Abstract: Aiming at addressing existing issues in current image encryption technologies regarding encryption speed, security, and sensitivity, this paper proposes a novel image encryption method based on a combined chaotic system and fractional numbertheoretic transform. First, a new chaotic structure is proposed by combining two traditional onedimensional mappings to create a fully chaotic mapping. Metrics such as bifurcation diagrams, Lyapunov exponents, and information entropy demonstrate that the proposed chaotic structure exhibits excellent chaotic performance, large parameter space, strong sensitivity, and high randomness. Subsequently, a new image encryption method is developed based on this chaotic mapping and multiparameter fractional number theoretic transform. The hash value of the plaintext image is linked with the parameters of the chaotic system to generate initial chaotic keys and scrambling parameters. A multiparameter fractional number theoretic transform is defined by constructing a number theoretic transform feature vector. The plaintext image undergoes one round of number theoretic transform to obtain an intermediate image, followed by Arnold scrambling to disrupt the image. Finally, another round of numbertheoretic transformation is applied to generate the ciphertext image. Experimental results indicate that the algorithm achieves excellent encryption performance: the pixel change rate (NPCR) and unified average changing intensity (UACI) closely approach their ideal values; the average correlation coefficient of ciphertext images is 0.0018, approaching zero; the normalized entropy of ciphertext images reaches 0.9994, nearing the maximum value of 1. With an average encryption time of 0.273s and decryption time of 0.324s, the method outperforms other comparative schemes in efficiency. It demonstrates robust resistance against common attacks including chosenplaintext attacks, differential attacks, and exhaustive attacks, exhibiting high security and promising application prospects in multimedia security fields.

Key words: image encryption, chaotic system, number theoretic transform, multipleparameter transform, robustness

摘要： 针对现有图像加密技术在加密速度、安全性、灵敏度等方面存在的问题，提出了一种基于新型组合混沌系统和分数数论变换的图像加密方法.首先提出了一种新型混沌结构，将2种传统的1维映射结合得到新的全混沌映射，分岔图、Lyapunov指数和信息熵等指标表明新的混沌结构具有混沌性能优良、参数空间大、敏感性强、随机性强等优点.基于这种新型混沌映射和多参数分数数论变换提出了一种新的图像加密方法，将明文图像的哈希值与新型混沌系统的参数进行关联，得到混沌的初始密钥和置乱参数；通过构造数论变换特征向量定义1个多参数分数数论变换，对明文图像进行1轮数论变换，得到中间图像，再使用Arnold置乱打乱图像，最后进行1轮数论变换得到密文图像.实验结果表明，该方法加密性能良好，像素变化率NPCR和平均变化强度UACI非常接近理想值；密文图像平均相关系数为0.0018，趋近于0；密文图像的归一化熵为0.9994，非常接近1；平均加密时间为0.273s，解密时间为0.324s，效率优于其他对比方法；能够抵御选择明文攻击、差分攻击和穷举攻击等常见攻击，具有较高的安全性，在多媒体安全领域具有很好的应用前景.

关键词: 图像加密, 混沌系统, 数论变换, 多参数变换, 鲁棒性