6.2.2. Entropy

The entropy is used to evaluate the level of privacy of vehicles in the network. It calculates the degree of uncertainty in information from an adversary's perspective by

linking various pseudonyms of a vehicle during communication and the pseudonym changing process. This measures the level of privacy achieved or anonymisation of vehicles. Let *V<sup>x</sup>* be a set of vehicles that may be taking part in the pseudonym changing procedure, and *V<sup>y</sup>* is a set of vehicles that successfully changed pseudonyms. Let *P*(*Vx*→*V<sup>y</sup>* ) be the probability of mapping the number of vehicles to the number of pseudonyms changed. The uniform probability of distribution evaluates the higher level of entropy and higher confusion for an adversary to identify the target vehicle. Consider the number of vehicles that have changed pseudonyms at time *t*; the entropy can be calculated as follows [12]:

$$H\_{\rm f} = \sum\_{V\_{\rm x}, V\_{\rm y} \in V} P\_{V\_{\rm x}} \to\_{V\_{\rm y}} \log\_2 P\_{V\_{\rm x}} \to\_{V\_{\rm y}}.\tag{24}$$

where *H<sup>t</sup>* is the entropy of vehicles anonymisation in the concerned area, and *V* is the total number of vehicles taking part in the pseudonym changing process. The average entropy can be calculated as follows:

$$H\_{\text{avg}} = \frac{1}{V} \sum\_{\mathbf{x}, \mathbf{y} \in V} H\_{\mathbf{f}}(\mathbf{x}, \mathbf{y}). \tag{25}$$
