Abstract Recently, chaotic maps possessing favorable chaotic properties have been extensively utilized in cryptography. One-dimensional (1D) chaotic maps, owing to their limited chaotic complexity, are not suitable for high-security requirements. Two-dimensional (2D) hyperchaotic maps, with simple structures and hyperchaotic behavior, are applied in image encryption. However, most current 2D hyperchaotic maps are derived from classical 1D chaotic maps, inheriting flaws associated with 1D chaotic maps such as discontinuous hyperchaotic intervals and uneven data distribution. To address this issue, based on the Li–Yorke theorem, we propose polynomial chaotic maps that exhibit continuous behavior across all parameters and possess a simple structure. These maps overcome the shortcomings of classical 1D chaotic maps. We create the two-dimensional Cubic-Sine hyperchaotic map (2D-CSHM) by combining the proposed polynomial chaotic map with Sine map. To further enhance the chaotic behavior and data distribution, we develop two-dimensional enhanced Cubic-Sine hyperchaotic map (2D-ECSHM) by incorporating a modulus function and multiplication factor. Compared to traditional 2D chaotic maps, the 2D-ECSHM exhibits hyperchaos across all parameters, ensures large Lyapunov exponents, and allows output range control of xₖ x k and yₖ y k via parameter d d, not restricted to [0, 1) [ 0, 1). We linearly combine the output of 2D-ECSHM to design a new pseudorandom number generator (PRNG) to verify its potential in cryptographic applications. Numerical simulations demonstrate that the PRNG has excellent performance and high speed.
Wu et al. (Sun,) studied this question.
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