On a method of constructing a biaxial multitype conservative chaotic system and an image encryption scheme

On the basis of single axis coupling for constructing conservative chaos, a method for constructing a biaxial multitype conservative chaotic system is proposed. The method constructs more types of chaotic systems with a wider range of traversal. When coupling the Eulerian subbody biaxially, it is discovered that the structural matrix is able to exhibit two different multistates, namely, 0 and the opposite state, 0 and the same state, and depending on the location of the introduced adjustable parameter, the constructed chaotic equations also exhibit multiple types. When the structure matrix exhibits 0 and opposite state, the chaotic equations exhibit three types, which are opposite, one-parameter, and two-parameter types; and when the structure matrix is 0 and the same state, the chaotic equations exhibit the same type, one-parameter, and two-parameter types. The relationship of each pair of adjustable parameters satisfies the structure matrix antisymmetry, which leads to many types of Hamiltonian conservative chaotic systems that can transition between quasi-periodic, hyperchaotic, and chaotic states, all of which pass the NIST test, increasing the diversity of chaotic system choices in image encryption. The chaotic system is applied in image encryption, using Hadamard product matrix permutation, index permutation and four-dimensional pixel diffusion algorithms, and finally generates the ciphertext image. The method of biaxial coupling can construct six different types of chaotic systems, after image encryption, the average value of information entropy reaches 7.9994, the correlation coefficient is close to 0, the NPCR and UACI are close to the ideal values of 99.61 % and 33.46 %, the algorithm can effectively resist the statistical attack, the robustness attack and the differential attack, and the results demonstrate that the algorithm has better security performance.