Design, Hardware Implementation, and Application in Video Encryption of the 2D Memristive Cubic Map

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.