Fig. 1. Schematic of laser chaos synchronization communication system based on reservoir computing (RC). C(t): laser chaotic carrier; M(t): original message; n(t): noise; C(t)＋M(t): encrypted signal; C′(t): synchronized chaotic carrier; M′(t): decrypted message; u(t): input variables of RC; y(t): predicted output variables of RC; LD₁/LD_2:laser diode; ISO: optical isolator; MZM: Mach–Zehnder modulator; Message: useful message; VOA: variable optical attenuator; OC₁/OC_2:optical coupler; ADC: analogue-to-digital converter; PD₁/PD_2:photodetector

Fig. 2. Principle diagram of reservoir computing

Fig. 3. Schematics of model-free prediction and cross-prediction. (a) Model-free prediction; (b) cross-prediction

Fig. 4. Temporal waveforms when mask coefficient α is 5.56% and signal-to-noise ratio R_SN is 20 dB. (a) Original message; (b) chaotic carrier; (c) encrypted signal

Fig. 5. Carrier synchronization results when mask coefficient α is 5.56% and signal-to-noise ratio R_SN is 20 dB. (a) Temporal waveforms of target carrier and predicted carrier, as well as the corresponding synchronization error, the inset shows the detail of prediction error; (b) chaotic synchronization plot of predicted synchronization carrier by RC and target carrier received from transmitter

Fig. 6. Temporal waveforms of message decryption when mask coefficient α is 5.56% and signal-to-noise ratio R_SN is 20 dB. (a) Original message and quantized recovered message; (b) original message with noise and recovered message before quantizing

Fig. 7. BER, NMSE and synchronization coefficient β versus reservoir nodes N when mask coefficient α is 5.56% and R_SN is 20 dB. (a) N ranges from 1000 to 3000 in intervals of 200; (b) enlarged details (N ranges from 1000 to 3000 in intervals of 200)

Fig. 8. NMSE and BER of RC decryption and BER of direct linear filtering (DLF) attack versus R_SN for the case with mask coefficient α of 5.56%

Fig. 9. Temporal waveforms of carrier synchronization and the corresponding SMSE when mask coefficient α＝2.23%, signal-to-noise ratio R_SN＝20 dB, training sample quantity is 20000, and testing sample quantity is 3000. (a1)(a2) Temporal waveforms of carrier synchronization; (b1)(b2) SMSE

Fig. 10. Original images, encrypted images, images of DLF attack, and RC decryption images when mask coefficient α is 2.23%, 4.45%, and 6.68%, respectively