## 3 Basic Concepts
### PRUDEnce Framework  
PRUDEnce, a privacy risk assessment framework proposed by [11], is recognized for its effectiveness in assessing privacy risks in trajectory data. It plays a crucial role in helping data providers (DPs) make informed decisions while maintaining data quality. The framework is designed to support GDPR compliance, with a particular focus on Article 25, which emphasizes data protection by design and default, aligning with the principles of Data Protection Impact Assessments. PRUDEnce is not limited to a specific country or jurisdiction, but it is primarily structured to comply with GDPR (European Union). However, due to its adaptable nature, PRUDEnce can be extended to assess privacy risks in other legal contexts. PRUDEnce provides a universal methodology for privacy risk assessment in any type of data. PRUDEnce assesses privacy risks in data sharing, particularly focusing on empirical privacy risks during the transfer of raw personal data from the DP to the Service Developer (SD). Background knowledge dimensions are crucial for evaluating potential privacy risks and outlining external information accessible to potential attackers. This context-dependent background knowledge impacts the effectiveness of privacy attacks. Background knowledge represents an adversary's knowledge subset regarding a user \(u\). The methodology evaluates privacy risks with varying levels of background knowledge, from minimal to maximal knowledge, enabling responsible decision-making. Defining attack models and background knowledge is critical, systematically balancing privacy risks and data utility. A _background knowledge category_ refers to information known by an adversary about the specific dimensions of an individual's data. For instance, in mobility data, typical dimensions include space, time, frequency of visiting a location, and probability of visiting a location. The number of elements the adversary knows, the size of the _background knowledge configuration_, is denoted by \(k\). An example of a background knowledge configuration could be the adversary knowing \(k=3\) points in the trajectory of an individual. An _instance of background knowledge_ represents specific information the adversary knows, such as a visit to a specific location; we can see an example of background knowledge in Figure 1. In Figure 1, we begin with a dataset containing trajectory data. In the example provided, the attacker has knowledge of location sequences, with a knowledge size of 2. The second table in Figure 1 illustrates the background knowledge instances generated from the input dataset. Location information is combined in pairs (two by two) to represent the potential knowledge an attacker might possess. These concepts are formalized as follows, according [11], in Definition 6. **Definition 6** (**Background Knowledge Category, Configuration and Instance)**. : _We consider a background knowledge category, denoted as \(\mathcal{B}\). Within this category, we define \(B_{k}\) as a specific configuration of background knowledge, where \(B_{k}\) belongs to the set \(\mathcal{B}=B_{1},B_{2},\ldots,B_{n}\). The value of \(k\) indicates the number of elements within \(\mathcal{B}\) that an adversary possesses. Each individual element \(b\) that is part of \(B_{k}\) represents a distinct instance of this background knowledge configuration._  
\[B_{k}=\bigg{\{}\bigg{(}\{ \begin{matrix}\{value_{1},\ldots,value_{n(u)}\}\\ k\end{matrix} \}\mid\forall\,u\bigg{\}}\]  
Let \(\mathcal{D}\) be a database, \(D\) a dataset extracted from \(\mathcal{D}\) as an aggregation of the data on specific dimensions (e.g., an aggregated data structure and filtering on some dimension), and \(D_{u}\) and \(D_{u}\) the subset of records corresponding to individual \(u\) within \(D\); we establish the likelihood of re-identification as follows in Definition 7 and in 2 in Figure 1.  
**Definition 7** (**Probability of re-identification)**.