# Bias Current of Semiconductor Laser: An Unsafe Key for Secure Chaos Communication
## 3 Results
### Cracking Results  
In the simulation, chaos masking was adopted to encrypt the message (binary pseudorandom sequences), for its simple structure. The electrical message was applied on an electro-optical modulator, to modulate a continuous-wave semiconductor laser, with a data rate of 2.5 Gb/s, of which the wavelength and polarization was identical to the transmitter laser, and then the generated optical  
Figure 3: Relaxation oscillation signature (ROS) as a function of the bias current of ECL: (**a**) location \(\tau_{\text{RO}}\) and (**b**) height of the ACF side peak. The black curve in (**a**) the plots \(\tau_{\text{RO}}\) of the solitary laser calculated from the formula of the relaxation period. message was masked into the optical chaos carrier, through an optical coupler. The external modulation index was 0.05. Furthermore, the decoded messages were obtained by a fourth-order low-pass Butterworth filter. We estimated the bit error rate (BER) of the deciphered data, by calculating the Q factor of the eye diagram. The BER threshold of \(1.8\times 10^{-3}\) was used to evaluate the quality of the chaotic communication [21]. That is, the message could be decoded when BER was lower than the BER threshold. Here, we set the bias current of the transmitter as \(I_{1}=1.6I_{\mathrm{th}}\). The eavesdropper extracted the \(\tau_{\mathrm{RO}}\) of 0.367 ns from the chaos carrier, and the \(I_{\mathrm{EO}}\) was considered to be \(1.8I_{\mathrm{th}}\), according to Equation (4). Figure 4 gives the eavesdropping results, including the chaotic temporal waveforms and the corresponding eye diagrams of the outputs of \(\mathrm{SL_{1}}\) and Eve, with different bias current \(I_{\mathrm{E}}=1.8I_{\mathrm{th}}\) and \(1.616I_{\mathrm{th}}\). For the eavesdropper \(\mathrm{Eve_{A}}\), when the \(I_{\mathrm{EA}}\) declined to \(1.616I_{\mathrm{th}}\), the chaos synchronization was established because of the matched bias current between the \(\mathrm{SL_{1}}\) and \(\mathrm{SLE_{\mathrm{EA}}}\). As a result, the opened eye diagram and the BER of \(3.12\times 10^{-5}\) meant that \(\mathrm{[PERSON]_{A}}\) had already decoded the message under this scenario, shown in Figure 4(a1,a2). It is worth nothing that the cracking could be achieved by only reducing the bias current of 2.2 mA, with several attempts by \(\mathrm{[PERSON]_{A}}\). For the eavesdropper \(\mathrm{[PERSON]_{B}}\), as shown in Figure 4b, the message was decoded with a BER of \(1.875\times 10^{-5}\) and the system was cracked by utilizing the bias current of \(I_{\mathrm{EB}}=1.8I_{\mathrm{th}}\). The reason was that \(\mathrm{[PERSON]_{B}}\) achieved a high-quality chaos synchronization with \(\mathrm{SL_{1}}\), through a unidirectional injection. Compared with \(\mathrm{[PERSON]_{A}}\), \(\mathrm{[PERSON]_{B}}\) directly cracked the system, with a bias current of \(1.8I_{\mathrm{th}}\). The results also proved that the security of bidirectionally-coupled synchronization was higher than the unidirectionally-coupled synchronization, in the optical chaos communication [22]. To better qualify the bias current crack range of this communication system, a more careful analysis has been carried out in Figure 5. Figure 5a shows the BER as a function of the bias current mismatches (\(\Delta I=I_{\mathrm{E}}-I_{1}\)). BER threshold is marked with red dash line. It is obvious that cracked \(\Delta I\) values ranged from \(-0.25\) to \(0.25\). Additionally, as the \(I_{\mathrm{E}}\) decreased, the BER gradually decreased to a minimum, and then rose to an unchanged value. The point where BER reached a minimum meant that the \(I_{\mathrm{EA}}\) was the closest value to \(I_{1}\). Thus, \(\mathrm{Eve_{A}}\) broke this communication system without knowing the bias current and the cracked area resembled the shape of the letter 'V', with the bias current mismatches. Figure 4: Examples of eavesdropping with an initial cracked bias current of \(1.8I_{\mathrm{th}}\).