# An Image Authentication Scheme Using Merkle Tree Mechanisms
## 3 Proposed Method
### Image Verification
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image** & **bits** & **16 \(\times\) 16** & **32 \(\times\) 32** & **64 \(\times\) 64** & **128 \(\times\) 128** \\ \hline \multirow{4}{*}{lena} & 3 bits & 3.29 & 3.85 & 6.88 & 10.52 \\ \cline{2-6}  & 4 bits & 2.66 & 3.12 & 5.70 & 8.99 \\ \cline{2-6}  & 5 bits & 0.62 & 0.84 & 1.33 & 2.12 \\ \cline{2-6}  & 6 bits & 0.13 & 0.23 & 0.34 & 0.45 \\ \hline \multirow{4}{*}{baboon} & 3 bits & 8.30 & 10.37 & 14.84 & 23.63 \\ \cline{2-6}  & 4 bits & 6.82 & 8.47 & 12.14 & 19.48 \\ \cline{2-6}  & 5 bits & 1.57 & 1.94 & 2.77 & 4.41 \\ \cline{2-6}  & 6 bits & 0.31 & 0.39 & 0.55 & 0.88 \\ \hline \multirow{4}{*}{airplane} & 3 bits & 7.12 & 9.80 & 20.25 & 35.92 \\ \cline{2-6}  & 4 bits & 6.19 & 8.41 & 16.55 & 28.52 \\ \cline{2-6}  & 5 bits & 1.36 & 1.89 & 3.77 & 6.45 \\ \cline{2-6}  & 6 bits & 0.27 & 0.38 & 0.77 & 1.31 \\ \hline \multirow{4}{*}{bouat} & 3 bits & 4.57 & 7.95 & 12.11 & 18.19 \\ \cline{2-6}  & 4 bits & 3.90 & 6.68 & 10.17 & 15.25 \\ \cline{2-6}  & 5 bits & 0.85 & 1.47 & 2.25 & 3.38 \\ \cline{2-6}  & 6 bits & 0.17 & 0.29 & 0.44 & 0.66 \\ \hline \multirow{4}{*}{peppers} & 3 bits & 41.62 & 39.83 & 38.03 & 17.00 \\ \cline{2-6}  & 4 bits & 42.50 & 40.75 & 38.89 & 14.11 \\ \cline{2-6}  & 5 bits & 49.05 & 47.29 & 45.33 & 3.27 \\ \cline{2-6}  & 6 bits & 55.94 & 54.23 & 52.32 & 0.65 \\ \hline \multirow{4}{*}{sailboat} & 3 bits & 4.48 & 6.75 & 10.22 & 34.23 \\ \cline{2-6}  & 4 bits & 3.65 & 5.46 & 8.39 & 35.33 \\ \cline{1-1} \cline{2-6}  & 5 bits & 0.81 & 1.21 & 1.90 & 41.70 \\ \cline{1-1} \cline{2-6}  & 6 bits & 0.17 & 0.25 & 0.38 & 48.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The mean squared error (MSE) value on different images with different measurements. The false positive rate of the tampering area evaluations is not suitable for the proposed method--because of the features of IPFS, the same image file has only one corresponding fingerprint, even when adjusting the brightness or contrast of the image. Our proposed method can not only work on grayscale images but also on any type and any size of digital image. See Figure 22a, where the testing image size is \(768\times 512\) pixels 24-bit color images, and the tampered image is shown in Figure 22b. Figure 22c shows the result of using our proposed method on an RGB image. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Image** & **bits** & **16 \(\times\) 16** & **32 \(\times\) 32** & **64 \(\times\) 64** & **128 \(\times\) 128** \\ \hline \multirow{3}{*}{lena} & 3 bits & 42.96 & 42.27 & 39.75 & 37.90 \\ \cline{2-6}  & 4 bits & 43.88 & 43.19 & 40.57 & 38.59 \\ \cline{2-6}  & 5 bits & 50.22 & 49.44 & 46.89 & 44.86 \\ \cline{2-6}  & 6 bits & 57.15 & 54.59 & 52.87 & 51.57 \\ \hline \multirow{3}{*}{baboon} & 3 bits & 38.93 & 37.97 & 36.41 & 34.39 \\ \cline{2-6}  & 4 bits & 39.79 & 38.85 & 37.28 & 35.23 \\ \cline{2-6}  & 5 bits & 46.18 & 45.26 & 43.71 & 41.68 \\ \cline{2-6}  & 6 bits & 53.15 & 52.24 & 50.70 & 48.69 \\ \hline \multirow{3}{*}{airplane} & 3 bits & 39.60 & 38.21 & 35.06 & 32.57 \\ \cline{2-6}  & 4 bits & 40.21 & 38.88 & 35.94 & 33.57 \\ \cline{2-6}  & 5 bits & 46.79 & 45.36 & 42.39 & 40.03 \\ \cline{2-6}  & 6 bits & 53.77 & 52.32 & 49.29 & 46.95 \\ \hline \multirow{3}{*}{b boat} & 3 bits & 41.52 & 39.12 & 37.29 & 35.53 \\ \cline{2-6}  & 4 bits & 42.21 & 39.88 & 38.05 & 36.29 \\ \cline{2-6}  & 5 bits & 48.82 & 46.45 & 44.61 & 42.84 \\ \cline{2-6}  & 6 bits & 55.87 & 53.53 & 51.67 & 49.90 \\ \hline \multirow{3}{*}{peppers} & 3 bits & 41.62 & 39.83 & 38.03 & 35.82 \\ \cline{2-6}  & 4 bits & 42.50 & 40.75 & 38.89 & 36.63 \\ \cline{2-6}  & 5 bits & 49.05 & 47.29 & 45.33 & 42.98 \\ \cline{2-6}  & 6 bits & 55.94 & 54.23 & 52.32 & 49.98 \\ \hline \multirow{3}{*}{sailboat} & 3 bits & 44.23 & 41.96 & 38.14 & 34.23 \\ \cline{2-6}  & 4 bits & 45.59 & 43.20 & 39.46 & 35.33 \\ \cline{1-1} \cline{2-6}  & 5 bits & 52.20 & 49.80 & 45.91 & 41.70 \\ \cline{1-1} \cline{2-6}  & 6 bits & 59.11 & 56.68 & 52.92 & 48.65 \\ \hline \end{tabular}
\end{table}