High-Precision Authentication Scheme Based on Matrix Encoding for AMBTC-Compressed Images
Abstract
:1. Introduction
2. Related Works
2.1. AMBTC Compression
2.2. The Matrix Encoding
- Step 1:
- Compute to derive vector M.
- Step 2:
- Calculate the syndrome vector, .
- Step 3:
- Search for the same syndrome value as z in Table 2, then the gth column can be located, where . The corresponding identifier (ID) is also g, which is the to-be-flipped bit-location later in this paper. At the same time, the corresponding coset leader vector is mapped as eg.
- Step 4:
- Change the gth bit of the cover vector CV by . Note that if the syndrome value, z = (000) or g = 0, then there is nothing to be changed; that is, CV′ = CV.
3. Proposed Scheme
3.1. AMBTC Compression and Preprocessing Phase
3.2. Authentication Code Generation Phase
3.3. Embedding Phase
3.3.1. The Matrix Encoding Based Data Hiding
- Step 1.
- Divide the original image, I, into non-overlapping blocks by a size of 4 × 4 pixels.
- Step 2.
- Generate the AMBTC compression codes (H, L, BM) for the image, I, as explained in Section 2.1. For each block, assume its preprocessed AMBTC compression code is .
- Step 3.
- Generate the authentication code, AC, as explained in Section 3.2. For each block, assume the first three-bit sub-code is and the second three-bit sub-code is .
- Step 4.
- Extract the first seven bits of bm as the first cover vector, CV1 = = (bm(1, 1), bm(1, 2), bm(1, 3), bm(1, 4), bm(2, 1), bm(2, 2), bm(2, 3)). Extract the last seven bits of bm as the second cover vector, CV2 = = (bm(3, 2), bm(3, 3), bm(3, 4), bm(4, 1), bm(4, 2), bm(4, 3), bm(4, 4)).
- Step 5.
- Perform matrix encoding, as explained in Section 2.2, to embed the first three-bit sub-code, ac1, into the first cover vector, CV1, then derive the to-be-flipped bit-location, g1. The second three-bit sub-code, ac2, is embedded into the second cover vector, CV2, and then used to derive the to-be-flipped bit-location, g2. Note that we only record the to-be-flipped bit-location information but nothing is modified for the bm. Hence, for each block, two-tuple location information (g1, g2) can be derived.
- Step 6.
- Perform Steps 2 to 5 until all blocks have been processed.
- Step 7.
- Output all location information (g1, g2) for each block to the to-be-flipped bit-location information, G.
- Step 8.
- End.
3.3.2. Adjusted Quantization Levels Matching Based Data Hiding
- Step 1.
- Get a triple for one block from preprocessed AMBTC compression codes .
- Step 2.
- Get the corresponding to-be-flipped bit-location information (g1, g2) for this block from G.
- Step 3.
- Calculate the factors for and for the current block by:
- Step 4.
- Calculate the remaining values for and for the current block by:
- Step 5.
- Perform adjusted quantization level matching-based data hiding. If the remainder, rvh, is equal to g1, the matching work of is done; otherwise, the candidates at the quantization level, , should be adjusted by:
- Step 6.
- Let hcf = ha and lcf = lb be the final, selected solution under the constraint of the least distortion, dist(a,b), which can be calculated by:
- Step 7.
- Perform Steps 1 to 6 until all blocks have been processed.
- Step 8.
- Output the watermarked AMBTC compression code for each block, and the watermarked image, WI, is achieved.
- Step 9.
- End.
3.4. Tampering Detection Phase
3.4.1. Extraction of Bit-Location Information
- Step 1.
- Divide the watermarked image, WI, into non-overlapping blocks by a size of 4 × 4 pixels.
- Step 2.
- Perform the AMBTC compression technique for one block to derive the corresponding AMBTC compression code (h’, l’, bm’).
- Step 3.
- Extract the bit-location information (, ) for this block by the following equation:
- Step 4.
- Perform Steps 2 and 3 until all blocks have been processed.
- Step 5.
- Output all location information (, ) for each block to provide the bit-location information, G′.
- Step 6.
- End.
3.4.2. Extraction of the Authentication Code
- Step 1.
- Get a triple (h’, l’, bm’) for one block from AMBTC compression codes (H’, L’, BM’).
- Step 2.
- Get a tuple bit-location information (, ) for the corresponding block from G′.
- Step 3.
- Recombine the first seven bits of bm’ as the first cover vector, = . Recombine the last seven bits of bm’ as the second cover vector, .
- Step 4.
- Flip the th bit for the first cover vector, , and denoted as , then flip the th bit for the first cover vector, , and denoted as . Note that if or is equal to zero, the corresponding flipping operation is skipped. In Figure 5b, the red digit represents the flipped bit-location.
- Step 5.
- Extract the authentication code. Two three-bit sub-codes (, ) can be computed by:Then, the six-bit authentication code, , can be derived by:
- Step 6.
- Perform Steps 1 to 5 until all blocks have been processed.
- Step 7.
- Output the authentication code, , for each block to provide the extracted authentication code, EAC.
- Step 8.
- End.
3.4.3. Tampering Detection
- Step 1.
- Generate the authentication code, as mentioned in Section 3.2, and denote it as RAC.
- Step 2.
- Get an authentication code for one block from RAC and denote it as Rac’.
- Step 3.
- Get an authentication code for the corresponding block from EAC and denote it as Eac’.
- Step 4.
- Mark the tampered map, TM, according to the comparison results of Rac’ and Eac’. If they are equal, the corresponding position of TM is marked as ‘0’, which means the current block is valid; otherwise, it is marked as ‘1’, which indicates the current block is invalid.
- Step 5.
- Perform Steps 2 to 4 until all blocks have been processed.
- Step 6.
- Output the tampered map, TM.
- Step 7.
- End.
4. Experimental Results
4.1. Statistical Metrics
4.2. Tampering Detection Analyses
4.2.1. Cropping Attack
4.2.2. Constant Average Attack
4.2.3. Collage Attack
4.2.4. AMBTC Compression Codes’ Attacks
4.3. Performance Comparisons
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Methods | Tampering Detection Result for First Stage (%) | Requirement of Reference Matrix | Main Limitation |
---|---|---|---|
Scheme in [23] | 93.75 | No | Compression codes’ attack, Collage attack |
Scheme in [25] | 96.87 | No | |
Scheme in [26] | 93.75 | Yes | |
Scheme in [27] | 93.75 | No | |
Scheme in [28] | 93.75 | Yes | |
Scheme in [29] | 93.75 | Yes | Compression codes’ attack |
Scheme in [30] | 93.75 | Yes | More computation |
Scheme in [31] | 98.50/99.61 | No | Collage attack |
Proposed scheme | 99.85 | No | - |
ID | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|
Syndrome | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 |
Coset leader | 0000000 | 1000000 | 0100000 | 0010000 | 0001000 | 0000100 | 0000010 | 0000001 |
Symbols | Definitions | Symbols | Definitions |
---|---|---|---|
I | Original image | WI | Watermarked image |
H | Parity check matrix | TM | Tampered map |
h | High quantization level for a block in I | H | A set of h |
l | Low quantization level for a block in I | L | A set of l |
bm | Bitmap for a block in I | BM | A set of bm |
Preprocessed high quantization level | A set of | ||
Preprocessed low quantization level | A set of | ||
Preprocessed bitmap | A set of | ||
h′ | High quantization level for a block in WI | H′ | A set of h′ |
l′ | Low quantization level for a block in WI | L′ | A set of l′ |
bm′ | Bitmap for a block in WI | BM′ | A set of bm′ |
g1, g2 | Bit-location information of a block | ac | Authentication code for a block |
Original Images | Number of Tampered Blocks (4 × 4) | The First Hierarchical Tampering Detection Results (%) | The Second Hierarchical Tampering Detection Results (%) | ||||||
---|---|---|---|---|---|---|---|---|---|
Total | First Hierarchy | Second Hierarchy | TDR | FPR | FNR | TDR | FPR | FNR | |
Lena | 961 | 949 | 961 | 98.75 | 0 | 0.0777 | 100 | 0 | 0 |
Elaine | 5700 | 5620 | 5698 | 98.60 | 0 | 0.7432 | 99.96 | 0 | 0.0187 |
Woman | 296 | 293 | 296 | 98.99 | 0 | 0.0186 | 100 | 0 | 0 |
Average | 98.78 | 0 | 0.3356 | 99.99 | 0 | 0.0063 |
Size of Blocks | Original Images | Number of Tampered Blocks | The First Hierarchical Tampering Detection Results (%) | The Second Hierarchical Tampering Detection Results (%) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Total | First Hierarchy | Second Hierarchy | TDR | FPR | FNR | TDR | FPR | FNR | ||
4 × 4 | Zelda | 1225 | 1196 | 1225 | 97.63 | 0 | 0.1909 | 100 | 0 | 0 |
Baboon | 1225 | 1213 | 1225 | 99.02 | 0 | 0.0791 | 100 | 0 | 0 | |
2 × 2 | Zelda | 1369 | 1320 | 1367 | 96.42 | 0 | 0.3253 | 99.85 | 0 | 0.0133 |
Baboon | 1369 | 1333 | 1368 | 97.37 | 0 | 0.2392 | 99.93 | 0 | 0.0067 | |
Average | 97.61 | 0 | 0.2086 | 99.95 | 0 | 0.0050 |
Original Mages | Number of Tampered Blocks (4 × 4) | The First Hierarchical Tampering Detection Results (%) | The Second Hierarchical Tampering Detection Results (%) | ||||||
---|---|---|---|---|---|---|---|---|---|
Total | First Hierarchy | Second Hierarchy | TDR | FPR | FNR | TDR | FPR | FNR | |
Lake | 4126 | 4062 | 4121 | 98.45 | 0 | 0.5194 | 99.88 | 0.0485 | 0.0408 |
Boat | 1350 | 1331 | 1350 | 98.59 | 0 | 0.1262 | 100 | 0 | 0 |
Average | 98.52 | 0 | 0.3228 | 99.94 | 0.0243 | 0.0204 |
Original image | Kinds of Attacks | Number of Tampered Blocks (4 × 4) | The First Hierarchical Tampering Detection Results (%) | The Second Hierarchical Tampering Detection Results (%) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Total | First Hierarchy | Second Hierarchy | TDR | FPR | FNR | TDR | FPR | FNR | ||
Lena | (H or L) | 961 | 961 | 961 | 100 | 0 | 0 | 100 | 0 | 0 |
(H or L) and flower | 1211 | 1204 | 1208 | 99.42 | 0 | 0.0461 | 99.75 | 0.0827 | 0.0198 | |
BM | 651 | 651 | 651 | 100 | 0 | 0 | 100 | 0 | 0 | |
BM and flower | 901 | 894 | 898 | 99.22 | 0 | 0.0452 | 99.67 | 0.1112 | 0.0194 | |
Average | 99.66 | 0 | 0.0228 | 99.86 | 0.0485 | 0.0098 |
Original Images | PSNRs (dB) | |
---|---|---|
AMBTC | Proposed Scheme | |
Couple | 31.27 | 30.38 |
Boat | 31.87 | 30.89 |
Zelda | 37.99 | 35.07 |
Lena | 33.23 | 31.99 |
Woman | 37.98 | 35.03 |
Elaine | 33.91 | 32.41 |
Baboon | 28.30 | 27.78 |
Lake | 29.88 | 29.21 |
Peppers | 33.43 | 32.15 |
Average | 33.10 | 31.66 |
Methods | Number of Authentication Bits | Hierarchy of Detection Strategies | TDR of First Hierarchy (%) | TDR of Multi-Hierarchy (%) | Average PSNRs (dB) |
---|---|---|---|---|---|
Lin et al. [29] | 4 | 2 | 93.75 | 98.19 | 33.07 |
Hong et al. [30] | 4 | 2 | 93.75 | 99.83 | 32.33 |
Hong et al. [31] (LSBP)/(MSBP) | 6 | 2 | 98.50 | 99.66 | 31.27/31.73 |
8 | 99.61 | 28.92/29.84 | |||
Proposed scheme | 6 | 2 | 98.55 | 99.85 | 31.66 |
Compared Lists | Lin et al.’s Scheme [29] | Hong et al.’s Scheme [30] | Hong et al.’s Scheme [31] | Proposed Scheme |
---|---|---|---|---|
Components to embed AC | Quantization levels or bitmap | Quantization levels | Quantization levels | Quantization levels and bitmap |
Generation of AC | Pseudo-random generator | Hash function | Hash function | Hash function |
Detection of the special modification of bitmap | No | Yes | Yes | Yes |
Detection of the special modification of quantization levels | No | Yes | Yes | Yes |
Detection of the cropping attack | Yes | Yes | Yes | Yes |
Detection of the constant average attack | Yes | Yes | Yes | Yes |
Detection of the collage attack | Yes | Yes | No | Yes |
Authentication for AMBTC compression codes | Yes | Yes | Yes | Yes |
Authentication for AMBTC compressed image | Yes | No | No | Yes |
Methods | Compression Methodology | Domain | Detectable Block Size | Length of AC for a Block | PSNR (dB) |
---|---|---|---|---|---|
Scheme in [17] | JPEG | Frequency | 4 × 4 | 1 | [40.33, 44.12] |
Scheme in [18] | JPEG | Frequency | 8 × 8 | 3 | 44.63 |
Scheme in [19] | VQ | Space | 4 × 4, 8 × 8 | [1, 3] | ≈[29.00, 31.50] |
Proposed scheme | AMBTC | Space | 4 × 4 | [1, 6] | [31.66, 33.10] |
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Share and Cite
Su, G.-D.; Chang, C.-C.; Lin, C.-C. High-Precision Authentication Scheme Based on Matrix Encoding for AMBTC-Compressed Images. Symmetry 2019, 11, 996. https://doi.org/10.3390/sym11080996
Su G-D, Chang C-C, Lin C-C. High-Precision Authentication Scheme Based on Matrix Encoding for AMBTC-Compressed Images. Symmetry. 2019; 11(8):996. https://doi.org/10.3390/sym11080996
Chicago/Turabian StyleSu, Guo-Dong, Chin-Chen Chang, and Chia-Chen Lin. 2019. "High-Precision Authentication Scheme Based on Matrix Encoding for AMBTC-Compressed Images" Symmetry 11, no. 8: 996. https://doi.org/10.3390/sym11080996
APA StyleSu, G.-D., Chang, C.-C., & Lin, C.-C. (2019). High-Precision Authentication Scheme Based on Matrix Encoding for AMBTC-Compressed Images. Symmetry, 11(8), 996. https://doi.org/10.3390/sym11080996