Abstract A new multi-image encryption scheme based on quaternion discrete fractional Hartley transform (QDFrHT) and an improved pixel adaptive diffusion is proposed, which can simultaneously increase the encryption capacity and reduce the consumption of keys. In the proposed scheme, the QDFrHT is proposed to generalize the discrete fractional Hartley transform to quaternion transform domain and then applied to multi-image encryption. The original images are compressed into four fusion images by discrete cosine transform (DCT) and Zigzag operations and then the resulting four images are represented as quaternion algebra. Afterward, the quaternion signal is processed with the proposed QDFrHT and the double random phase encoding technique. To enhance the security of the algorithm, the plaintext-related pixel adaptive diffusion and the pixel scrambling operation based on chaotic systems are followed to obtain the final encryption image. Different from the traditional cryptosystem whose secret keys are dependent on the plaintext, the designed cryptosystem ensures the sensitivity of the cryptosystem to plaintext while the selection of the secret keys is independent on plaintext by introducing an improved diffusion mechanism. Numerical experiments verify the feasibility and the efficiency of the proposed multi-image compression and encryption scheme.

中文翻译：

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基于四元数离散分数Hartley变换和改进像素自适应扩散的多图像压缩-加密方案

摘要 提出了一种基于四元数离散分数哈特利变换(QDFrHT)和改进的像素自适应扩散的多图像加密方案，可以同时增加加密容量和减少密钥消耗。在所提出的方案中，提出了QDFrHT将离散分数Hartley变换推广到四元数变换域，然后应用于多图像加密。原始图像通过离散余弦变换 (DCT) 和 Zigzag 操作压缩为四张融合图像，然后将所得的四张图像表示为四元数代数。然后，四元数信号用提出的 QDFrHT 和双随机相位编码技术进行处理。为了提高算法的安全性，遵循与明文相关的像素自适应扩散和基于混沌系统的像素置乱操作，得到最终的加密图像。不同于传统的密钥依赖于明文的密码体制，所设计的密码体制通过引入改进的扩散机制，保证了密码体制对明文的敏感性，同时密钥的选择独立于明文。数值实验验证了所提出的多图像压缩和加密方案的可行性和效率。所设计的密码系统通过引入改进的扩散机制，确保了密码系统对明文的敏感性，同时密钥的选择独立于明文。数值实验验证了所提出的多图像压缩和加密方案的可行性和效率。所设计的密码系统通过引入改进的扩散机制，确保了密码系统对明文的敏感性，同时密钥的选择独立于明文。数值实验验证了所提出的多图像压缩和加密方案的可行性和效率。