# Key Distribution Scheme for Optical Fiber Channel Based on SNR Feature Measurement
## 2 Key Generation Scheme for Optical Fiber Communication  
### Channel Model  
As shown in Figure 1, the signal sent by the legitimate client [PERSON] is \(A^{n}\), while the legitimate receiver [PERSON] receives the signal sequence \(B^{n}\). The eavesdropping signal obtained by [PERSON] is \(E^{n}\). The legitimate receiver obtains the SNR by comparing the signal from the receiver with that from the transmitter. According to information theory, the mutual information between [PERSON] and [PERSON] as Equation (1) should be as small as possible for reliable transmission. [PERSON] cannot correctly obtain [PERSON]'s key information, indicating that the key of communication negotiation is secure when \(I(A^{n};E^{n})\to 0\).  
\[I(A^{n};E^{n})=H(A^{n})-H(A^{n}|E^{n}) \tag{1}\]  
The keys generated by [PERSON], [PERSON], and [PERSON] are \(K_{A}=f_{A}(A^{n})\), \(K_{B}=f_{A}(B^{n})\), and \(K_{E}=f_{E}(E^{n})\), respectively, to achieve the security of the physical layer. Assuming that the coefficient of key consistency \(\varepsilon\) is large enough for \(n\) to satisfy the following relation, the system is secure [9; 23].  
\[P(K_{A}=K_{B})\geq\varepsilon \tag{2}\]  
\[I(K_{A};E^{n})\leq 1-\varepsilon \tag{3}\]  
In the best case, the key consistency rate approached in Equation (2) indicates that the completion of the key generated by [PERSON] and [PERSON] is consistent. Equation (3) indicates that [PERSON] receives the information irrespective of the key generated by the legitimate. The maximum security key capacity is shown in Equation (4). The key capacity is \(C_{AB}\) when the communication between legitimate parties is normal, and the generated key capacity is \(C_{AE}\) when [PERSON] eavesdrops. The maximum value \(C_{K}\) is obtained by subtracting \(C_{AE}\) from \(C_{AB}\).  
\[C_{K}=[C_{AB}-C_{AE}]=\max[I(A^{n};B^{n})-I(A^{n};E^{n})] \tag{4}\]\[C_{K}=[C_{AB}-C_{AE}]=[\frac{1}{2}\log(1+\frac{p}{\sigma_{1}^{2}})-\frac{1}{2}\log( 1+\frac{p}{\sigma_{1}^{2}+\sigma_{2}^{2}})] \tag{5}\]  
The security capacity \(C_{K}>0\) under the Gaussian Tap channel is shown in Equation (5), where \(p\) is the power of the signal, and \(\sigma_{i}(i=1,\;2)\) are, respectively, the noise variance of [PERSON] and [PERSON] stealing channels in the normal transmission main channel.  
### Channel Model  
Figure 2 shows the proposed key generation scheme based on the SNR measurement in the optical fiber loop. Due to the changes in temperature, external stress, and physical parameters, the measured SNR fluctuates randomly. Specific physical layer channel features are extracted as follows: [PERSON] and [PERSON] simultaneously measure the SNR parameter changes in the fiber loop. Data from [PERSON] and [PERSON] are transmitted in the fiber loop link through time-division multiplexing. [PERSON] and [PERSON] occupy different time slots, i.e., even and odd symmetric time slots, respectively. First, [PERSON] generates random data and random ground state \(C^{A}\) through a PRNG. Afterwards, the DSP module of the transmitter generates the signal \(D^{AB}\) from the signal \(D^{A}\) and the ground state \(C^{A}\). The signal \(D^{AB}\) reaches the [PERSON] terminal after transmission in the optical fiber. [PERSON]'s DSP module processes the received signal with a random ground state \(C^{B}\) to generate the data \(D^{AB}\). After the data \(D^{AB}\) signal is transmitted in the optical fiber, the signal \(N^{AB}\) with channel noise reaches [PERSON]. The receiver's DSP module generates data \(D^{ABA}\) based on the received signal \(D^{AB}\) and random ground state \(C^{A}\). The SNR performance of the fiber loop can be obtained by comparing the data \(D^{A}\) with \(D^{ABA}\). Similarly, [PERSON] can measure the fiber loop simultaneously to acquire the SNR change rate of the fiber loop backlink.  
Figure 1: Key generation model diagram.  
Figure 2: Schematic diagram of key generation principle at the physical layer. PRNG: pseudo-random number generator. DSP: digital signal processing.