{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T21:02:36Z","timestamp":1773262956426,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T00:00:00Z","timestamp":1601942400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NSFC)","award":["61731014; 61671316; 61601319"],"award-info":[{"award-number":["61731014; 61671316; 61601319"]}]},{"name":"Research Project Supported by Shanxi Scholarship Council of China","award":["2017-key-2"],"award-info":[{"award-number":["2017-key-2"]}]},{"DOI":"10.13039\/501100004480","name":"Natural Science Foundation of Shanxi Province","doi-asserted-by":"publisher","award":["201801D121145"],"award-info":[{"award-number":["201801D121145"]}],"id":[{"id":"10.13039\/501100004480","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013317","name":"Key Research and Development Plan of Shanxi Province","doi-asserted-by":"publisher","award":["201703D321037"],"award-info":[{"award-number":["201703D321037"]}],"id":[{"id":"10.13039\/501100013317","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e22101134","type":"journal-article","created":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T10:46:17Z","timestamp":1601981177000},"page":"1134","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Deep Learning-Based Security Verification for a Random Number Generator Using White Chaos"],"prefix":"10.3390","volume":"22","author":[{"given":"Cai","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Jianguo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Luxiao","family":"Sang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Lishuang","family":"Gong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Longsheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Anbang","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Yuncai","family":"Wang","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Photonics Information Technology, Guangzhou 510006, China"},{"name":"School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,6]]},"reference":[{"key":"ref_1","unstructured":"Barker, E., and Kelsey, J. 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