# Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers
## 3 Results
### Quantum Bit Error Rate Due to Excess Photons  
Applying the photon rates determined in Section 3.3 to the QBER calculation outlined in Section 2.5 we can estimate the effect the excess photons from the laser terminal will have on the QKD rate. Figure 6 shows additional QBER caused by the excess photons detected from a 1 kW laser terminal with a 10 cm telescope 100 km away, and Figure 7 shows the additional QBER due to a 1 kW laser terminal with a 30 cm aperture 1000 km away. In both figures, the green trace shows the detected QKD signal photon rate while the blue trace shows the detected excess noise photon rate. The dashed red line shows the QBER threshold at which no secret key can be produced and the QKD is completely disrupted.  
Our analysis assumes that the laser terminal is emitting a continuous wave (CW) laser and that the excess photons from the terminal reaching the QKD receiver are uniformly temporally distributed. The red trace shows the additional QBER caused by the excess photons. Where this additional QBER exceeds the QBER threshold indicated by the dashed red line, no secure quantum key can be generated.  
Figure 6 shows that, from 100 km away, the laser terminal can completely disrupt the QKD transmission for 70% of the duration of transmission window, and significantly increase the QBER over much of the remaining fraction. For the 1000 km case (Figure 7), the laser terminal is only able to completely disrupt the QKD for 55% of the transmission window, limited primarily by visibility of the satellite. A shown in Figure 8 second symmetrically placed laser terminal, such that the first terminal has sight of the QKD satellite in the early part of the transmission window, and the second terminal the later half would allow total disruption of the QKD transmission. Even with a reduction in received noise photons by a factor of two this symmetric attack would prohibit any secure key being generated during a satellite pass.  
It should be noted that this analysis only considers the impact of the additionally created noise due to the attack. It does not consider the already existing noise due to other sources such as light pollution or sources of noise within the QKD system itself. Therefore, all disruption attempts will be more effective in a real-world scenario than estimated here as the QBERs due to other noise sources are cumulative.  
Figure 5: Excess photon rate at the QKD ground station and optical power loss over time (represented in seconds elapsed since the satellite came into view of the ground station) achieved for a 1 kW laser launched via a 30 cm telescope 1000 km from the ground station. (The satellite moves out of view of the laser terminal around 220 s assuming a lower elevation limit of 10\({}^{\circ}\)).  
Figure 6: Additional QBER due to laser terminal with 10 cm optic from 100 km distance with 1 kW laser power. Green trace, detected QKD signal photon rate; blue trace, detected excess noise photon rate; red trace, additional QBER due to excess noise photons; dashed red line, QBER limit at which no secure key can be generated.  
Figure 7: Additional QBER due to laser terminal with 10 cm optic from 1000 km distance with 1 kW laser power. Green trace, detected QKD signal photon rate; blue trace, detected excess noise photon rate; red trace, additional QBER due to excess noise photons; dashed red line, QBER limit at which no secure key can be generated.