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Chaos systems find extensive applications in cryptography and pseudorandom number generation due to their ability to generate pseudo-random signals. This paper focuses on enhancing the complexity of chaotic systems by introducing the memristor, a nonlinear component. We propose a novel map called the 2D memristive Cubic map (2D-MCM), which integrates the memristor with the Cubic map to create a discrete mapping. The 2D-MCM exhibits rich dynamical behavior and a broad parameter space. Notably, the 2D-MCM displays boosting bifurcation behavior. As the control parameters increase, the 2D-MCM demonstrates an expanded range of values, indicating its ability to generate a larger number of pseudo-random sequences. To validate its performance, we establish a hardware platform to physically capture the attractors of the 2D-MCM. To verify the performance of the 2D-MCM in generating pseudorandom sequences, we designed a video encryption algorithm based on the 2D-MCM. This algorithm selectively encrypts specific areas within the video, with correlation coefficients of the encrypted video in the horizontal, vertical, and diagonal directions being 0.0002, -0.0005, and 0.0004, respectively. Through simulation experiments and security analysis, we demonstrate that the 2D-MCM performs well in video encryption tasks.
Gao et al. (Tue,) studied this question.