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. 2020 Oct 6;22(10):1134.
doi: 10.3390/e22101134.

Deep Learning-Based Security Verification for a Random Number Generator Using White Chaos

Cai Li  1   2 , Jianguo Zhang  1   2 , Luxiao Sang  1   2 , Lishuang Gong  1   2 , Longsheng Wang  1   2 , Anbang Wang  1   2 , Yuncai Wang  3   4
Affiliations

Deep Learning-Based Security Verification for a Random Number Generator Using White Chaos

Cai Li et al. Entropy (Basel). .

Abstract

In this paper, a deep learning (DL)-based predictive analysis is proposed to analyze the security of a non-deterministic random number generator (NRNG) using white chaos. In particular, the temporal pattern attention (TPA)-based DL model is employed to learn and analyze the data from both stages of the NRNG: the output data of a chaotic external-cavity semiconductor laser (ECL) and the final output data of the NRNG. For the ECL stage, the results show that the model successfully detects inherent correlations caused by the time-delay signature. After optical heterodyning of two chaotic ECLs and minimal post-processing are introduced, the model detects no patterns among corresponding data. It demonstrates that the NRNG has the strong resistance against the predictive model. Prior to these works, the powerful predictive capability of the model is investigated and demonstrated by applying it to a random number generator (RNG) using linear congruential algorithm. Our research shows that the DL-based predictive model is expected to provide an efficient supplement for evaluating the security and quality of RNGs.

Keywords: deep learning; predictive model; random number generator; security analysis; semiconductor laser; white chaos.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Experimental scheme for evaluating the security of RNGs, which comprises data collection and preprocessing, model training and validation, and system evaluation.
Figure 2
Figure 2
The structure of a NRNG based on white chaos. DFB1,2: distributed feedback semiconductor laser; PC1,2: polarization controller; FC1,2, FC: fiber coupler; OI1,2: optical isolator; VA1,2: variable attenuator; M1,2: fiber mirror; BPD: balanced photo-detector; ADC: analog-to-digital converter; LSBs: least significant bits.
Figure 3
Figure 3
Data preprocessing in a conventional approach where 10 consecutive adjacent numbers within the random sequence are used as one input sequence, whereas the next number after the input sequence is used as the output (label). The new sequence and corresponding output are updated by shifting three positions in the dataset.
Figure 4
Figure 4
Deep learning model based on temporal pattern attention, which consists of a one-hot encoder, a LSTM layer, a temporal pattern attention (TPA) layer, and a fully connected (FC) layer.
Figure 5
Figure 5
Distribution of standardized numbers from RNGs with different stages. (a–c) represent the probability distribution of the data from the output of LC-RNG with the period of 224, the output of the ECL1, and the output of the NRNG, respectively.
Figure 6
Figure 6
Prediction performance of the deep learning-based predictive model at different stages of LC-RNG and the white chaos-based NRNG.
Figure 7
Figure 7
Temporal properties of the chaos of the ECL1 as well as the white chaos-based NRNG. (a1,b1) respectively represent the RF spectra of the chaos of the ECL1 and the white chaos. (a2,b2) respectively represent the autocorrelation traces of the chaos of the ECL1 and the white chaos.
See this image and copyright information in PMC

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