Construction Of Chaotic Mapping And Its Application In Cryptographic Algorithms

Classical chaotic mapping has some unavoidable disadvantages,such as dense branches,too many Windows,small key space,poor randomness,etc.,which make it not suitable for direct application in cryptographic algorithms.In order to construct ergodic chaotic maps in a larger parameter range,we design non-degenerate hyperchaotic maps based on several seed maps,and analyze its dynamic characteristics such as bifurcation diagram,phase diagram,Lyapunov exponent,correlation dimension and Kolmogorov entropy to demonstrate its ergodicity and randomness.The newly constructed chaotic map is applied to the design of cryptographic algorithms.The main research work in this paper includes:(1)The introduction and development history of chaos theory are expounded,the classical chaos mapping is analyzed,and their dynamic characteristics are evaluate experimentally,and their shortcomings are pointed out.(2)Construct a three-dimensional hyperchaotic map without degeneracy,analyze its dynamic characteristics and compare it with the classical chaotic map to verify its effectiveness as a pseudo-random sequence generator.(3)An irreversible parallel key extension algorithm is designed,which overcomes the shortcomings of AES,SM4.0,such as most round constants are linear,any round of key can be derived from the previous round or the next round of key,and the original key of n×128-bit can be divided into several 128-bit parallel extension,improving the computational efficiency.(4)In the key extension algorithm,aiming at the defects of the S-Box used by AES and SM4.0,such as fixed point,inverse fixed point and short period ring,random sequence is obtained by using the constructed chaotic map,and a strong S-Box and nonlinear wheel constant are generated to eliminate these weaknesses.This paper introduces in detail the criteria for evaluating the performance of the S-Box,and verifies that the performance of the generated strong S-Box meets the security requirements of the cryptographic algorithm.Compared with AES,SM4.0 and many reference S-Boxes,the effectiveness of the generated strong S-Box meets the security requirements of the cryptographic algorithm is further verified.(5)A chaotic image encryption algorithm is designed,which is based on the random sequence obtained from chaotic mapping,realizes confusion and diffusion,and encrypts the plaintext image into noise-like cipher image.Compared with traditional image encryption algorithms,chaotic image encryption algorithm gives full play to the advantages of chaotic mapping’s sensitive dependence on initial values and high computational efficiency,and uses random sequences with good randomness and high encryption speed.The experiment verifies that the algorithm can encrypt the plain image effectively,and has better encryption effect compared with the existing image encryption schemes,and can satisfy the needs of image encryption security.