PNSR and SSIM under different noise attacks.

This paper proposes a structurally simplified 2D quadratic sine map (2D-SQSM). This map effectively addresses the insufficient chaos performance of traditional chaotic maps while avoiding the overly complex structures of emerging chaotic maps. Evaluated using multiple chaos performance metrics, the 2D-SQSM demonstrates high Lyapunov exponents, and sample entropy, with chaotic characteristics superior to some advanced chaotic maps proposed in recent years. Based on the 2D-SQSM, this paper further designs a highly robust color image encryption algorithm. First, by introducing different hash functions multiple times, the correlation between the key and plaintext is enhanced, significantly improving resistance against brute-force attacks; second, cyclic shifting and segmentation-recombination operations are applied separately to the three RGB channels to effectively disrupt pixel distribution and significantly reduce spatial correlation between pixels; finally, the chaotic sequence generated by the 2D-SQSM is utilized for XOR diffusion, further enhancing the randomness and diffusion capability of the ciphertext. A large number of simulation results demonstrate that this algorithm can significantly enhance the image information entropy, and can effectively reduce pixel correlation, possessing good statistical properties. Furthermore, it is robust against differential attacks, noise attacks, cropping attacks, chosen plaintext attacks, etc., and is suitable for secure image transmission.本文提出一种结构简化的二维二次正弦映射（2D quadratic sine map，2D-SQSM）。该映射在有效解决传统混沌映射混沌性能不足问题的同时，规避了新兴混沌映射结构过于复杂的弊端。经多项混沌性能指标评估后，2D-SQSM展现出较高的李雅普诺夫指数（Lyapunov exponents）与样本熵（sample entropy），其混沌特性优于近年提出的部分先进混沌映射。基于该2D-SQSM，本文进一步设计了一种高鲁棒性彩色图像加密算法。首先，通过多次引入不同哈希函数（hash functions），增强密钥与明文间的相关性，显著提升了抗暴力攻击（brute-force attacks）能力；其次，分别对RGB通道（RGB channels）执行循环移位（cyclic shifting）与分割重组（segmentation-recombination）操作，有效打乱像素分布，大幅降低像素间的空间相关性；最后，利用2D-SQSM生成的混沌序列进行异或（XOR）扩散操作，进一步提升密文的随机性与扩散能力。大量仿真实验结果表明，该算法可显著提升图像信息熵（information entropy），有效降低像素相关性，具备良好的统计特性。此外，该算法对差分攻击（differential attacks）、噪声攻击（noise attacks）、裁剪攻击（cropping attacks）、选择明文攻击（chosen plaintext attacks）等均具有较强鲁棒性，适用于安全图像传输场景。