*4.1. Eve's Attack*

The intensity of Eves' attack is affected by the spatial distribution. In Figure 3a, when we compare the blue line with the red and yellow line, respectively, we find that the covering radius *RS* has little effect on STP while density *λ<sup>p</sup>* significantly reduces the STP. However, in Figure 3b, both the value of *RS* and *λ<sup>p</sup>* have significant impacts on the STP. The reason is that the SNR of multiple eavesdroppers in the non-colluding case depends on the 'nearest' Eve which has the best channel quality while the SNR in the colluding case only depends on the total number. The parameter *RS* can barely increase the chance of the 'nearest' Eve as the THz transmit power quickly attenuates with the distance but indeed increases the total number of them. Therefore, from Eves' perspective, they have to focus on 'a better channel' or 'a better location' rather than the total number in a non-colluding

case, as we can see the STP of the case when *NE* = 17 performs even better than the STP when *NE* = 7 in Figure 3a.

**Figure 3.** Secure transmission probability (STP) under different *RS* and *λ<sup>p</sup>* for (**a**) non-colluding case and (**b**) colluding case. Parameters are given by: *G* = 25 dBi; *N* = 5; *f* = 300 GHz; and *P* = −10 dBm.

In Figure 4, we use normalized secrecy capacity [30] to show the extent to which Eves reduce the secrecy capacity in non-colluding and colluding cases, respectively. It is shown that for *d*<sup>2</sup> = 20, the existence of Eves reduces the original capacity by 20% in non-colluding case and by nearly 40% in colluding case.

**Figure 4.** The normalized secrecy capacity as a function of *d*<sup>2</sup> in the non-colluding and colluding cases. Here, all the eavesdroppers have the same distance *d*<sup>2</sup> to the PEC and the channel fading is ignored. Other parameters are given by: *G* = 25 dBi; *f* = 300 GHz; *P* = −10 dBm; *RS* = 15 m; and *d*<sup>3</sup> = 1 m.

Eve can move the PEC closer to Alice to strengthen the attack. In Figure 5, we find that the ESC monotonically increases with *d*<sup>3</sup> (PEC) while decreasing with the *d*<sup>1</sup> (Bob). In addition, the parameters *d*<sup>1</sup> and *d*<sup>3</sup> may have interacted with each other. For example, for *d*<sup>1</sup> = 3, a unit increase in *d*<sup>3</sup> will give birth to the improved ESC by ΔESC = 1.45. For *d*<sup>1</sup> = 5, ΔESC becomes 1.95. That is to say, *d*3(*d*1) may exhibit a different effect when the other factor changes. Furthermore, if PEC is located in the midpoint between Alice and Bob, the ESC will not change significantly with the increase in *d*1, as we can see that the white line in Figure 5 nearly remains unchanged at ESC = 4.85.

**Figure 5.** Ergodic secrecy capacity (ESC) as a function of *d*<sup>1</sup> (Alice–Bob) and *d*<sup>3</sup> (Alice–PEC) for (**a**) non-colluding eavesdroppers and (**b**) colluding eavesdroppers. Other parameters are given by: *G* = 25 dBi; *N* = 3; *f* = 300 GHz; *P* = −10 dBm; *RS* = 15 m; and *λ<sup>p</sup>* = 0.015.

Eve can increase the size of PEC to strengthen the attack. In Figure 6a, we find that the STP will decrease when the radius *a* rises from 20 mm to 40 mm, regardless of whether it is in the non-colluding case or in the colluding case. As shown in Figure 2, as *a* grows from 20 mm to 40 mm, the electromagnetic field around the PEC will be augmented and hence Eves obtains better signal quality. Additionally, we find that Eves benefit from increasing *a* to various degrees when the location of PEC *d*<sup>3</sup> changes. For *d*<sup>3</sup> = 5 m, as shown in Figure 6b, reducing *a* from 10 mm to 50 mm will lead to an ESC decrease of 36%. For *d*<sup>3</sup> =1m, however, reducing *a* from 10 to 50 decreases the ESC by 87% to nearly 0 which means that Eves can almost intercept all the information. Since being too near to Alice will increases the risk of being detected, Eve's strategy is to select a proper size and optimal location in such a way she can obtain as good a signal strength as possible and hide herself simultaneously.

**Figure 6.** (**a**) Influence of radius *a* on STP. (**b**) ESC versus radius *a* under different PEC location *d*3. The solid line describes the non-colluding case while the dashed line describes the colluding case. Other parameters are given by: *G* = 25 dBi; *N* = 3; *f* = 300 GHz; *P* = −10 dBm; *RS* = 15 m; and *λp* = 0.04.
