# Wireless-Channel Key Distribution Based on Laser Synchronization
## 2 Principle and Experimental Setup  
The principle of the proposed scheme is shown in Figure 1a. Two identical nonlinear oscillators are authorized to the legitimate users [PERSON] and Bob. Each nonlinear oscillator has a set \(V\) of parameters that can be changed. These parameters can take on one of \(M\) possible values. \(V_{A}\) and \(V_{B}\) are generated by two independent random bit generators (RBG). A complex drive signal is transmitted through an antenna, and then it is received and injected into the nonlinear oscillators to achieve chaos synchronization. Only in the time slots when \(V_{A}=V_{B}\), do the chaotic waveforms synchronize. This process is called random keying. Subsequently, the output signals of the oscillators are sampled and quantized to generate the correlated random bits \(X_{A}\) and \(X_{B}\) privately and independently. They repeat this procedure many times to acquire sequences of the pairs (\(V_{A,i}\), \(X_{A,i}\)) and (\(V_{B,i}\), \(X_{B,i}\)), \(i=1\), 2,..., \(n\), respectively. Next, they exchange the parameters sequences \(\{V_{A,i}\}\) and \(\{V_{B,i}\}\), \(i=1\), 2,..., \(n\), over a public channel to sift bits. Only the bits \(X_{A,i}\) and \(X_{B,i}\) for \(i\) such that \(V_{A,i}=V_{B,i}\) are retained, otherwise the bits are discarded. These retained bits, denoted as \(\{Y_{A,i}\}\) and \(\{Y_{B,i}\}\), \(i=1\), 2,..., \(n\), are used to generate a common secret key \(K_{A}=K_{B}\) by using an information reconciliation protocol and a privacy amplification protocol [27] in post processors. To evaluate the security of this scheme, we assume an eavesdropper, [PERSON], who can inject the drive signal into one or more nonlinear oscillators. Additionally, we assume that [PERSON] can obtain any information exchanged through a public channel between [PERSON] and [PERSON]. It has been proven that [PERSON] and [PERSON] can generate a key that is completely secret to [PERSON] when [PERSON] has no way of inferring the bits generated by [PERSON] and [PERSON] without errors [8]. In our scheme, we utilize two characteristics of common-signal-induced synchronization to facilitate this condition [28; 29]. Firstly, the outputs of two nonlinear oscillators can synchronize under the drive of a common noise signal, while there is no simple functional relationship between the drive signal and the oscillator outputs. This makes it difficult for [PERSON] to obtain sufficient information about the retained bits even if she can get the drive signal from the wireless channel. Secondly, the synchronization is sensitive to the parameter mismatches of the nonlinear oscillators. This means that even if [PERSON] can access all information on the public channel, it is difficult for [PERSON] to obtain enough oscillators with parameter matches to observe the outputs for all possible parameter values. These characteristics give [PERSON] and [PERSON] a certain probability of retaining bits that cannot be obtained by [PERSON], thus enabling the establishment of a common secret key. It is worth noting that [PERSON] and [PERSON] can further reduce the amount of information obtained by [PERSON] by applying privacy amplification techniques [27], so they do not need to know which bits [PERSON] has obtained. In the subsequent section, we conduct a proof-of-concept experiment using semiconductor lasers as nonlinear oscillators to verify the feasibility of the scheme and estimate the secure key generation rate under reasonable assumptions. Figure 1b illustrates the experimental setup for wireless-channel key distribution. [PERSON] and [PERSON] are assigned a pair of parameter-matched distributed-feedback semiconductor lasers (DFB). These lasers were selected from an identical fabrication batch that was supplied by the company Eblana Photonics. An arbitrary waveform generator (AWG) generates a noise signal as the common wireless drive signal, which is broadcasted via an antenna (5.38-8.17 GHz standard gain horn antenna) Tx.