Research On Some Key Problems Of Chaotic Cryptography

With the rapid pace of information integration,information technology not only brings great convenience to our lives,but also has some potential security risks,such as information leakage.Scholars have deeply explored the protection of digital information such as digital images,and put forward some effective strategies.However,the problems of small key space,insensitive encryption and decryption process to plaintext information,and weak robustness to common attacks are common in some image encryption algorithms.Designing more secure and effective image encryption algorithms has gradually become a research hotspot.Thanks to many characteristics of chaotic system closely related to cryptography,such as pseudo randomness and initial value sensitivity,image cryptography based on chaotic theory has become a common research direction.Combined with the research of cross coupled image lattice in spatiotemporal chaotic system,this thesis proposes several image encryption algorithms based on cross coupled image lattice by combining theoretical analysis and numerical calculation.The main work is as follows:(1)An improved one-dimensional chaotic system is constructed and applied to pixel level image encryption algorithm.Firstly,to enhance the ability of pixel gray image algorithm to resist common attacks,an encryption process based on one-dimensional Logistic map,image block scrambling and various diffusion models is constructed.Then,aiming at the problems of too small chaotic region and uneven distribution of chaotic sequence values in one-dimensional chaotic system,a one-dimensional chaotic system with power exponential structure is constructed,which can output different chaotic sequences by constantly replacing the embedded one-dimensional chaotic map.Then,the proposed chaotic system is applied to enhance the relationship between different color components of color image,and a pixel level color image encryption strategy is proposed.Theoretical analysis and experimental results show that the proposed one-dimensional chaotic system with power exponential structure can effectively expand the chaotic region of the original one-dimensional chaotic map,and the distribution of chaotic sequences is more uniform.The proposed algorithm has good security and effectiveness,and the chaotic characteristics of the proposed one-dimensional system are further verified from the perspective of pixel level image encryption.(2)An improved one-dimensional cross coupled image lattice is constructed and applied to bit-level image encryption algorithm.Firstly,aiming at the problems existing in the onedimensional cross coupled map lattice,such as the spatiotemporal chaotic behavior of the model caused by a limited number of parameter pairs,two improved one-dimensional cross coupled map lattice models are constructed by replacing the low-dimensional chaotic map embedded in the model,introducing modular operation and constructing dynamic coupling coefficients.Secondly,based on the pixel level image encryption and the improved one-dimensional cross coupled image model,two bit-level image encryption strategies are proposed to further enhance the ability of the encryption algorithm to resist common attacks.The theoretical analysis and experimental results show that the improved one-dimensional cross coupled image lattice model can effectively improve the ratio of parameters to make the model show spatiotemporal chaotic behavior,and the image encryption algorithm based on the model has good security and effectiveness,The better spatiotemporal chaotic behavior of the proposed improved onedimensional cross coupled map lattice model is further verified from the perspective of bit level image encryption.(3)A two-dimensional cross coupled image lattice is constructed and applied to image compression and encryption algorithm.Firstly,the one-dimensional cross coupled image lattice model is extended from the spatial dimension to construct a two-dimensional cross coupled image lattice model.Secondly,combined with the compressed sensing theory and the proposed model,an image compression--encryption algorithm is proposed to improve the security of the encryption algorithm and enhance the efficiency of image transmission.Theoretical analysis and experimental results show that compared with the one-dimensional cross coupled image model,the constructed two-dimensional cross coupled image lattice model can further improve the ratio of parameters that make the model show spatiotemporal chaotic behavior,and the image compression encryption algorithm based on this model and compressed sensing theory has better security and effectiveness,From the point of view of image compression and encryption,the good spatiotemporal chaos characteristics of the constructed two-dimensional cross coupled image lattice model are verified.To sum up,this thesis studies the application of chaos theory in image encryption,and proposes five image encryption algorithms.Firstly,the one-dimensional chaotic system and its improved model are applied to pixel level gray and color image encryption strategies respectively,which effectively improves the poor correlation between key and plaintext information in the existing pixel level image encryption strategies.Then,two improved onedimensional spatiotemporal chaotic models are constructed and applied to bit level gray and color image encryption strategies respectively,which effectively improves the problem of lack of change in the key generation process in the existing biter level image encryption strategies,and enhances the ability of image encryption strategies to resist common attacks.Then,a twodimensional spatiotemporal chaotic model is constructed in the spatial dimension and applied to the image compression-then-encryption strategy,which effectively improves the large storage space occupied by the measurement matrix in the image compression-then-encryption strategy and the weak resistance of the compression and encryption strategy to common attacks such as chosen plaintext attacks due to the lack of diffusion mechanism.The above algorithms are progressive in terms of image pixel operation and chaotic system.Specifically,the chaotic system progresses from low dimensional chaotic system to spatiotemporal chaotic system with complex chaotic characteristics.The operation object of the algorithm advances from pixel value to pixel bit form,and then to pixel compression-then-encryption.