Period Analysis Of Digital Chaotic System Under Finite Precisions And Applications Of Image Encryption

As the main carrier of information,digital images have the characteristics of large amount of data,strong correlation between pixels and high redundancy,which determines that traditional text-based encryption schemes(such as AES and DES)are difficult to process.Therefore,a secure and efficient image encryption method is needed in the face of the current situation.Chaotic systems have the characteristics of ergodicity,sensitivity to initial conditions,and unpredictability,etc.These characteristics are highly related to the operations of confusion and diffusion in modern cryptography.As a result,the encryption methods based on the chaotic system have been widely used in applications.However,due to the finite precision of the digital devices such as computers,the dynamic degradation and the short period phenomenon will occur,which seriously influences the application of chaotic systems in the fields of secure communication and multimedia encryption.Based on the analysis of the short period phenomenon of digital chaotic systems,a variety of secure and efficient chaotic image encryption methods are designed.The work of this paper can be mainly summarized in follows contributions:1.The research background of the subject is introduced,including the short period phenomenon of digital chaotic systems and the design theory based on chaotic image encryption.Then,the main innovations of the subject are described,in which the characteristics of digital chaotic systems and the structure of chaotic image encryption are illustrated.Moreover,two aspects that the short period phenomenon of digital chaotic systems under finite precision and the research status of chaotic image encryption are summarized.Finally,the critical issues of these two aspects are pointed out and gives the improvement and design ideas.2.Due to the finite precisions of the simulation software and digital devices,dynamic degradation and short period phenomenon will occur.Thus,the short period phenomenon severely affects the performances of chaotic system in its application of secure communication and multimedia encryption etc.In order to study the dynamical degradation issues of digital chaotic systems under finite precision,the hash table is used to fast position the period of chaotic systems.The function mapping idea of hash table is to associate the storage location of the digital chaotic system with the chaotic value to achieve the purpose of fast position and search.The experimental results show that the proposed method provides a quantitative analysis for the finite precision effect of the chaotic systems,which is helpful to design the mechanisms to counteract the dynamic degradations and enhance the security performance.3.A color image encryption method based on memristive hyperchaotic system and DNA encryption is designed,in which memristive hyperchaotic system can provide large key space and more complex chaotic dynamic behavior,and the DNA encryption can further improve the security of image encryption.Firstly,a keystream generation mechanism is designed,in which the pseudorandom sequences generated by the mechanism are highly sensitive to the plain image,i.e.,different images can generate different secret keys and keystreams by using the mechanism.Then,the memristive hyperchaotic system and image are dynamical DNA encoding,where the problem of fixed rules or operations in DNA encryption can be avoided.Finally,the cipher image is obtained after the diffusion and interaction among red,green and blue components.Experimental analysis and performance comparison show that this method has high efficiency,large enough key space to resist violent attack,and strong robustness to select plaintext attack.4.In order to address the problem of key distribution and management in symmetric encryption,an asymmetric image encryption method based on elliptic curve ElGamal(ECElGamal)cryptography and chaotic system is designed.Firstly,a method of crossover permutation based on coupled Logistic-Tent map(LTM)and coupled Tent-Sine map(TSM)is introduced.Then,a method of image pixels embedding into elliptic curve is proposed,which is simple for operating,and the EC-ElGamal encryption can greatly improves the encryption performance.Finally,a method of diffusion based on chaos game is presented,in which DNA sequence is introduced as the keys,and two sequences of chaos game are generated to diffuse the image.Experimental analysis and performance comparisons show that the proposed method has the characteristics of large key space,high information entropy,and strong robustness to chosenplaintext attack,which provides a potential solution for secure image encryption applications.