<p>With the rapid expansion of digital communication networks, ensuring the confidentiality and integrity of image data has become a critical challenge. Traditional image encryption schemes often face trade-offs between security, computational efficiency, and resistance to cryptographic attacks, primarily attributed to inefficient permutation and diffusion mechanisms, necessitating the development of more effective and high-performance encryption techniques. To address these challenges, this paper introduces a novel image encryption scheme that combines a two-dimensional Sine Infinite Chaotic Map (2D-SICM) with Pascal matrix diffusion. The 2D-SICM, a hyperchaotic system, exhibits significant nonlinearity, ergodicity, and unpredictability, making it ideal for generating random and complex key sequences crucial for encryption. Compared to existing methods, the 2D-SICM exhibits superior chaotic characteristics, as evidenced by its larger Lyapunov exponents of 11.53 and 8.06. The proposed encryption process consists of three main stages: key generation, pixel permutation, and pixel diffusion. Chaotic dynamics from the 2D-SICM are used to generate key sequences, ensuring a robust and random distribution of encryption keys. The permutation stage utilizes a one-round index matrix permutation to effectively disrupt pixel positions, while the diffusion stage applies Pascal matrix diffusion to enhance randomness and eliminate pixel correlations. Extensive simulations and quantitative security analyses substantiate the effectiveness of the proposed scheme. The proposed scheme achieves NPCR and UACI values of 99.7632% and 33.4430%, respectively, demonstrating high sensitivity to both key and plaintext variations. Further security evaluations confirm the robustness of the scheme, with PSNR values exceeding 10.2 dB under 30% salt-and-pepper noise and 13.5 dB despite 31.9% data loss from occlusion. Additionally, the scheme is computationally efficient, making it well-suited for real-time image encryption applications. The encryption of a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11196_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">$512 \times 512$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>512</mn> <mo>×</mo> <mn>512</mn> </mrow> </math></EquationSource> </InlineEquation> grayscale image requires only 0.1223s, highlighting its suitability for low-latency scenarios. By offering an effective balance between security, speed, and robustness, this work provides a promising solution for securing sensitive image data in domains such as healthcare and military applications.</p>

A novel image encryption scheme utilizing the 2D-SICM hyperchaotic map and Pascal matrix diffusion

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发表日期：

2025年4月25日

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Yuxiao Zheng,
Yuqi Chen,
Shuting Cai,
Xiaoming Xiong,
Linqing Huang

摘要

With the rapid expansion of digital communication networks, ensuring the confidentiality and integrity of image data has become a critical challenge. Traditional image encryption schemes often face trade-offs between security, computational efficiency, and resistance to cryptographic attacks, primarily attributed to inefficient permutation and diffusion mechanisms, necessitating the development of more effective and high-performance encryption techniques. To address these challenges, this paper introduces a novel image encryption scheme that combines a two-dimensional Sine Infinite Chaotic Map (2D-SICM) with Pascal matrix diffusion. The 2D-SICM, a hyperchaotic system, exhibits significant nonlinearity, ergodicity, and unpredictability, making it ideal for generating random and complex key sequences crucial for encryption. Compared to existing methods, the 2D-SICM exhibits superior chaotic characteristics, as evidenced by its larger Lyapunov exponents of 11.53 and 8.06. The proposed encryption process consists of three main stages: key generation, pixel permutation, and pixel diffusion. Chaotic dynamics from the 2D-SICM are used to generate key sequences, ensuring a robust and random distribution of encryption keys. The permutation stage utilizes a one-round index matrix permutation to effectively disrupt pixel positions, while the diffusion stage applies Pascal matrix diffusion to enhance randomness and eliminate pixel correlations. Extensive simulations and quantitative security analyses substantiate the effectiveness of the proposed scheme. The proposed scheme achieves NPCR and UACI values of 99.7632% and 33.4430%, respectively, demonstrating high sensitivity to both key and plaintext variations. Further security evaluations confirm the robustness of the scheme, with PSNR values exceeding 10.2 dB under 30% salt-and-pepper noise and 13.5 dB despite 31.9% data loss from occlusion. Additionally, the scheme is computationally efficient, making it well-suited for real-time image encryption applications. The encryption of a $512 \times 512$ $512 \times 512$ grayscale image requires only 0.1223s, highlighting its suitability for low-latency scenarios. By offering an effective balance between security, speed, and robustness, this work provides a promising solution for securing sensitive image data in domains such as healthcare and military applications.