Construction of a novel class of five-dimensional hamiltonian conservative chaos families and fibonacci spiral image encryption
Wenjing Zhang, Zhipeng Kang, Jialu Chen · Results in Engineering · 2026
To address the limitations of existing image encryption methods—namely the monotonicity of chaotic dynamics and the high linearity of scrambling mechanisms—this paper proposes a novel encryption algorithm based on a five-dimensional Hamiltonian conservative chaotic family combined with Fibonacci spiral transformations. First, based on generalized Hamiltonian system theory, a five-dimensional conservative chaotic construction framework was established, yielding 42 novel chaotic families with 3 constants and 1 variable, as well as 16 families with 2 constants and 2 variables. This chaotic family exhibits complex dynamic properties, significantly expanding the key space while eliminating potential risks of dynamic degradation. Secondly, a Fibonacci spiral radial decomposition randomization combined with a bidirectional spiral diffusion strategy has been designed. By thoroughly breaking pixel spatial correlations through nonlinear spiral mapping and radial decomposition, pixel values are guided to diffuse bidirectionally along spiral trajectories, amplifying the avalanche effect. Experiments demonstrate that this approach achieves near-ideal information entropy, effectively resists differential and statistical attacks, and exhibits outstanding robustness against shear and noise.