Watermarking technique for copyright protection of digital images using coupled differential equations

Advancement and expansion of the internet, along with regular software upgrades, have generated many benefits in communication patterns. This rapid growth has also had a negative impact on the security of communicated content, such as images, audio/video messages, and especially on copyright protection for important images. In this paper, a novel watermarking technique is proposed to address the challenge of copyright protection more effectively. Initially, a chaotic dynamical system presented by coupled differential equations is utilized to generate three random, as well as chaotic, sequences of numbers. These sequences are then processed on each channel (red, green, and blue) of a colored image, respectively. Subsequently, the watermark (logo image) is embedded by converting its most significant bits (MSBs) to least significant bits (LSBs). The watermark in the processed image is nearly invisible due to the presence of third-order nonlinearity in the chaotic system and the complexity of the watermarking technique. This technique has demonstrated remarkable resistance to various attacks, such as noise attacks, compression attacks, and more specifically cropping attacks, confirming its applicability in copyright protection for digital images.