# A Fragile Watermarking Scheme for Authenticity Verification of 3D Models in GLB Format
## 4 Results and Discussion
### Thread Model, Vector Attacks and Resilience  
Our method is based on fragile watermarking, and any attack on a marked model should result in a broken watermark. In particular, operations such as vertex reordering, model simplification, model clipping, or file format conversion (e.g., glb\(\rightarrow\).blend or another format\(\rightarrow\).glb) inevitably break the watermark as they modify the underlying bits of the 3D model. On the other hand, it is necessary to discuss the possibility of removing or replacing the watermark.  
In the event that the stego key is compromised, an adversary would possess sufficient information to remove or substitute the embedded watermark. However, the stego key can be designed to be both compact and human-memorable, thereby reducing the risk of exposure through insecure storage.  
Now consider the scenario in which an attacker does not have access to the stego key and instead attempts a brute-force attack--i.e., systematically guessing the key. In such a case, the successful recovery of the entire key is computationally infeasible due to the high entropy and large keyspace associated with the key, which makes exhaustive search methods ineffective.  
Consider the following stego key format: \(0 NSSSS*POSITION*HHHHHHHHHH\), where  
* \(N\) represents a digit from 1 to 4 (4 possible values);
* Each \(S\) represents a digit from 0 to 9 (10 possible values per position);
* Each \(H\) represents a character from the ASCII range 33 to 126 inclusive (94 possible values per position, since \(126-33+1=94\)).  
The stego key consists of 1 character for the prefix 0 (fixed), 1 character for \(N\), 4 characters for \(S\), and 10 characters for \(H\), totalling 15 characters in length. It is one of the simplest. An additional assumption was made that the attacker knows the vertex attribute in which the watermark was embedded. So the probability of correctly guessing the stego key on a single try is  
\[P=\frac{1}{4\cdot 10^{4}\cdot 94^{10}}\approx 4.67\cdot 10^{-25}. \tag{7}\]  
This demonstrates a high level of resistance to brute-force attacks.  
As demonstrated, guessing the entire key is computationally infeasible; however, if a short seed is used, the probability of successfully removing the watermark increases significantly. Consider the case where the seed consists of four characters, and the attacker attempts to erase all four least significant bits (LSBs). The probability of correctly guessing the seed in this scenario is  
\[P=\frac{1}{10^{4}}=10^{-4}. \tag{8}\]  
It is recommended to use long seeds, preferably longer than 10 digits, to ensure sufficient randomness. The same discussion and recommendation applies to the HMAC key, which should also be sufficiently long to ensure security; short keys should be avoided.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Attribute** & **Original** & **8b** & **16b** & **24b** & **32b** \\ \hline \multirow{4}{*}{gate} & normal & 1.06 & 1 & 1.06 & 1.06 & 1.18 \\  & position & 1 & 1.06 & 2.88 & 3 & 3 \\ \cline{1-1}  & texcoord & 1 & 1 & 1 & 1 & 1.06 \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._