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Data hiding and watermarking are considered one of the most important topics in cyber security. This article proposes an optimized method for embedding a watermark image in a cover medium (color image). First, the color of the image is separated into three components (RGB). Consequently, the discrete wavelet transform is applied to each component to obtain four bands (high–high, high–low, low–high, and low–low), resulting in 12 bands in total. By omitting the low–low band from each component, a new square matrix is formed from the rest bands to be used for the hiding process after adding keys to it. These keys are generated using a hybrid approach, combining two chaotic functions, namely Gaussian and exponential maps. The embedding matrix is divided into square blocks with a specific length, each of which is converted using Hessenberg transform into two matrices, P and H. For each block, a …