Blind color image watermarking scheme using invertible matrix based on energy aggregation
Xiaodong Chen, Ziyang Liu, Chongyu Shi, Huanying Wang, Qingtang Su · Physica Scripta · 2025
Abstract With the rapid development of digital media, data security and integrity have become increasingly critical issues. However, existing schemes still exhibit critical limitations, including high computational complexity from redundant matrix operations, inadequate security with restricted key space, and poor key sensitivity. To address these challenges, this paper proposes a blind color image watermarking scheme using an invertible matrix based on energy aggregation. For the first time, the invertible matrix, constructed by the Mobius function, aggregates the image energy with sequential left and right multiplication. In the watermark embedding stage, the digital watermark is embedded into the upper-left element of the matrix by quantization index modulation. In the watermark extraction stage, the blind watermark extraction is realized without requiring the host image. The Lorenz chaotic system is utilized, and its high sensitivity to initial conditions and complex dynamic behavior are leveraged to ensure a larger key space and enhanced key sensitivity. Compared with some traditional schemes, the proposed scheme simplifies the operation process, avoids complex transformation or matrix decomposition steps, and reduces computational complexity. The utilized Lorenz chaotic system significantly enhances security. Experimental results demonstrate the average peak signal-to-noise ratio is greater than 40 dB , the average structural similarity index measure value is 0.978, and the running time is about 0.752 s. Under conventional attacks and geometric attacks, the scheme achieves an average normalized correlation value of 0.967, outperforming existing approaches. These results highlight the scheme’s superior invisibility, robustness, security, and real-time performance.