Multi-image Encryption Algorithms With Quaternion Fractional Moment Transform And Coupling Operation

With the deepening of the global information integration process,the digital content industry is booming.Among them,digital images are widely popular due to their ability to convey rich information objectively and vividly,thus have become one of the most important carriers in information transmission.However,while people enjoy the convenience of the digital content industry,their private information is also facing threats such as leakage,destruction and tampering.In view of the security threats faced by digital images,it is of great practical significance and application value to study a secure and efficient multi-image encryption algorithm.Inspired by the existing research work,two multi-image encryption algorithms based on quaternion fractional orthogonal moment transform and cross-coupled chaotic system are proposed.The main research work of this dissertation is as follows.A new multi-image encryption scheme based on quaternion discrete fractional Tchebyshev moment transform(QDFr TMT)and the cross-coupling chaotic system is suggested.With quaternion theory,the traditional discrete fractional Tchebyshev transform is extended to the quaternion algebra domain for multi-image processing.Combining Euler’s formula and the quaternion theory,calculation relationship between the discrete fractional Tchebyshev moment transform and discrete fractional Tchebyshev moment transform with the quaternion symplectic form representation are derived.The fractional orthogonal moment transforms in the quaternion symplectic form representation will balance the computational efficiency and robustness of the encryption algorithm.In the encryption process,the original images are confused by fractal sort matrix and then divided into four equal size sub-images.Combined with the quaternion symplectic form representation,the segmented matrix is converted into quaternion signal.Subsequently,the quaternion signal is encrypted by the QDFr TMT,which is based on double random phase encoding technique.To evade the weakness of permutation-diffusion operation based on a single chaotic map,Logistic-Sine exponential chaotic map and piece-wise linear chaotic map(PWLCM)are crosscoupled for the generation of two chaotic sequences.The final ciphertext images can be acquired by carrying out the dual-layer encryption processes in horizontal and vertical directions.Numerical simulations and security analyses demonstrate that the encryption scheme performs well in terms of efficiency,security and robustness.A multiple color image encryption algorithm based on quaternion discrete fractional Krawtchouk moment transform and cross-coupled double PWLCM system is proposed.In order to increase the encryption capacity while maintaining the security of the cryptosystem,the discrete fractional Krawtchouk moment transform is combined with quaternion theory.Firstly,the three color components of four images are extracted for matrix reconstruction and pixel confusion.Then the confused output is segmented and represented in quaternion algebraic field,which are modulated by combining three quaternion random phase masks and quaternion discrete fractional Krawtchouk moment transform(QDFr KMT).Subsequently,one real part and three imaginary parts of the modulated quaternion signal are extracted for reorganization,and the rowcolumn confusion and diffusion operations are applied to the reorganization matrix by using the chaotic sequences.Finally,the three color component matrices are reconstructed to obtain the final encryption images.In addition,the statistical information of the plaintext is mapped to the initial value of the coupled chaotic system through the SHA-256,which improved the sensitivity of the algorithm to the original images.The cross-coupled PWLCM system improves the operation efficiency of the algorithm.Besides,two sets of chaotic sequences generated by the coupling control of different chaotic orbits are used for pixel confusion and diffusion,which further improves the security of the encryption algorithm.Numerical simulation experiments verify the feasibility and robustness of the proposed algorithm against a variety of common attacks.