Dynamic time-delay perturbation: a strategy for enhancing chaotic system performance and its applications

Chaotic systems have random-like properties and are extremely sensitive to initial conditions. This property makes chaos have a wide range of potential applications in fields such as cryptography and security technologies, especially in digital watermarking techniques for enhancing multimedia copyright protection. However, the degradation of digital chaotic systems may hinder their effective application in cryptography. To overcome this problem, an innovative control strategy is proposed in this work. By combining two delayed states with dynamic binary dissimilarity operations, this strategy aims to significantly enhance the complexity of chaotic systems. On this basis, a pseudo-random number generator (PRNG) is designed. The sequence generated by this PRNG successfully passed the standard tests such as NIST SP800-22 and TestU01. In addition, a new digital watermarking scheme is proposed by combining it with discrete wavelet transform and two-dimensional variational mode decomposition (2D-VMD). The satisfying performance of the proposed scheme is demonstrated by analyzing the invisibility of the watermarking scheme and its resistance to various attacks.