## 3 Identification Scheme with Privacy-Preserving
### Identification of Multiple Secondary Users  
Binary hypothesis testing is a statistical decision-making method used to select the most likely hypothesis from two possible hypotheses. In source camera identification, to determine whether a given image comes from a known camera model, we typically model the task as a binary hypothesis testing problem. One hypothesis (\(H_{0}\)) represents the case where the image originates from a known camera model, while the other hypothesis (\(H_{1}\)) suggests that the image comes from an unknown camera model. The goal of binary hypothesis testing is to calculate the likelihood of the data and decide which camera model the image is more likely to belong to. We consider a camera identification network consisting of \(K\) camera fingerprint extraction modules (secondary users) and a central classifier, as shown in Figure 1. We assume that each fingerprint extraction module independently extracts fingerprint information from the inquiry images and then sends local decisions to the central classifier, which can fuse all available decision information to infer whether an image is from a known camera model. We define \(C_{0}\) and \(C_{1}\) as two different camera models. Hypothesis \(H_{0}\) means that the image is from camera model \(C_{0}\), and hypothesis \(H_{1}\) represents that the image is from camera model \(C_{1}\). Meanwhile, we define \(M=\{m_{k}\}\), \(k=1,\dots,K\), as an image. Actually, the nature of source camera identification is a binary hypothesis testing problem, which can be formulated as  
\[ \begin{cases}H_{0}:\{M_{h,i}\sim N(\mu_{h},f(\mu_{h};c_{0},d_{0}))\}\\ H_{1}:\{M_{h,i}\sim N(\mu_{h},f(\mu_{h};c_{1},d_{1}))\},\end{cases}  \tag{6}\]  
where the image \(M\) is horizontally divided into \(H\) non-overlapping sections, with each section containing \(s_{h}\) pixels (\(h=1,...,H\)); \(M_{h,i}\) represents the pixel in the \(h\)-th section with index \(i\) (\(i=1,...,s_{h}\)) pixels in the \(h\)-th section; \(\mu_{h}\) is the mean value of all the pixels in the \(h\)-th section; and \(f(\mu_{h};p,q)\) denotes the variance derived from the hybrid fingerprint model. For source camera identification, True Positive Rate (TPR) and False Alarm Rate (FAR) are two crucial evaluation metrics that measure the effectiveness of identification methods. TPR represents the proportion of correctly identified true positives (i.e., images correctly classified as being from the source camera) out of all actual positive instances. A higher TPR indicates that the identification approach is effective at correctly identifying images from the source camera. FAR measures the proportion of false positives (i.e., images incorrectly classified as being from the source camera) out of all actual negative instances. A lower FAR indicates a better results in terms of minimizing false alarms or incorrect identifications. In this paper, we utilize TPR and FAR as two of our primary evaluation metrics. The specific formulas can be calculated as  
\[\text{TPR}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{7}\]  
where TP represents True Positives, the number of images correctly identified as being from the known camera and FN means False Negatives, the number of images incorrectly identified as not being from the known camera. \[\text{FAR}=\frac{\text{FP}}{\text{FP}+\text{TN}} \tag{8}\]  
where FP denotes False Positives, the number of images incorrectly identified as being from the source camera and TN represents True Negatives, the number of images correctly identified as not being from the source camera. In collaborative source camera identification, each collaborative module makes a binary decision based on its locally extracted camera fingerprint information. Then, each collaborative module sends one bit of the decision \(D_{i}\) (1 means that the image is from a known camera \(C_{0}\) and 0 means that the image is not from the known camera \(C_{0}\)) to the public classifier.