{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T11:14:22Z","timestamp":1780053262324,"version":"3.54.0"},"reference-count":36,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&D Program of China","award":["2018YFB0804300"],"award-info":[{"award-number":["2018YFB0804300"]}]},{"name":"National Key R&D Program of China","award":["61872357"],"award-info":[{"award-number":["61872357"]}]},{"name":"National Key R&D Program of China","award":["61802396"],"award-info":[{"award-number":["61802396"]}]},{"name":"National Key R&D Program of China","award":["MMJJ20180113"],"award-info":[{"award-number":["MMJJ20180113"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2018YFB0804300"],"award-info":[{"award-number":["2018YFB0804300"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61872357"],"award-info":[{"award-number":["61872357"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61802396"],"award-info":[{"award-number":["61802396"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["MMJJ20180113"],"award-info":[{"award-number":["MMJJ20180113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Cryptography Development Fund of China","award":["2018YFB0804300"],"award-info":[{"award-number":["2018YFB0804300"]}]},{"name":"National Cryptography Development Fund of China","award":["61872357"],"award-info":[{"award-number":["61872357"]}]},{"name":"National Cryptography Development Fund of China","award":["61802396"],"award-info":[{"award-number":["61802396"]}]},{"name":"National Cryptography Development Fund of China","award":["MMJJ20180113"],"award-info":[{"award-number":["MMJJ20180113"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2020,2,17]]},"abstract":"Random number generator (RNG) is a fundamental and important cryptographic element, which has made an outstanding contribution to guaranteeing the network and communication security of cryptographic applications in the Internet age. In reality, if the random number used cannot provide sufficient randomness (unpredictability) as expected, these cryptographic applications are vulnerable to security threats and cause system crashes. Min-entropy is one of the approaches that are usually employed to quantify the unpredictability. The NIST Special Publication 800-90B adopts the concept of min-entropy in the design of its statistical entropy estimation methods, and the predictive model-based estimators added in the second draft of this standard effectively improve the overall capability of the test suite. However, these predictors have problems on limited application scope and high computational complexity, e.g., they have shortfalls in evaluating random numbers with long dependence and multivariate due to the huge time complexity (i.e., high-order polynomial time complexity). Fortunately, there has been increasing attention to using neural networks to model and forecast time series, and random numbers are also a type of time series. In our work, we propose several new and efficient approaches for min-entropy estimation by using neural network technologies and design a novel execution strategy for the proposed entropy estimation to make it applicable to the validation of both stationary and nonstationary sources. Compared with the 90B\u2019s predictors officially published in 2018, the experimental results on various simulated and real-world data sources demonstrate that our predictors have a better performance on the accuracy, scope of applicability, and execution efficiency. The average execution efficiency of our predictors can be up to 10 times higher than that of the 90B\u2019s for \n \n \n \n \n 10<\/a:mn>\n <\/a:mrow>\n \n 6<\/a:mn>\n <\/a:mrow>\n <\/a:msup>\n <\/a:mrow>\n <\/a:math>\n <\/jats:inline-formula> sample size with different sample spaces. Furthermore, when the sample space is over \n \n \n \n \n 2<\/c:mn>\n <\/c:mrow>\n \n 2<\/c:mn>\n <\/c:mrow>\n <\/c:msup>\n <\/c:mrow>\n <\/c:math>\n <\/jats:inline-formula> and the sample size is over \n \n \n \n \n 10<\/e:mn>\n <\/e:mrow>\n \n 8<\/e:mn>\n <\/e:mrow>\n <\/e:msup>\n <\/e:mrow>\n <\/e:math>\n <\/jats:inline-formula>, the 90B\u2019s predictors cannot give estimated results. Instead, our predictors can still provide accurate results. Copyright\u00a9 2019 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1155\/2020\/4241713","type":"journal-article","created":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T23:31:49Z","timestamp":1581982309000},"page":"1-18","source":"Crossref","is-referenced-by-count":8,"title":["High-Efficiency Min-Entropy Estimation Based on Neural Network for Random Number Generators"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8890-1393","authenticated-orcid":true,"given":"Na","family":"Lv","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4097-681X","authenticated-orcid":true,"given":"Tianyu","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuangyi","family":"Zhu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Ma","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiwu","family":"Jing","sequence":"additional","affiliation":[{"name":"China Information Technology Security Evaluation Center, Beijing 100085, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingqiang","family":"Lin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2009.235"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/jlt.2018.2817512"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1364\/ol.44.002446"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2008.227"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1145\/1609956.1609966"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1109\/sp.2006.5"},{"key":"7","first-page":"673","article-title":"Predicting, decrypting, and abusing WPA2\/802.11 group keys","author":"M. Vanhoef"},{"key":"8","volume-title":"Sp 800-22 Rev. 1a. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications","author":"A. L. Rukhin","year":"2010"},{"key":"9","volume-title":"AIS 31: Functionality Classes and Evaluation Methodology for True (Physical) Random Number Generators Version 3.1","author":"W. Killmann","year":"2001"},{"key":"10","article-title":"The marsaglia random number CDROM including the diehard battery of tests of randomness","author":"G. Marsaglia","year":"1996"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1145\/1268776.1268777"},{"key":"12"},{"key":"13","article-title":"Nist draft special publication 800-90B: recommendation for the entropy sources used for random bit generation","author":"E. Barker","year":"2012"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-010-9089-3"},{"key":"15","first-page":"146","article-title":"A design for a physical RNG with robust entropy estimators","author":"W. Killmann"},{"key":"16","first-page":"544","article-title":"Entropy evaluation for oscillator-based true random number generators","author":"Y. Ma"},{"key":"17","first-page":"165","article-title":"On the entropy of oscillator-based true random number generators","author":"Y. Ma"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1364\/ol.42.002699"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.87.062327"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1364\/oe.25.006511"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1364\/oe.20.012366"},{"key":"22","article-title":"(Second draft) NIST special publication 800-90b: recommendation for the entropy sources used for random bit generation","author":"M. S. Turan","year":"2016"},{"key":"23","article-title":"NIST special publication 800-90B: recommendation for the entropy sources used for random bit generation","author":"M. S. Turan","year":"2018"},{"key":"24","first-page":"373","article-title":"Predictive models for min-entropy estimation","author":"J. Kelsey"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2015.10.036"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-011-0741-0"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2011.6033576"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/0925-2312(91)90040-i"},{"key":"29","volume-title":"Deep Learning","author":"I. Goodfellow","year":"2016"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2005.12.138"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2006.03.002"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2008.01.030"},{"key":"33","article-title":"Entropy bounds and statistical tests","author":"P. Hagerty","year":"2012"},{"issue":"3","key":"34","doi-asserted-by":"crossref","first-page":"151","DOI":"10.46586\/tosc.v2017.i3.151-168","article-title":"Analysis and improvement of entropy estimators in NIST SP 800-90b for non-IID entropy sources","author":"S. Zhu","year":"2017","journal-title":"IACR Transactions on Symmetric Cryptology"},{"key":"35","volume-title":"Handbook of Applied Cryptography","author":"A. Menezes","year":"1996"},{"key":"36","first-page":"231","article-title":"Neural network based min-entropy estimation for random number generators","author":"J. Yang"}],"updated-by":[{"DOI":"10.1155\/2020\/3451823","type":"erratum","label":"Erratum","source":"publisher","updated":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T00:00:00Z","timestamp":1603411200000}}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/4241713.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/4241713.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/4241713.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T16:47:51Z","timestamp":1610642871000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2020\/4241713\/"}},"subtitle":[],"editor":[{"given":"Clemente","family":"Galdi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2020,2,17]]},"references-count":36,"alternative-id":["4241713","4241713"],"URL":"https:\/\/doi.org\/10.1155\/2020\/4241713","relation":{"erratum":[{"id-type":"doi","id":"10.1155\/2020\/3451823","asserted-by":"object"}]},"ISSN":["1939-0122","1939-0114"],"issn-type":[{"value":"1939-0122","type":"electronic"},{"value":"1939-0114","type":"print"}],"subject":[],"published":{"date-parts":[[2020,2,17]]}}}