The proposal of satellite-based FSO/QKD system using GEO and LEO satellites.

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... the paper is concluded in Sec. VI. Figure 1 presents the proposed FSO/QKD system, in which a GEO satellite (Charlie) distributes secret keys to a legitimate server, i.e., Alice and multiple users Bob i , i ∈ {1, 2 . . . N }, via FSO channels with the help of two LEO satellites for amplifying the signal. ...

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... consider the scenario in which Eavesdroppers (Eves) can compromise the system by attempting URA or BSA, as shown in Fig. 1. In the former, Eves locate on the ground and try to tap the transmitted signal from LEO satellites by being within the beam footprint near legitimate users, either at Alice or Bob's location. In the case of URA, the countermeasure is to limit the damage by designing and setting appropriate system parameters. In the latter, we assume ...

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... addition, we consider the case that LEO satellites are attacked by BSA. Figure 10 shows Eve's error probability versus the modulation depth and the splitting percentage of the signal received at LEO satellites for different modulation depths δ. It is observed that if δ is decreased, Eve needs a more significant amount of the received power at LEO satellites to reduce its error probability. ...

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... Alice's Receiver Design: Firstly, the selection of ς A should satisfy two requirements: (i) the sift probability is above 10 −3 to achieve sifted-key rates at Mbps with Gbps transmission rates of FSO communications; (ii) QBER is kept below 10 −3 so that the error can be corrected efficiently at Mbps of sifted-key rates by error-correcting code. From Figs. 11 (a), (b), and (c), we can determine the range of ς A values to satisfy two conditions with the sift probability and QBER. For this purpose, Figs. 11(a), 11(b), and 11(c) show the values of ς U satisfying (i), (ii) and both during the communicable period between Starlink-1293 and Alice. It is seen that from the elapsed time of 1293s, any value ...

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... at Mbps with Gbps transmission rates of FSO communications; (ii) QBER is kept below 10 −3 so that the error can be corrected efficiently at Mbps of sifted-key rates by error-correcting code. From Figs. 11 (a), (b), and (c), we can determine the range of ς A values to satisfy two conditions with the sift probability and QBER. For this purpose, Figs. 11(a), 11(b), and 11(c) show the values of ς U satisfying (i), (ii) and both during the communicable period between Starlink-1293 and Alice. It is seen that from the elapsed time of 1293s, any value between 0 and 4 can be chosen for ς A . In addition to the above requirements, Alice should be able to detect BSA attacks. It can be done by comparing the ...

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... any value between 0 and 4 can be chosen for ς A . In addition to the above requirements, Alice should be able to detect BSA attacks. It can be done by comparing the difference in the sift probability between Charlie and Alice P C,A sift in the case of BSA and no BSA. The larger the difference is, the more likely a BSA is detected. As shown in Fig. 12, this difference increases as ς A decreases. The question is how much difference would be enough to detect BSAs with high accuracy. To answer this, we first simulate in Fig. 13 the value of P C,A sift during the first 10-second period assuming that the transmission rate is 1 Gbps. The time resolution is set to 10 −2 . Assume that BSAs ...

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... in the sift probability between Charlie and Alice P C,A sift in the case of BSA and no BSA. The larger the difference is, the more likely a BSA is detected. As shown in Fig. 12, this difference increases as ς A decreases. The question is how much difference would be enough to detect BSAs with high accuracy. To answer this, we first simulate in Fig. 13 the value of P C,A sift during the first 10-second period assuming that the transmission rate is 1 Gbps. The time resolution is set to 10 −2 . Assume that BSAs with the power splitting percentage (SP) of 1.5% happen with a probability of 0.01 (i.e., 1% of the simulation time). Since 10 7 bits are transmitted at each time instance, P ...

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... BSA that can not be detected due to the low deviation of P C,A sift compared with the threshold d BSA . A probable BSA event is an event that is either a false alarm or an actual BSA. To prevent frequent false alarms (which may interrupt the communication session), d BSA ≥ 2σ sd is considered. A visualization of these events is displayed in Fig. 14 for the case that d BSA = 2.25σ sd . For different settings of d BSA and differences in P C,A sift between BSA and no BSA, the numbers of actual BSA events, probable BSA events, false alarms, and correct BSA detections are tabulated in Table. II. Here, it can be seen that increasing d BSA results in higher percentages of correct attack ...

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... BSA events, false alarms, and correct BSA detections are tabulated in Table. II. Here, it can be seen that increasing d BSA results in higher percentages of correct attack detection and lower percentages of false alarms. Specifically, when the difference in P C,A sift between BSA and no BSA is higher than 2% (corresponding to ς ≥ 2.5 as shown in Fig. 12), the percentages of correct detection (w.r.t both No. actual BSA and probable BSA events) can be made to 100% by choosing d BSA = 3σ sd . Together with the requirements of the sift probability and QBER described above, ς A should satisfy that 2.5 ≤ ς A ≤ 4. Nonetheless, according to Fig. 11(a), as ς A increases, the sift probability ...

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... is higher than 2% (corresponding to ς ≥ 2.5 as shown in Fig. 12), the percentages of correct detection (w.r.t both No. actual BSA and probable BSA events) can be made to 100% by choosing d BSA = 3σ sd . Together with the requirements of the sift probability and QBER described above, ς A should satisfy that 2.5 ≤ ς A ≤ 4. Nonetheless, according to Fig. 11(a), as ς A increases, the sift probability decreases. Since high values of the sift probability are preferable, ς A = 2.5 is chosen for our ...

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... 10 −3 . Observing from Figs. 15(a), 15(b), and 15(c), any value of ς Bi between 0 and 2.5 satisfies these requirements. In addition, regarding the detection of BSAs, to achieve a higher 2% difference in the sift probability between Charlie and Bob i between no BSA and BSA (performed by L B with SP = 1.5%), ς Bi should be at least 2.25 as shown in Fig. 16. Therefore, ς Bi = 2.25 is chosen to maximize the sift probability between Alice and Bob i ...

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... this section, we investigate the secret-key performance of the proposed system in terms of the total final-key creation rates of all users. The number of users at Bob's cluster is N = 4. We assume that there are two eavesdroppers performing URAs at Alice's and Bob cluster's locations as depicted in Fig. 1. The eavesdroppers are assumed to be located 26 meters away from the legitimate users. Under the design of Alice's and Bob i 's receiver presented in the previous sections, Fig. 17 illustrates the total final-key creation rates of all users R f versus the exclusion ratio coefficient ε at different elapsed time instances that Charlie ...

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... users. The number of users at Bob's cluster is N = 4. We assume that there are two eavesdroppers performing URAs at Alice's and Bob cluster's locations as depicted in Fig. 1. The eavesdroppers are assumed to be located 26 meters away from the legitimate users. Under the design of Alice's and Bob i 's receiver presented in the previous sections, Fig. 17 illustrates the total final-key creation rates of all users R f versus the exclusion ratio coefficient ε at different elapsed time instances that Charlie transmits the signal to the relays. It is observed that R f of the TDMA method is nearly three times lower than that of the proposed system. To ensure that different secret keys are ...

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... Fig. 18 investigates R f with respect to the number of users at Bob's cluster at the elapsed time t = 1323 s. In addition to ς Bi = 2.25 chosen from the previous section, we also examine other lower values of ς Bi in the operational region of ς Bi . In the case of TDMA, it can be seen that R f keeps unchanged when the number of users ...

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... TDMA, it can be seen that R f keeps unchanged when the number of users increases. In the proposed method, for each value of ς Bi , there exist an optimal number of users that maximizes R f . For example, the optimal number of users is about 30 when ς Bi = 2.25. As ς Bi decreases, the sift probability between Alice and Bob i increases as shown in Fig. 15(c), leading to an increase in R f at the optimal number of ...