic Map System in IoHT Using 5G Network,” Multimedia Tools and Applications, vol. 83, no. 10, pp. 30819-30845, 2024. https://link.springer.com/article/10.1007/s11042- 023-16730-x

[11] Gu L. and Chen G., “Chi-Square Linear Trend Test and SPSS Software Implementation,” Preventive Medicine, vol. 36, no. 1, pp. 89-90, 2024. http://www.zjyfyxzz.com/EN/abstract/abstract28 10.shtml

[12] Guo Z., Ren J., Liu B., Zhong Q., Li Y., Mao Y., Wu X., Xia W., Song X., Chen S., Tu B., and Wu Y., “Sliced Chaotic Encrypted Transmission Scheme Based on Key Masked Distribution in a W-Band Millimeter-Wave System,” Optics Express, vol. 32, no.11, pp. 19019-19033, 2024. https://opg.optica.org/oe/fulltext.cfm?uri=oe-32- 11-19019&id=549991

[13] Hosny K., Kamal S., and Darwish M., “A Color Image Encryption Technique Using Block Scrambling and Chaos,” Multimedia Tools and Applications, vol. 81, no. 1, pp. 505-525, 2022. https://doi.org/10.1007/s11042-021-11384-z

[14] Hosny K., Kamal S., and Darwish M., “A Novel Color Image Encryption Based on Fractional Shifted Gegenbauer Moments and 2D Logistic- Sine Map,” The Visual Computer, vol. 39, no. 3, pp. 1027-1044, 2023. https://link.springer.com/article/10.1007/s00371- 021-02382-1

[15] Hua Z., Zhou Y., Pun C., and Chen C., “2D Sine Logistic Modulation Map for Image Encryption,” Information Sciences, vol. 297, pp. 80-94, 2015. https://doi.org/10.1016/j.ins.2014.11.018

[16] Huang H., “Novel Scheme for Image Encryption Combining 2D Logistic-Sine-Cosine Map and Double Random-Phase Encoding,” IEEE Access, vol. 7, pp. 177988-177996, 2019. https://ieeexplore.ieee.org/document/8928566

[17] Jiang M. and Yang H., “Image Encryption Using a New Hybrid Chaotic Map and Spiral Transformation,” Entropy, vol. 25, no. 11, pp. 1- 19, 2023. https://www.mdpi.com/1099- 4300/25/11/1516

[18] Jiang Z. and Liu X., “Image Encryption Algorithm Based on Discrete Quantum Baker Map and Chen Hyperchaotic System,” International Journal of Theoretical Physics, vol. 62, no. 2, pp. 26-32, 2023. https://link.springer.com/article/10.1007/s10773- 023-05277-0#citeas

[19] Kaur G., Agarwal R., and Patidar V., “Color Image Encryption Scheme Based on Fractional Hartley Transform and Chaotic Substitution- Permutation,” The Visual Computer: International Journal of Computer Graphics, vol. 38, no. 3, pp. 1027-1050, 2022. https://link.springer.com/article/10.1007/s00371- 021-02066-w

[20] Kesenheimer E., Wendebourg M., Weigel M., Weidensteiner C., Haas T., Richter L., Sander L., Horvath A., Barakovic M., Cattin P., Granziera C., Bieri O., and Schlaeger R., “Normalization of Spinal Cord Total Cross-Sectional and Gray Matter Areas as Quantified With Radially Sampled Averaged Magnetization Inversion Recovery Acquisitions,” Frontiers in Neurology, vol. 25, no. 12, pp. 637198, 2021. https://pubmed.ncbi.nlm.nih.gov/33841307/

[21] Li C., “Information Entropy Algorithm for Image and Video Signal Processing,” Advances in Computer, Signals and Systems, vol. 6, no. 4, pp. 1-5, 2022. https://clausiuspress.com/article/4281.html

[22] Li C., Luo G., and Li C., “A Parallel Image Encryption Algorithm Based on Chaotic Duffing Oscillators,” Multimedia Tools and Applications, vol. 77, no. 15, pp. 19193-19208, 2018. https://link.springer.com/article/10.1007/s11042- 017-5391-5

[23] Li H., Yu S., Feng W., Chen Y., Zhang J., Qin Z., Zhu Z., and Wozniak M., “Exploiting Dynamic Vector-Level Operations and a 2D-Enhanced Logistic Modular Map for Efficient Chaotic Image Encryption,” Entropy, vol. 25, no. 8, pp. 28-36, 2023. https://doi.org/10.3390/e25081147 Efficient Image Encryption via 2D Logistic Chaos Mapping: Strengthening Security with ... 923

[24] Li X., Yu C., and Guo J., “Multi-Image Encryption Method via Computational Integral Imaging Algorithm,” Entropy, vol. 24, no. 7, pp. 996, 2022. https://doi.org/10.3390/e24070996

[25] Liang Y., Luo Y., Zhang S., “Review of chaotic image Encryption Based on Compressed Sensing,” Journal of Guangxi Normal University, vol. 40, no. 5, pp. 49-58, 2022. DOI:10.16088/j.issn.1001-6600.2022012003

[26] Lin J., “Measuring and Analyzing the Information Entropy Value of Key Audit Matters (KAMs) Disclosure at the System and Reporting Scale,” Heliyon, vol. 10, no. 1, pp. 23255-23262, 2024. https://www.sciencedirect.com/science/article/pii /S2405844023104634

[27] Liu G. and Wu Q., “Improved Logistic Chaotic Mapping and its Application in Image Encryption and Hiding,” Journal of Electronics and Information Technology, vol. 44, no. 10, pp. 3602- 3609, 2022. DOI:10.11999/JEIT210763

[28] Liu L., Zhang L., Jiang D., Guan Y., Zhang Z., “A Simultaneous Scrambling and Diffusion Color Image Encryption Algorithm Based on Hopfield Chaotic Neural Network,” IEEE Access, vol. 7, pp. 185796-185810, 2019. https://ieeexplore.ieee.org/document/8937765

[29] Liu S., Li C., and Li Y., “A Novel Image Encryption Algorithm Based on Exponent-Cosine Chaotic Mapping,” Journal of Electronics and Information Technology, vol. 44, no. 5, pp. 1754- 1762, 2022. https://jeit.ac.cn/en/article/doi/10.11999/JEIT210270

[30] Lyle M., Sarosh P., and Parah S., “Adaptive Image Encryption Based on Twin Chaotic Maps,” Multimedia Tools and Applications, vol. 81, no. 6, pp. 8179-8198, 2022. https://doi.org/10.1007/s11042-022-11917-

[31] Masood F., Driss M., Boulila W., Ahmad J., Rehman S., Jan S., Qayyum A., and Buchanan W., “A Lightweight Chaos-based Medical Image Encryption Scheme Using Random Shuffling and XOR Operations,” Wireless Personal Communications, vol. 127, no. 2, pp. 1405-1432, 2022. https://doi.org/10.1007/s11277-021-08584-z

[32] Niu Y. and Zhang X., “Image Encryption Method Based on Filling Curve and Adjacent Pixel Bit Scrambling,” Journal of Electronics and Information, vol. 44, no. 3, pp. 1137-1146, 2022. DOI:10.11999/JEIT210023

[33] Niwa T., Torii I., and Ishii N., “Line-of-Sight Detection Using Center of Gravity with Pixel Number Variation,” International Journal of Software Innovation, vol. 5, no. 3, pp. 64-76, 2017. DOI:10.4018/IJSI.2017070105

[34] Norouzi B. and Mirzakuchaki S., “A Fast Color Image Encryption Algorithm Based on Hyper- Chaotic Systems,” Nonlinear Dynamics, vol. 78, no. 2, pp. 995-1015, 2014. https://link.springer.com/article/10.1007/s11071- 014-1492-0

[35] Qu L., Li M., Sun Y., Su S., Liu Y., and Zhang L., “Security Analysis of a Reversible Data Hiding Scheme in Encrypted Images by Redundant Space Transfer,” Journal of King Saud University- Computer and Information Sciences, vol. 36, no. 1, pp. 101914, 2024. https://doi.org/10.1016/j.jksuci.2024.101914

[36] Ren Q., Teng L., Jiang D., Si R., andWang X., “Visual Image Encryption Algorithm Based on Compressed Sensing and 2D Cosine -Type Logistic Map,” Physica Scripta, vol. 98, no. 9, pp. 56-63, 2023. DOI:10.1088/1402-4896/aceb24

[37] Rohhila S. and Singh A., “Deep learning-based Encryption for Secure Transmission Digital Images: A Survey,” Computers and Electrical Engineering, vol. 116, pp. 109236, 2024. https://doi.org/10.1016/j.compeleceng.2024.109236

[38] Setiadi D. and Rijati N., “An Image Encryption Scheme Combining 2D Cascaded Logistic Map and Permutation-Substitution Operations,” Computation, vol. 11, no. 9, pp. 1-18, 2023. https://doi.org/10.3390/computation11090178

[39] Wang Z., Zhuang J., Ye S., Xu N., Xiao J., and Peng C., “Image Restoration Quality Assessment Based on Regional Differential Information Entropy,” Entropy, vol. 25, no. 1, pp. 1-16, 2023. https://www.mdpi.com/1099-4300/25/1/144

[40] Wu Y., Noonan J., and Agaian S., “NPCR and UACI Randomness Tests for Image Encryption,” Journal of Selected Areas in Telecommunications, vol. 1, no. 2, pp. 31-38, 2011. https://www.cyberjournals.com/Papers/Apr2011/05.pdf

[41] Yang F., An X., and Xiong L., “A New Discrete Chaotic Map Application in Image Encryption Algorithm,” Physica Scripta, vol. 97, no. 3, pp. 035202, 2022. DOI:10.1088/1402-4896/ac4fd0

[42] Zhang B. and Liu L., “Chaos-Based Image Encryption: Review, Application, and Challenges,” Mathematics, vol. 11, no. 11, pp. 2585, 2023. https://doi.org/10.3390/math11112585

[43] Zhang F., Zhang X., Cao M., Ma F., and Li Z., “Characteristic Analysis of 2D Lag-Complex Logistic Map and Its Application in Image Encryption,” IEEE MultiMedia, vol. 28, no. 4, pp. 96-106, 2021. DOI:10.1109/MMUL.2021.3080579

[44] Zhang H. and Hu H., “An Image Encryption Algorithm Based on a Compound-Coupled Chaotic System,” Digital Signal Processing, vol. 146, pp. 104367, 2024. https://doi.org/10.1016/j.dsp.2023.104367

[45] Zhang H., Hu H., and Ding W., “Image Encryption Algorithm Based on Hilbert Sorting Vector and New Spatiotemporal Chaotic System,” Optics and Laser Technology, vol. 167, pp. 924 The International Arab Journal of Information Technology, Vol. 21, No. 5, September 2024 109655, 2023. https://doi.org/10.1016/j.optlastec.2023.109655

[46] Zhang X., Liu G., and Di J., “An Image Encryption Scheme Based on the Four- Dimensional Chaotic System and the Mealy Finite State Machine,” Physica Scripta, vol. 99, no. 5, pp. 11-16, 2024. https://iopscience.iop.org/article/10.1088/1402- 4896/ad3487