A Reversible Data-Hiding Method for Encrypted Images Based on Adaptive Quadtree Partitioning and MSB Prediction
Abstract
:1. Introduction
- The paper integrates adaptive quadtree partitioning and MSB prediction, to propose an innovative RDH-EI technique that overcomes the KPA vulnerability of the BPCX algorithm in RDH-ED and improves the embedding capacity.
- During the encryption phase, Arnold permutation is introduced for pixel bit modulation, enhancing the security of the BPCX encryption algorithm and defending against KPA attacks.
- Throughout the data embedding process, tagging bits serve to denote the state of the pixel block, optimizing the utilization of inter-pixel redundancy and, thereby, elevating the embedding capacity.
2. Related Works
2.1. Adaptive MSB Prediction
- 1.
- Eight bits of the upper-left pixel P and three bits of MD.
- 2.
- Arrange the prediction errors , respectively, where () is the remainder of after removing the shared MSBs.
- 3.
- The remaining three × MD bits are the space available for data-hiding represented by .
- 1.
- Eight bits of the upper-left pixel P, two bits of dim type (the sizes 16 × 16, 8 × 8, 4 × 4, 2 × 2 are denoted by 00, 01, 10, 11, respectively), and three bits of MD.
- 2.
- Arrange the prediction errors (), respectively, where is the remainder of after removing the shared MSBs.
- 3.
- The remaining bits are the space available for data-hiding represented by .
2.2. BPCX Analysis
- 1.
- The maximum number of 0-bit and 1-bit values within an image block remains constant before and after encryption.
- 2.
- The arrangement of pixels within a block does not alter the average value of the block.
- 3.
- The arrangement of pixels within a block does not effectively cover the low frequency information in the image, resulting only in a transformation to a high-definition and fuzzy image.
3. Proposed Method
3.1. Image Encryption
Algorithm 1 Adaptive quadtree partitioning |
|
3.2. Data-Hiding
- 1.
- Eight bits of the upper-left pixel P, three bits of Dim (according to the value of dim obtained through (5)), and three bits of MD.
- 2.
- Arrange the prediction errors (), respectively, where is the remainder of after removing the shared LSBs.
- 3.
- The remaining bits are the space available for data-hiding, represented by .
- 1.
- Determine whether it is the first 2 × 2 pixel block to be processed; if so, perform step a; otherwise, perform step b.
- (a)
- Eight bits of the upper-left pixel P, three bits of Dim (for the case where there are unusable blocks, it is encoded as ).
- (b)
- Eight bits of the upper-left pixel P.
- 2.
- Determine whether the current block is a usable block; if yes then perform step c; otherwise, perform step d.
- (c)
- Arrange a tagging bit ‘1’ to represent a usable block, three bits of MD. Next are the prediction errors (), where is the remainder of after removing the shared LSBs.
- (d)
- Arrange a tagging bit ‘0’ to represent an unusable block. Next are the original values of the remaining three pixels.
- 3.
- The remaining bits are the space available for data-hiding, represented by .
- 1.
- Determine whether it is the first 2 × 2 pixel block to be processed; if so, perform step a; otherwise, perform step b.
- (a)
- Eight bits of the upper-left pixel P, three bits of Dim (for this case, it is encoded as D(1)), and three bits of MD.
- (b)
- Eight bits of the upper-left pixel P and three bits of MD.
- 2.
- Arrange the prediction errors (), respectively, where is the remainder of after removing the shared LSBs.
- 3.
- The remaining bits are the space available for data-hiding, represented by .
3.3. Data Extraction and Image Recovery
- 1.
- Retrieve eight bits to obtain P and three bits to obtain Dim, according to the mapping relationship between Dim and dim in (5), which can be derived from the current retrieval of the pixel block size; if dim > 2 then perform the second step; otherwise, perform the third step.
- 2.
- Then, retrieve three bits to obtain MD, which gives md; then, retrieve number of 8-md bits to obtain ( ), and recover the pixel value according to (6).
- 3.
- When dim = 2, four pixel blocks of 2 × 2 size are taken as processing units and for each pixel block of 2 × 2 size, if Dim = D(0) execute step a; otherwise, execute step b.
- (a)
- Next, one bit is retrieved. If it is ‘1’, it means that the current 2 × 2 pixel block is usable, and if it is ‘0’, it is unusable. Then, retrieve three bits to obtain MD, which gives md; next, retrieve three 8-md bits to obtain (), and restore the pixel value according to (7).
- (b)
- Next, retrieve three bits to obtain MD, which gives md, then retrieve three 8-md bits to obtain (), and restore the pixel value according to (7).
4. Experimental Result and Analysis
4.1. Separability and Reversibility
4.2. Security
- 1.
- Shannon entropy
- 2.
- Histogram analysis
- 3.
- KPA attack
4.3. Embedded Capacity
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Image | Barbara | Boat | F16 | Goldhill | House | Lake | Peppers | Splash | Tiffany |
---|---|---|---|---|---|---|---|---|---|
Original image | 7.4664 | 7.1914 | 6.7140 | 7.4778 | 7.2336 | 7.4845 | 7.5925 | 7.2541 | 6.6009 |
Method [14] | 7.9965 | 7.9947 | 7.9915 | 7.9977 | 7.9861 | 7.9981 | 7.9914 | 7.9901 | 7.9899 |
Proposed method | 7.9979 | 7.9956 | 7.9912 | 7.9985 | 7.9869 | 7.9983 | 7.9944 | 7.9924 | 7.9913 |
EC (bit) | ||||||
---|---|---|---|---|---|---|
Image | [13] | [14] | [16] | [20] | [25] | Proposed method |
Barbara | 327,263 | 349,297 | 34,342 | 253,567 | 25,180 | 347,916 |
Boat | 334,343 | 386,905 | 27,262 | 259,864 | 29,561 | 376,904 |
F16 | 492,674 | 534,581 | 73,139 | 260,208 | 48,722 | 551,018 |
House | 419,121 | 440,927 | 44,009 | 261,024 | 26,058 | 446,916 |
Lake | 306,395 | 349,582 | 29,750 | 259,896 | 25,137 | 346,679 |
Peppers | 384,993 | 445,527 | 41,419 | 260,304 | 46,686 | 435,966 |
Average | Highest | Lowest | ||||
---|---|---|---|---|---|---|
(bit) | (bpp) | (bit) | (bpp) | (bit) | (bpp) | |
Method [13] | 593,090 | 2.2625 | 1,351,139 | 5.1542 | 50,273 | 0.1918 |
Method [14] | 638,698 | 2.4364 | 2,045,606 | 7.8034 | 15,444 | 0.0589 |
Proposed method | 648,298 | 2.4731 | 2,045,750 | 7.8039 | 16,150 | 0.0616 |
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Share and Cite
Yue, Y.; Zhang, M.; Di, F.; Lai, P. A Reversible Data-Hiding Method for Encrypted Images Based on Adaptive Quadtree Partitioning and MSB Prediction. Appl. Sci. 2024, 14, 6376. https://doi.org/10.3390/app14146376
Yue Y, Zhang M, Di F, Lai P. A Reversible Data-Hiding Method for Encrypted Images Based on Adaptive Quadtree Partitioning and MSB Prediction. Applied Sciences. 2024; 14(14):6376. https://doi.org/10.3390/app14146376
Chicago/Turabian StyleYue, Ya, Minqing Zhang, Fuqiang Di, and Peizheng Lai. 2024. "A Reversible Data-Hiding Method for Encrypted Images Based on Adaptive Quadtree Partitioning and MSB Prediction" Applied Sciences 14, no. 14: 6376. https://doi.org/10.3390/app14146376