A novel Collatz conjecture-based digital image watermarking method

Abstract

In this research, a novel Collatz conjecture-based image transformation and a modified logistic map are used for digital image watermarking. The proposed modified logistic map is utilized as a pseudo-random number generator (PRNG) to select the pixel to be watermarked. The host image is divided into nonoverlapping blocks, for instance, 2 × 2, 3 × 3, 4 × 4, 8 × 8, and 10 × 10 size blocks. A Collatz transformation is used on the selected pixel to generate a Collatz value because watermark embedding and extraction processes are implemented on the Collatz values. Evaluation criteria, such as visual quality, payload capacity, robustness, and execution time have been used to measure the performance of the proposed method. The results obtained and calculated clearly show that the proposed Collatz-based watermarking method has high visual quality, high payload capacity, and shorter execution time. Also, the proposed method has a basic mathematical structure and it can be programmed basically. This situation shows that the proposed method can be used in real-time applications. Collatz values can be changed with minimal distortions; therefore, this method is not robust against attacks. Finally, a successful image watermarking method is presented in this method using Collatz conjecture.