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The Lyapunov exponent serves as a measure of the average divergence or convergence between chaotic trajectories from the perspective of Lyapunov exponents (LEs). Chaotic systems with more and larger positive LEs have more complex dynamical behavior and can weaken the degeneration of digital chaos. Some existing control algorithms for chaos need more and larger preset parameters, which are not favorable for practical application; others require the original system to satisfy specific conditions, which lack generality. To address the deficiencies of these algorithms, this paper proposes a construction algorithm of N-dimensional discrete non-degenerate chaos based on two-parameter gain (ND-NCTG), which can realize the non-degenerate or non-chaotic control of chaotic systems by only two control parameters. We take a 3D chaotic system as an example and analyze the relationship between control parameters and LEs, as well as the characteristics of chaotic sequences, to verify the effectiveness and reliability of the algorithm. In addition, since the initial value sensitivity of the chaotic system coincides with the sensitivity in input information for the hash function, this paper takes the proposed chaotic construction algorithm as the basis to design a bidirectional diffusion chaotic hash function. The effectiveness and security of this hash algorithm are verified by sensitivity, statistical distribution and collision analysis. Compared with similar algorithms, both the non-degenerate chaotic construction algorithm and the hash function algorithm proposed in this paper have better performance and can meet the application requirements of secure communication.
Dai et al. (Thu,) studied this question.