High-Capacity Reversible Data Hiding in Encrypted Images Using D4-Symmetry Bidirectional Pixel Shifting and Context-Aware Recovery

Reversible data hiding in encrypted images (RDHEI) allows a cloud server to embed data into an encrypted image and allows an authorized receiver to later extract the data and restore the original image exactly. One family of methods embeds data by rearranging the pixels inside small blocks, which keeps the histogram of each permuted block unchanged. The bidirectional pixel-shifting scheme is a strong recent member of this family, but it has two limits: it enlarges only the cyclic set of patterns, so the geometric symmetries of a square block are unused, and its blind recovery, in which the receiver guesses the permutation of each block from the image alone, relies on intra-block smoothness alone. This paper addresses both limits. First, we combine the eight dihedral (D4) symmetries with the two cyclic shifts, which gives 2048 distinct patterns, that is 11 bits, per 4×4 block, and we verify by exhaustive enumeration that these 2048 patterns are pairwise distinct for the 4 × 4 block used throughout. Second, we add a context-aware term that makes the recovery agree with the already-restored neighbouring blocks, and we choose the block size dynamically. The two changes act against the usual capacity–quality trade-off: the method embeds more data and at the same time resolves fewer blocks wrongly than the baseline. A compressed location map removes the small residual error and is embedded in the marked image itself, so an authorised receiver holding the two keys and the public image identifier needs no separate side channel for the reconstruction data. On twelve standard images, the method reaches an average net embedding rate of 0.68 bpp under exact reconstruction, 12.8% above the bidirectional baseline, and raises the accuracy of the blind recovery by 7.0 dB over that baseline. It has the highest net rate on all twelve images; on three large databases it leads the baseline by 6.5% to 20.0%, and against the strongest competitor it leads on two databases and is level on the third. All comparisons are drawn within the pixel-rearrangement family, which embeds without altering pixel values; prediction-based schemes reach higher rates under a different constraint.