# Discrete Cartesian Coordinate Transformations: Using Algebraic Extension Methods
## 2 Background: Technical Aspect  
Let us demonstrate that the developed approach is indeed of interest for practical applications. For clarity, we will consider the simplest possible example, which, nevertheless, is of considerable interest from the point of view of developing methods of physical protection of information, allowing to refuse the use of cryptographic methods. As noted above, the issue of information protection by physical methods is currently quite acute, which makes it possible to abandon the use of cryptographic methods, and also significantly complicates electronic warf aimed at intercepting or suppressing UAVs. At the same time, there is a gradual transition to the use of UAVs as part of a group (swarm) [50; 51; 52]. One of the most important issues here is the development of control algorithms for the swarm that would allow it to act as a single unit [53; 54; 55]. It is appropriate to emphasize that such algorithms involve not only information exchange between the UAV and the operator, but also between the individual vehicles forming the group [56; 57]. The approach to information protection proposed in [25] meets this trend. It is focused on identifying the meta-location of the coordinates of the point where the operator is located. The commands that are executed are those coming from the radio signal source located at such a point. This method is suitable for use only in the zone of direct radio visibility, but with the ever-wider use of UAVs, including for military purposes, this formulation of the issue is becoming increasingly important. This follows, among other things, from the increasing use of FPV drones controlled via ultra-thin optical fiber by both sides of the current conflict in Ukraine. It is obvious that the zone of direct radio visibility is comparable in scale to the zone for which information transmission via optical fiber can be used. It should also be noted that the identification of the source of the radio signal transmitting commands by its location is of interest, among other things, for the civil use of UAVs. As the airspace becomes saturated with such devices, the issue of the efficiency of using the corresponding radio frequency range will inevitably become relevant. The identification of the source of the radio signal by location is of interest from this point of view as well. Further, regardless of the technical implementation, the identification of the location of the signal source is reduced to solving a very specific geometric problem. This fact can be conveniently demonstrated using the \"hyperbola method\" used to establish the coordinates of an object exchanging signals with stationary radio stations [58; 59]. Let us assume that there are two devices, separated in space, and equipped with radio signal receivers. Let us also assume that the communication channel between these devices operates in real time and allows, for example, to determine the phase difference between the harmonic signals coming from their source. This means that the two devices under consideration, acting together, allow us to determine the difference between the distances from each of these devices to the radio wave source. We emphasize that the registration of the phase difference is considered only as an example. We can also consider time delays between the arrival of pulses. This already depends on the hardware implementation of the computing systems used. But with any hardware implementation, a pair of devices by themselves will not be able to determine the coordinates of the radio signal source. This pair will allow us to record only the difference in distances, which was discussed above (Figure 1). This figure emphasizes the fact used in the \"hyperbola method.\" If the above-mentioned distance difference is known, then it can be stated that the signal source lies on one of the hyperbola branches satisfying the equation. In Figure 1, the corresponding hyperbola branches are highlighted with red lines. To register the source coordinates, therefore, one more pair of devices must be used.