Multi-image Encryption Algorithms With Chaotic System And Quaternion Fractional Transform

The vigorous development of multimedia communication and computer technology makes more and more information spread on the Internet.While enjoying the convenience of information sharing,people are also troubled by security issues such as information theft,tampering and counterfeiting,and the risk of information leakage is increasing.As an important information carrier,digital images are widely spread on the Internet.Compared with traditional text information,digital images contain a larger amount of data,which requires high storage resources and bandwidth.Therefore,How to transmit multiple images safely and efficiently within a limited bandwidth has become the goal pursued by the majority of researchers.Inspired by existing image encryption schemes,two multi-image compression encryption algorithms based on chaotic systems and quaternion fractional transform are designed.The main research work is as follows.A new multi-image encryption scheme based on quaternion discrete fractional Hartley transform(QDFr HT)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 QDFr HT is proposed to generalize the discrete fractional Hartley transform to quaternion transform domain and then applied to multi-image encryption.Combining the quaternion operation rules and Euler's formula,the calculation relationship between the quaternion discrete fractional Hartley transform and discrete fraction Hartley transform is derived.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 QDFr HT 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 typical 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.For many existing transform-based image compression-encryption algorithms,they bore security risks due to the linear properties of transform and have the shortcoming of low quality of image reconstruction.To solve these weaknesses and achieve multiple color images encryption,a secure double-color-image encryption algorithm is designed based on the quaternion multiple parameter discrete fractional angular transform(QMPDFr AT),a nonlinear operation and a plaintext-related joint permutation-diffusion mechanism.In the designed algorithm,the low-frequency and high-frequency sub-bands of the three color components of each plaintext image are obtained by two-dimensional discrete wavelet transform(DWT),respectively.Then the high-frequency sub-bands are further made sparse and the main features of these sub-bands are extracted by a Zigzag scan.Subsequently,all the low-frequency sub-bands and high-frequency fusion images are represented as three quaternion signals,which are modulated by the proposed QMPDFr AT with three quaternion random phase masks,respectively.The spherical transform,as a nonlinear operation,is followed to nonlinearly make the three transform results interact.For better security,a joint permutation-diffusion mechanism based on plaintext-related random pixel insertion is performed on the three intermediate outputs to yield the final encryption image.This mechanism only needs to execute one-time traversal of the to-be-encrypted sequence to sufficiently confuse and diffuse the image pixel values.The effect of different components of the high-frequency sub-bands on the quality of the decryption image is discussed and a more reasonable feature fusion method of the high-frequency part is implemented by combining DWT with Zigzag operation.Compared with many similar color image compression-encryption schemes,the proposed algorithm can encrypt double-color-image with higher quality of image reconstruction.Numerical simulation results demonstrate that the proposed double-color-image encryption algorithm is feasibility with high security and robustness.