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A novel 1D powered Chebyshev quadratic map-based image encryption using dynamic permutation-diffusion
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DOI：10.1038/s41598-026-38483-x.png)
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Abstract
En 中文
Chaotic maps have gained significant attention in image encryption systems due to their intrinsic features, including sensitive dependence on initial conditions, non-linear dynamics, high entropy, and ergodicity. These properties enable the generation of complex, pseudo-random sequences that enhance unpredictability and randomness over time. However, many existing chaotic maps suffer from limited chaotic ranges and low adaptability, resulting in reduced encryption strength and vulnerability to differential or statistical attacks. This limitation motivates the development of a new chaotic system with stronger non-linearity, wider chaotic behavior, and improved dynamic flexibility. Based on this, the 1D-Powered Chebyshev Quadratic Map (1D-PCQM) is integrated into a cryptographic framework that aims to improve both security and efficiency. The proposed image encryption scheme referred as Dynamic Triple Chaotic Map Image Encryption Scheme (D3CM-IES) is based on the use of three chaotic maps: the Sine-cosine map, the Sine-Tangent-Sine (STS) map, and the novel 1D-PCQM map. These maps are employed to generate chaotic sequences, and a dynamic selection mechanism is then used to select one of these sequences during encryption, enhancing attack resistance. This scheme is performed through four main steps: (i) generating three chaotic sequences built from the aforementioned chaotic maps; (ii) performing a dynamic selection procedure that selects a single chaotic sequence for encryption; (iii) dynamic switching, where spatial locations (the spatial position of pixels) within the image are rearranged; and (iv) dynamic diffusion, where pixel values are modified to further conceal the image content. A series of experiments and tests were conducted to measure the performance of the proposed scheme and evaluate its ability to withstand known cryptographic attacks. Statistical and security results demonstrated that the proposed scheme exhibits a high degree of robustness. In particular, the method achieves Number of Pixels Change Rate (NPCR) of 99.66% and a Unified Average Changing Intensity (UACI) of 49.94%. Which reflect a high resistance to differential attacks small changes in the plain-text lead to significantly altered cipher-text. These results confirm the method’s effectiveness in providing strong confusion and diffusion, essential for modern image encryption systems.
Keywords:
Quadratic map
Chebyshev map
Chaotic map
Image encryption
Dynamic permutation and diffusion
Security analysis
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