In this paper, we propose a novel reversible data hiding in encrypted images (RDH-EI) method that achieves the highest hiding capacity in the RDH-EI research field and full flexibility in the processing order without restrictions. In the previous work in this field, there exist two representative methods; one provides flexible processing with a high hiding capacity of 2.17 bpp, and the other achieves the highest hiding capacity of 2.46 bpp by using the BOWS-2 dataset. The latter method has critical restrictions on the processing order. We focus on the advantage of the former method and introduce two efficient algorithms for maximizing the hiding capacity. With these algorithms, the proposed method can predict each pixel value with higher accuracy and refine the embedding algorithm. Consequently, the hiding capacity is effectively enhanced to 2.50 bpp using the BOWS-2 dataset, and a series of processes can be freely conducted without considering any restrictions on the order between data hiding and encryption. In the same way, there are no restrictions on the processing order in the restoration process. Thus, the proposed method provides flexibility in the privileges requested by users. Experimental results show the effectiveness of the proposed method in terms of hiding capacity and marked-image quality.
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