为增强数字图像在传输中的安全性，同时解决图像像素间关联性强、数据量大等问题，提出了一种基于分数阶2D-TFCDM映射和改进的Hilbert曲线置乱的图像加密算法。首先，利用分数阶2D-TFCDM映射产生伪随机序列；其次，对明文图像进行分块，将改进的Hilbert曲线对子块图像进行置乱，为充分地削弱图像的相关性，进一步提高图像的置乱度，再对图像进行M×N次Arnold变换，同时改变每次Arnold变换的参数；最后，将异或运算与明文图像的平均像素值相结合进行扩散，得到最终的加密图像。对3幅256×256大小的灰度图像进行测试，结果表明，加密图像的像素间关联性较弱，具有较好的加密效果、良好的统计特征和强大的抗干扰能力，可有效抵抗各种常见的攻击，在图像加密方面具有较好的实用价值。


To enhance the security of digital images in transmission and solve the problems of strong correlation between image pixels and large amount of data, an image encryption algorithm based on fractional 2D- TFCDM mapping and improved Hilbert curve scrambling is proposed. Firstly, pseudo-random sequences are generated by fractional 2D-TFCDM mapping. Secondly, the plaintext image is partitioned and the subblock image is scrambled by the improved Hilbert curve. To fully weaken the correlation of the image and further improve the scrambling degree of the image, M×N Arnold transforms are performed on the image, and the parameters of each Arnold transform are changed. Finally, the XOR operation is combined with the average pixel value of the plaintext image for diffusion to obtain the final encrypted image. Three gray-scale images of 256×256 size are tested. The results show that the correlation between the pixels of the encrypted image is weak, and the encrypted image has good encryption effect, good statistical characteristics and strong anti-jamming ability, it can resist all kinds of common attacks effectively, and has good practical value in image encryption. 


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