National security, economic stability, and people’s privacy are affected via information security. In recent decades, laser chaos synchronization communication has realized rapid development because of its enhanced physical security. It is based on the message being mixed with the transmitting end’s laser chaotic carrier to generate the encrypted signal, and then the encrypted signal being transmitted to the receiving end as its input signal. The receiver employs its chaos pass filtering effect to output the synchronized chaotic carrier signal, and the message is recovered through subtractive demodulation of the encrypted signal and the synchronized chaotic carrier. Thus, synchronization is the key to chaotic synchronization communication, and achieving high-quality synchronization necessitates the completely matched parameters between the sender and receiver, which not only causes a lower synchronization coefficient but increases the difficulty of hardware implementation. This study proposes a reservoir computing-based secure communication approach to laser chaos synchronization. The reservoir computing, as the chaos synchronization communication system’s receiver, is synchronized with the sender’s chaotic carrier and then obtains the message by subtracting the output variable synchronized chaotic carrier from the reservoir computing’s input variable encrypted signal. The proposed approach overcomes the difficulty of a lower synchronization coefficient in traditional chaotic synchronization communication because the parameters of the transmitter and receiver are difficult to match completely.

One of the machine learning algorithms is cross-prediction, the present study proposes the cross-prediction algorithm based on chaotic synchronization communication. Among them, the encrypted and chaotic carrier signals are employed as the reservoir computing’s input and output variables, respectively. Its non-linear structure with the following functions is obtained using the encrypted signal and part of the target chaotic carrier signal, which is transmitted back to back from the sender to receiver to train the reservoir computing. When the encrypted signal from the sender is continued to be input into the reservoir computing, the corresponding synchronized chaotic carrier can be automatically output. After synchronization, subtractive demodulation between the encrypted signal and synchronized chaotic carrier can be employed to decrypt the message. Compared with the currently widely employed model-free prediction algorithm, cross-prediction removes the effect of carrier synchronization error accumulation and enhances the prediction accuracy, then the long-term prediction and communication can be realized.

Simulation exploration comprises three parts. First, the synchronization performance and communication performance of the proposed system are explored, concluding that the system can realize high-quality chaotic synchronization and communication with the synchronization coefficient of 99.90% under the premise of ensuring security (Figs. 5, 8). The simulation results reveal that the carrier prediction mean square error can reach 10^-4 orders of magnitude (Fig. 9), and the decryption bit error rate can reach the order of 10^-9 (Fig. 6). The influences of the signal-to-noise ratio and the number of reservoir nodes on the system synchronization performance and communication performance are explored. The results reveal that the carrier prediction error and bit error rate decrease with increasing signal-to-noise ratio (Fig. 8). The optimal number of reservoir nodes is 1800 when the signal-to-noise ratio is 20 dB and the masking coefficient is 5.56% (Fig. 7). Second, when the cross-prediction and model-free prediction algorithms are applied to the system, the synchronization performance and communication performance are compared, respectively. The results reveal that the cross-prediction eliminates the carrier prediction error accumulation effect, and its prediction error shall not accumulate with the increase of the prediction length. Thus, the prediction accuracy is greatly improved, and long-term synchronization and communication can be realized (Fig. 9). Finally, the system’s feasibility is verified using the image communication simulation experiment. The results reveal the proposed system has good anti-attack performance and high decryption quality. Additionally, the security and system’s communication quality can be assured at the same time (Fig. 10).

In this study, reservoir computing based on the cross-prediction algorithm for laser chaos synchronization secure communication is proposed. Its advantages are as follows. 1) When compared with traditional chaotic synchronization communication, reservoir computing is employed as the receiver that avoids the difficulty of a lower synchronization coefficient due to the difficulty of completely matched parameters between the sender and receiver. The proposed system can realize high-quality chaotic synchronization and communication with a synchronization coefficient of 99.90% under the premise of ensuring security. 2) The cross-prediction algorithm based on reservoir computing applied to the chaotic synchronization communication realizes long-term prediction and communication. The cross-prediction algorithm removes the effect of carrier synchronization error accumulation, enhancing prediction accuracy by 3 orders of magnitude over model-free prediction. The prediction mean square error can reach 10^-4 orders of magnitude, and the decryption bit error rate can reach the order of 10^-9. Furthermore, the image communication simulation experiment demonstrates that the security and proposed system’s communication quality are assured at the same time.