## 1 Introduction
### Previous Work  
Emergency vehicles (EVs) have been using warning devices for a long time. Currently, the most used warning system deployed by EVs is a combination of flashing lights and sirens. This system has obvious disadvantages, as has been demonstrated by several studies. For instance, a siren is a severely limited warning device effective only for very short range and very low speeds. On top of that, hearing loss of siren-exposed personnel has also been documented in several studies [10; 11; 12]. Currently, many cars are equipped with multimedia entertainment systems, which can lead to a situation where a driver is not able to hear the audio warning system of the approaching EV. Furthermore, many cars are now virtually sound-proof. Due to the limited range of the audio alerts, even if a driver notices the siren, he/she often does not have enough time to react in time. Such situations may lead to traffic accidents, mostly occurring at intersections [13]. Both the scientific community as well as the public authorities believe that these limitations can be addressed by the deployment of information and communication technologies (ICT). There are two major communication technologies capable of transferring warning messages--Vehicular Ad hoc Networks (VANETs) and 5G [14; 15]. Currently, it is not certain, which technology will dominate the future market, however, when it comes to the available standards (e.g., frequency allocations), VANET is the most mature technology [15]. Moreover, it provides an adequate communication range, non-line-of-sight message dissemination, and innovative use of data transmission methods, easing the information interpretation and thus leveraging the benefits of an electronic-communication-based warning system. For these reasons, we selected VANET to implement the privacy ensuring emergency vehicle approaching warning system (PEEV-WS). Some works have already explored the possibilities of EVA implementation using VANETs [16; 17]. All these works are based on broadcasting the expected EV route to all vehicles. Based on a projected route, a receiving vehicle determines whether the warning message is relevant or not. This practice introduces two issues. First, the EV route needs to be properly interpreted. The route can be transmitted in two forms--either as a sequence of geographical coordinates, or as a succession of map-specific edges (e.g., road segments and lanes). In both cases, the sender as well as the receiver must use the same reference map, to reliably recognize the transport infrastructure objects (e.g., lanes) which will be used by the EV. Hence, the map must be either agreed on in advance or transmitted together with the EV route. As presented in [18], updates of high-definition maps can take a significant amount of communication network resources, decreasing the available bandwidth for application payload, and increasing the communication latency. Difficulties of map exchanges can be avoided if the EV is responsible for the decision-making process and determines which vehicles can potentially interfere with the EV in the near future and notifies those vehicles only by unicasting the vehicle-customizedinformation (e.g., a request to change the lane). To predict vehicle trajectory and the probability of a lane change, techniques based on the extended Kalman filter [19], long-short-term-memory networks [20], and support vector machine in combination with Bayesian filter [21] were already explored. Second, there is a significant risk that the information about the route of the EV can be misused. This can be prevented by encrypting the message content. In the general context, several research projects systematically targeted the security issues in the VANETs, for example the Cooperative Vehicle-Infrastructure Systems (CVIS), E-safety Vehicle Intrusion Protected Applications (EVITA), and Secure Vehicular Communication (SeVeCom) [22; 23; 24]. In [25], [PERSON] evaluated various digital signature schemes [26].