Chaotic laser is proved able to be used in key distribution systems to provide a reliable physical entropy source. High-speed random keys can be extracted from a constructed chaotic laser synchronization system. The common externally driven optical injection is the main synchronization structure of chaotic key distribution systems. External-cavity semiconductor lasers (ECSLs) are driving sources easiest to realize in practice and have good robustness. However, this synchronization system faces the following problems in application: 1) optical feedback introduces time delay characteristics into chaotic synchronization signals, which limits signal complexity; 2) chaotic signals have asymmetric amplitude distribution, which affects the randomness of key generation; 3) there is a high correlation between the external driving signal and the local synchronization signal, which reduces the security of the synchronization system.

Generative adversarial networks (GANs) are a kind of powerful generative model, which includes two neural networks that are pitted against each other in a game-like scenario. They can finally reach a Nash equilibrium through continuous iterative optimization in the training process. The main learning task of a GAN is to realize the transformation of a probability distribution, namely to generate data approaching the target probability distribution through input data. The introduction of a GAN into a chaotic laser synchronization system can optimize the symmetry of chaotic signal amplitude distribution and then realize the generation of random keys at a higher rate.

Fig. 4 compares the autocorrelation function (ACF) and amplitude probability distribution of chaotic signals before and after optimization. Two commonly used analysis methods, ACF and permutation entropy (PE), are used to analyze the time delay signature (TDS) and complexity of chaotic signals. The optical-feedback ECSL-driven injection makes the initial chaotic signal generated from the laser have TDS, and an obvious correlation peak can be detected at the feedback delay of 62.3 ns, whose amplitude also shows an asymmetric probability distribution [Figs. 4 (a) and (b)]. After calculation, the complexity and skewness of the initial chaotic signal are 0.973 and 1.19, respectively. The results after GAN optimization [Figs. 4 (c) and (d)] demonstrate that the ACF curve of the optimized signal is approximate to a Dirac function. The TDS corresponding to the feedback delay is completely suppressed, and the complexity is increased to 0.99. In addition, the optimized amplitude distribution is close to the Gaussian distribution, and the symmetry is significantly improved. The skewness is reduced to 7.78×10^-4, increased by 3 orders of magnitude. Fig. 5(a) shows the suppression results of chaotic signal TDS before and after optimization under different parameter conditions. The results indicate that compared with the initial chaotic signal, the optimized signal has significantly suppressed TDS, which is reduced to a level below 0.01 under different injection powers. The Kullback-Leibler (KL) divergence of the original chaotic signal is greater than 3, while that of the optimized signal is greatly reduced, which remains at a low level of less than 0.01 under different injection powers, indicating that the optimized distribution is close to a standard normal distribution. Fig. 7 shows the influence of the threshold coefficient α on the bit error rate (BER) of synchronous random sequences. The BER of the optimized signal is significantly lower than that of the original chaotic synchronization signal because the symmetry of the amplitude distribution is significantly improved through optimization. BER is about 0.1 at α=0 (namely that no sampling point is discarded). With the increase in α, BER follows an approximately linear decline trend. When α is greater than 0.125, BER is below the forward error correction threshold (3.8×10^-3). Here α is set to 0.15 so that the BER of synchronous random bit sequences is lower than 10^-3, and the corresponding retention ratio γ is 0.82. The final generation rate of synchronized physical random numbers is 4.1 Gbit/s. To verify the quality of random numbers, this paper employs the randomness test set NIST SP800-22 as the evaluation standard, which is widely used internationally. The results show that the 4.1 Gbit/s synchronized physical random numbers generated by the proposed scheme can pass the standard test of randomness.

Chaos synchronization is the basis for the application of optical chaos in the field of secure communication. However, the existing experimental systems of chaos synchronization have problems of asymmetric amplitude distribution, limited complexity, and insufficient privacy. This paper proposes and verifies a chaos synchronization optimization scheme based on deep learning. To optimize the initial synchronized chaotic signals, the paper introduces a GAN into the common signal-induced synchronization system which is driven by an ECSL with optical feedback. The main advantages of the proposed scheme are as follows: 1) the initial chaotic signals have suppressed TDS and improved complexity; 2) the symmetry of the amplitude distribution is significantly improved; 3) the correlation between the driving signal and the local signal is greatly reduced, which enhances the privacy of the synchronization system. In addition, the optimized chaotic signals are applied to the physical entropy source. On the basis of chaos synchronization, the paper verifies the generation of synchronized physical random numbers with a high rate of 4.1 Gbit/s and a BER lower than 10^-3.