Comparison of NPCR among different algorithms.

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）。该映射有效解决了传统混沌映射混沌性能不足的问题，同时规避了新兴混沌映射结构过于复杂的缺陷。通过多项混沌性能指标评估，2D-SQSM展现出较高的李雅普诺夫指数与样本熵，其混沌特性优于近年提出的部分先进混沌映射。基于2D-SQSM，本文进一步设计了一种高鲁棒性彩色图像加密算法。其一，通过多次引入不同哈希函数，增强了密钥与明文之间的相关性，显著提升了抗暴力攻击能力；其二，分别对RGB三通道执行循环移位与分块重组操作，有效打乱像素分布，大幅降低像素间的空间相关性；其三，利用2D-SQSM生成的混沌序列执行异或扩散操作，进一步提升密文的随机性与扩散能力。大量仿真结果表明，该算法可显著提升图像信息熵，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、噪声攻击、裁剪攻击、选择明文攻击等均具备良好鲁棒性，适用于安全图像传输场景。