{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T15:51:01Z","timestamp":1784217061763,"version":"3.55.0"},"reference-count":117,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T00:00:00Z","timestamp":1743984000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T00:00:00Z","timestamp":1743984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"atural Science Basic Research Plan in Shaanxi Province of China","award":["2024JC-YBMS-546"],"award-info":[{"award-number":["2024JC-YBMS-546"]}]},{"name":"National Defense Innovation","award":["ZZKY20222411"],"award-info":[{"award-number":["ZZKY20222411"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. King Saud Univ. Comput. Inf. Sci."],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1007\/s44443-025-00007-4","type":"journal-article","created":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T10:03:21Z","timestamp":1744106601000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Pseudorandom number generators based on neural networks: a review"],"prefix":"10.1007","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9168-0605","authenticated-orcid":false,"given":"Xuguang","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiliang","family":"Han","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minqing","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ShuaiShuai","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Su","family":"Cui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanyuan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yixuan","family":"Peng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,7]]},"reference":[{"key":"7_CR1","doi-asserted-by":"publisher","unstructured":"Abadi M, Andersen DG (2016) Learning to protect communications with adversarial neural cryptography. https:\/\/doi.org\/10.48550\/arXiv.1610.06918","DOI":"10.48550\/arXiv.1610.06918"},{"key":"7_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-29642-0","author":"CC Aggarwal","year":"2023","unstructured":"Aggarwal CC (2023) Neural networks and deep learning: a textbook. Springer International Publishing, Cham. https:\/\/doi.org\/10.1007\/978-3-031-29642-0","journal-title":"Springer International Publishing, Cham."},{"issue":"7","key":"7_CR3","doi-asserted-by":"publisher","first-page":"717","DOI":"10.3390\/e22070717","volume":"22","author":"M Ahmad","year":"2020","unstructured":"Ahmad M, Al-Solami E (2020) Evolving dynamic s-boxes using fractional-order hopfield neural network based scheme. Entropy 22(7):717. https:\/\/doi.org\/10.3390\/e22070717","journal-title":"Entropy"},{"key":"7_CR4","doi-asserted-by":"publisher","unstructured":"Alani MM (2019) Applications of machine learning in cryptography: a survey. In: Proceedings of the 3rd international conference on cryptography, security and privacy. Association for Computing Machinery, New York, NY, USA, pp 23\u201327. https:\/\/doi.org\/10.1145\/3309074.3309092","DOI":"10.1145\/3309074.3309092"},{"issue":"3","key":"7_CR5","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1515\/jmc-2015-0016","volume":"9","author":"MR Albrecht","year":"2015","unstructured":"Albrecht MR, Player R, Scott S (2015) On the concrete hardness of learning with errors. J Math Cryptol 9(3):169\u2013203","journal-title":"J Math Cryptol"},{"key":"7_CR6","doi-asserted-by":"publisher","unstructured":"Allam AM, Abbas HM, El-Kharashi MW (2013) Authenticated key exchange protocol using neural cryptography with secret boundaries. In: The 2013 International Joint Conference on Neural Networks (IJCNN), pp 1\u20138. https:\/\/doi.org\/10.1109\/IJCNN.2013.6707125","DOI":"10.1109\/IJCNN.2013.6707125"},{"issue":"3","key":"7_CR7","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1109\/TAI.2022.3161893","volume":"4","author":"Y Almardeny","year":"2023","unstructured":"Almardeny Y, Benavoli A, Boujnah N et al (2023) A reinforcement learning system for generating instantaneous quality random sequences. IEEE Trans Artif Intell 4(3):402\u2013415. https:\/\/doi.org\/10.1109\/TAI.2022.3161893","journal-title":"IEEE Trans Artif Intell"},{"key":"7_CR8","doi-asserted-by":"publisher","unstructured":"Bai Y, Jones A, Ndousse K et\u00a0al (2022) Training a helpful and harmless assistant with reinforcement learning from human feedback. https:\/\/doi.org\/10.48550\/arXiv.2204.05862","DOI":"10.48550\/arXiv.2204.05862"},{"issue":"12","key":"7_CR9","doi-asserted-by":"publisher","first-page":"5907","DOI":"10.1109\/TCSI.2024.3382259","volume":"71","author":"B Bao","year":"2024","unstructured":"Bao B, Tang H, Su Y et al (2024) Two-dimensional discrete bi-neuron hopfield neural network with polyhedral hyperchaos. IEEE Trans Circuits Syst 71(12):5907\u20135918. https:\/\/doi.org\/10.1109\/TCSI.2024.3382259","journal-title":"IEEE Trans Circuits Syst"},{"key":"7_CR10","unstructured":"Bassham LE, Rukhin AL et\u00a0al (2010) Sp 800-22 rev. 1a. a statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical report, National Institute of Standards & Technology, Gaithersburg, MD, USA. https:\/\/www.nist.gov\/publications\/statistical-test-suite-random-and-pseudorandom-number-generators-cryptographic\/"},{"key":"7_CR11","unstructured":"Bernstein DJ et\u00a0al (2008) Chacha, a variant of salsa20. In: Workshop record of SASC. Citeseer, pp 3\u20135"},{"key":"7_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2022.100471","volume":"45","author":"K Bhattacharjee","year":"2022","unstructured":"Bhattacharjee K, Das S (2022) A search for good pseudo-random number generators: survey and empirical studies. Comput Sci Rev 45:100471. https:\/\/doi.org\/10.1016\/j.cosrev.2022.100471","journal-title":"Comput Sci Rev"},{"issue":"3","key":"7_CR13","doi-asserted-by":"publisher","first-page":"21","DOI":"10.14738\/tmlai.83.8219","volume":"8","author":"J Blackledge","year":"2020","unstructured":"Blackledge J, Mosola N (2020) Applications of artificial intelligence to cryptography. Trans Mach Learn Artif Intell 8(3):21\u201360. https:\/\/doi.org\/10.14738\/tmlai.83.8219","journal-title":"Trans Mach Learn Artif Intell"},{"issue":"2","key":"7_CR14","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1137\/0215025","volume":"15","author":"L Blum","year":"1986","unstructured":"Blum L, Blum M, Shub M (1986) A simple unpredictable pseudo-random number generator. SIAM J Comput 15(2):364\u2013383. https:\/\/doi.org\/10.1137\/0215025","journal-title":"SIAM J Comput"},{"key":"7_CR15","unstructured":"Brown RG (2024) Dieharder: a random number test suite version 3.31.1. [Online]. https:\/\/webhome.phy.duke.edu\/~rgb\/General\/dieharder.php\/"},{"key":"7_CR16","unstructured":"Brown TB, Mann B, Ryder N et\u00a0al (2020) Language models are few-shot learners. In: Proceedings of the 34th international conference on neural information processing systems. Curran Associates Inc., Red Hook, NY, USA, pp 1877\u20131901. https:\/\/dl.acm.org\/doi\/abs\/10.5555\/3495724.3495883"},{"key":"7_CR17","doi-asserted-by":"publisher","unstructured":"Cho K, van Merri\u00ebnboer B, Gulcehre C et\u00a0al (2014) Learning phrase representations using rnn encoder\u2013decoder for statistical machine translation. In: Moschitti A, Pang B, Daelemans W (eds) Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). Association for Computational Linguistics, Doha, Qatar, pp 1724\u20131734. https:\/\/doi.org\/10.3115\/v1\/D14-1179","DOI":"10.3115\/v1\/D14-1179"},{"issue":"5","key":"7_CR18","doi-asserted-by":"publisher","first-page":"1306","DOI":"10.3390\/s18051306","volume":"18","author":"M Coutinho","year":"2018","unstructured":"Coutinho M, de Oliveira Albuquerque R, Borges F et al (2018) Learning perfectly secure cryptography to protect communications with adversarial neural cryptography. Sensors 18(5):1306. https:\/\/doi.org\/10.3390\/s18051306","journal-title":"Sensors"},{"key":"7_CR19","doi-asserted-by":"publisher","unstructured":"De\u00a0Bernardi M, Khouzani MHR, Malacaria P (2019) Pseudo-random number generation using generative adversarial networks. In: ECML PKDD 2018 workshops, vol 11329. Springer International Publishing, Cham, pp 191\u2013200. https:\/\/doi.org\/10.1007\/978-3-030-13453-2_15","DOI":"10.1007\/978-3-030-13453-2_15"},{"key":"7_CR20","doi-asserted-by":"publisher","unstructured":"Desai VV, Deshmukh VB, Rao DH (2011) Pseudo random number generator using elman neural network. In: 2011 IEEE recent advances in intelligent computational systems. IEEE, pp 251\u2013254. https:\/\/doi.org\/10.1109\/RAICS.2011.6069312","DOI":"10.1109\/RAICS.2011.6069312"},{"issue":"10","key":"7_CR21","first-page":"165","volume":"2","author":"V Desai","year":"2012","unstructured":"Desai V, Patil RT, Deshmukh V et al (2012) Pseudo random number generator using time delay neural network. World J Sci Technol 2(10):165\u2013169","journal-title":"World J Sci Technol"},{"key":"7_CR22","doi-asserted-by":"publisher","unstructured":"Devlin J, Chang MW, Lee K et\u00a0al (2019) Bert: pre-training of deep bidirectional transformers for language understanding. In: Proceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, Volume 1 (Long and Short Papers). Association for Computational Linguistics, pp 4171\u20134186. https:\/\/doi.org\/10.18653\/v1\/N19-1423","DOI":"10.18653\/v1\/N19-1423"},{"issue":"3","key":"7_CR23","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10462-011-9270-6","volume":"39","author":"S Ding","year":"2013","unstructured":"Ding S, Li H, Su C et al (2013) Evolutionary artificial neural networks: A review. Artif Intell Rev 39(3):251\u2013260. https:\/\/doi.org\/10.1007\/s10462-011-9270-6","journal-title":"Artif Intell Rev"},{"issue":"11","key":"7_CR24","doi-asserted-by":"publisher","first-page":"4999","DOI":"10.1109\/TNNLS.2019.2955165","volume":"31","author":"T Dong","year":"2020","unstructured":"Dong T, Huang T (2020) Neural cryptography based on complex-valued neural network. IEEE Trans Neural Netw Learn Syst 31(11):4999\u2013500. https:\/\/doi.org\/10.1109\/TNNLS.2019.2955165","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7_CR25","doi-asserted-by":"publisher","unstructured":"Dosovitskiy A, Beyer L, Kolesnikov A et\u00a0al (2021) An image is worth 16x16 words: transformers for image recognition at scale. https:\/\/doi.org\/10.48550\/arXiv.2010.11929. arXiv:2010.11929","DOI":"10.48550\/arXiv.2010.11929"},{"key":"7_CR26","doi-asserted-by":"publisher","unstructured":"Duan X, Han Y, Wang C et\u00a0al (2021) Optimization of encrypted communication length based on generative adversarial network. In: 2021 IEEE 4th international conference on Big Data and Artificial Intelligence (BDAI). IEEE, pp 165\u2013170. https:\/\/doi.org\/10.1109\/BDAI52447.2021.9515301","DOI":"10.1109\/BDAI52447.2021.9515301"},{"key":"7_CR27","unstructured":"Elaine\u00a0Barker JK (2015) Recommendation for random number generation using deterministic random bit generators (Revised). National Institute of Standards and Technology (NIST). https:\/\/nvlpubs.nist.gov\/nistpubs\/SpecialPublications\/NIST.SP.800-90Ar1.pdf"},{"issue":"2","key":"7_CR28","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1207\/s15516709cog1402_1","volume":"14","author":"JL Elman","year":"1990","unstructured":"Elman JL (1990) Finding structure in time. Cogn Sci 14(2):179\u2013211. https:\/\/doi.org\/10.1207\/s15516709cog1402_1","journal-title":"Cogn Sci"},{"key":"7_CR29","doi-asserted-by":"publisher","unstructured":"Faure E, Fedorov E, Myronets I et\u00a0al (2022) Method for generating pseudorandom sequence of permutations based on linear congruential generator. In: CMIS, pp 175\u2013185.https:\/\/doi.org\/10.32782\/cmis\/3137-15","DOI":"10.32782\/cmis\/3137-15"},{"key":"7_CR30","doi-asserted-by":"publisher","unstructured":"Goodfellow IJ, Pouget-Abadie J, Mirza M et\u00a0al (2014) Generative adversarial network. https:\/\/doi.org\/10.48550\/arXiv.1406.2661. arXiv:1406.2661","DOI":"10.48550\/arXiv.1406.2661"},{"issue":"11","key":"7_CR31","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1145\/3422622","volume":"63","author":"I Goodfellow","year":"2020","unstructured":"Goodfellow I, Pouget-Abadie J, Mirza M et al (2020) Generative adversarial networks. Commun ACM 63(11):139\u2013144. https:\/\/doi.org\/10.1145\/3422622","journal-title":"Commun ACM"},{"issue":"1","key":"7_CR32","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1109\/TEVC.2002.806856","volume":"7","author":"SU Guan","year":"2003","unstructured":"Guan SU, Zhang S (2003) An evolutionary approach to the design of controllable cellular automata structure for random number generation. IEEE Trans Evol Comput 7(1):23\u201336. https:\/\/doi.org\/10.1109\/TEVC.2002.806856","journal-title":"IEEE Trans Evol Comput"},{"key":"7_CR33","doi-asserted-by":"publisher","unstructured":"Gulati A, Qin J, Chiu CC et\u00a0al (2020) Conformer: convolution-augmented transformer for speech recognitio. https:\/\/doi.org\/10.48550\/arXiv.2005.08100. arXiv:2005.08100","DOI":"10.48550\/arXiv.2005.08100"},{"key":"7_CR34","unstructured":"Gulrajani I, Ahmed F, Arjovsky M et\u00a0al (2017) Improved training of wasserstein gans. In: Proceedings of the 31st international conference on neural information processing systems, pp 5769\u20135779. https:\/\/dl.acm.org\/doi\/10.5555\/3295222.3295327"},{"key":"7_CR35","doi-asserted-by":"publisher","unstructured":"Hameed SM, Ali LMM (2018) Utilizing hopfield neural network for pseudo-random number generator. In: 2018 IEEE\/ACS 15th international conference on computer systems and applications (AICCSA). IEEE, Aqaba, pp 1\u20135. https:\/\/doi.org\/10.1109\/AICCSA.2018.8612890","DOI":"10.1109\/AICCSA.2018.8612890"},{"key":"7_CR36","unstructured":"Han Y, Li Y, Li Z (2021) A key exchange optimization scheme based on tree parity machine. J Electron Inf Technol 43(8):2140\u20132148. https:\/\/jeit.ac.cn\/en\/article\/doi\/10.11999\/JEIT200633"},{"key":"7_CR37","doi-asserted-by":"publisher","unstructured":"Haykin S (1998) Neural networks: a comprehensive foundation, 2nd edn. Prentice Hall PTR, US. https:\/\/doi.org\/10.5555\/521706","DOI":"10.5555\/521706"},{"issue":"8","key":"7_CR38","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735\u2013178. https:\/\/doi.org\/10.1162\/neco.1997.9.8.1735","journal-title":"Neural Comput"},{"key":"7_CR39","doi-asserted-by":"publisher","unstructured":"Hopfield JJ (1986) Neural networks and physical systems with emergent collective computational abilities. In: World scientific lecture notes in physics. World Scientific, pp 411\u2013415. https:\/\/doi.org\/10.1073\/pnas.79.8.2554","DOI":"10.1073\/pnas.79.8.2554"},{"issue":"5","key":"7_CR40","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","volume":"2","author":"K Hornik","year":"1989","unstructured":"Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359\u2013366. https:\/\/doi.org\/10.1016\/0893-6080(89)90020-8","journal-title":"Neural Netw"},{"issue":"12","key":"7_CR41","doi-asserted-by":"publisher","first-page":"656","DOI":"10.3390\/e19120656","volume":"19","author":"C Huang","year":"2017","unstructured":"Huang C, Kairouz P, Chen X et al (2017) Context-aware generative adversarial privacy. Entropy 19(12):656. https:\/\/doi.org\/10.3390\/e19120656","journal-title":"Entropy"},{"key":"7_CR42","doi-asserted-by":"publisher","unstructured":"Jeong YS, Oh K, Cho CK et\u00a0al (2018) Pseudo random number generation using lstms and irrational numbers. In: 2018 IEEE international conference on big data and smart computing (BigComp). IEEE, Shanghai, pp 541\u2013544. https:\/\/doi.org\/10.1109\/BigComp.2018.00091","DOI":"10.1109\/BigComp.2018.00091"},{"issue":"10","key":"7_CR43","doi-asserted-by":"publisher","first-page":"8324","DOI":"10.1007\/s11227-020-03229-7","volume":"76","author":"YS Jeong","year":"2020","unstructured":"Jeong YS, Oh KJ, Cho CK et al (2020) Pseudo-random number generation using lstms. J Supercomput 76(10):8324\u20138342. https:\/\/doi.org\/10.1007\/s11227-020-03229-7","journal-title":"J Supercomput"},{"issue":"1","key":"7_CR44","doi-asserted-by":"publisher","first-page":"6680782","DOI":"10.1155\/2021\/6680782","volume":"2021","author":"S Jeong","year":"2021","unstructured":"Jeong S, Park C, Hong D et al (2021) Neural cryptography based on generalized tree parity machine for real-life systems. Secur Commun Netw 2021(1):6680782. https:\/\/doi.org\/10.1155\/2021\/6680782","journal-title":"Secur Commun Netw"},{"key":"7_CR45","unstructured":"Jordan MI (1990) Attractor dynamics and parallelism in a connectionist sequential machine. In: Artificial neural networks: concept learning. IEEE Press, pp 112\u2013127. https:\/\/dl.acm.org\/doi\/abs\/10.5555\/104134.104148"},{"issue":"1","key":"7_CR46","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1209\/epl\/i2002-00552-9","volume":"57","author":"I Kanter","year":"2002","unstructured":"Kanter I, Kinzel W, Kanter E (2002) Secure exchange of information by synchronization of neuralnetworks. Europhys Lett 57(1):141. https:\/\/doi.org\/10.1209\/epl\/i2002-00552-9","journal-title":"Europhys Lett"},{"key":"7_CR47","doi-asserted-by":"publisher","unstructured":"Katti RS, Kavasseri RG (2008) Secure pseudo-random bit sequence generation using coupled linear congruential generators. In: 2008 IEEE International Symposium on Circuits and Systems (ISCAS), pp 2929\u20132932. https:\/\/doi.org\/10.1109\/ISCAS.2008.4542071","DOI":"10.1109\/ISCAS.2008.4542071"},{"key":"7_CR48","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010756","author":"J Katz","year":"2007","unstructured":"Katz J, Lindell Y (2007) Introduction to modern cryptography: principles and protocols. Chapman and Hall\/CRC, New York. https:\/\/doi.org\/10.1201\/9781420010756","journal-title":"Chapman and Hall\/CRC, New York."},{"key":"7_CR49","doi-asserted-by":"publisher","first-page":"83092","DOI":"10.1109\/access.2021.3085861","volume":"9","author":"G Kim","year":"2021","unstructured":"Kim G, Kim H, Heo Y et al (2021a) Generating cryptographic s-boxes using the reinforcement learning. IEEE Access 9:83092\u201383104. https:\/\/doi.org\/10.1109\/access.2021.3085861","journal-title":"IEEE Access"},{"key":"7_CR50","doi-asserted-by":"publisher","unstructured":"Kim H, Kwon Y, Sim M et\u00a0al (2021b) Generative adversarial networks-based pseudo-random number generator for embedded processors. In: Information security and cryptology \u2013 ICISC 2020. Springer, Cham, pp 215\u2013234. https:\/\/doi.org\/10.1007\/978-3-030-68890-5_12","DOI":"10.1007\/978-3-030-68890-5_12"},{"key":"7_CR51","doi-asserted-by":"publisher","unstructured":"Kinzel W, Kanter I (2002) Interacting neural networks and cryptography. In: Kramer B (ed) Advances in solid state physics, vol 42. Springer Berlin Heidelberg, pp 383\u2013391.https:\/\/doi.org\/10.1007\/3-540-45618-X_30","DOI":"10.1007\/3-540-45618-X_30"},{"key":"7_CR52","doi-asserted-by":"publisher","unstructured":"Klimov A, Mityagin A, Shamir A (2002) Analysis of neural cryptography. In: Zheng Y (ed) Advances in cryptology \u2014 ASIACRYPT 2002. Springer, pp 288\u2013298.https:\/\/doi.org\/10.1007\/3-540-36178-2_18","DOI":"10.1007\/3-540-36178-2_18"},{"key":"7_CR53","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127423500670","author":"K Kouba\u00e2","year":"2023","unstructured":"Kouba\u00e2 K, Derbel N (2023) Dna image encryption scheme based on a chaotic lstm pseudo-random number generator. Int J Bifurc Chaos. https:\/\/doi.org\/10.1142\/S0218127423500670","journal-title":"Int J Bifurc Chaos"},{"key":"7_CR54","doi-asserted-by":"publisher","unstructured":"Lamenca-Martinez C, Hernandez-Castro JC, Estevez-Tapiador JM et\u00a0al (2006) Lamar: a new pseudorandom number generator evolvedby meansof genetic programming. In: Parallel problem solvingfrom nature- PPSN IX. Springer, pp 850\u2013859. https:\/\/doi.org\/10.1007\/11844297_86","DOI":"10.1007\/11844297_86"},{"key":"7_CR55","doi-asserted-by":"publisher","unstructured":"Lecca C, Zegarra A, Santisteban J (2023) Random number generator based on hopfield neural network with xorshift and genetic algorithms. In: Mexican international conference on artificial intelligence, Springer, pp 283\u2013295.https:\/\/doi.org\/10.1007\/978-3-031-47765-2_21","DOI":"10.1007\/978-3-031-47765-2_21"},{"issue":"11","key":"7_CR56","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y Lecun","year":"1998","unstructured":"Lecun Y, Bottou L, Bengio Y et al (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278\u20132324. https:\/\/doi.org\/10.1109\/5.726791","journal-title":"Proc IEEE"},{"key":"7_CR57","doi-asserted-by":"publisher","unstructured":"L\u2019Ecuyer P (2012) Random number generation. In: Gentle JE, H\u00e4rdle WK, Mori Y (eds) Handbook of computational statistics: concepts and methods. Springer, Berlin, Heidelberg, p 35\u201371. https:\/\/doi.org\/10.1007\/978-3-642-21551-3_3","DOI":"10.1007\/978-3-642-21551-3_3"},{"issue":"3","key":"7_CR58","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1145\/321765.321777","volume":"20","author":"TG Lewis","year":"1973","unstructured":"Lewis TG, Payne WH (1973) Generalized feedback shift register pseudorandom number algorithm. J ACM 20(3):456\u2013468. https:\/\/doi.org\/10.1145\/321765.321777","journal-title":"J ACM"},{"key":"7_CR59","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.neucom.2020.08.041","volume":"415","author":"Z Li","year":"2020","unstructured":"Li Z, Yang X, Shen K et al (2020) Information encryption communication system based on the adversarial networks foundation. Neurocomputing 415:347\u2013357. https:\/\/doi.org\/10.1016\/j.neucom.2020.08.041","journal-title":"Neurocomputing"},{"issue":"16\u201318","key":"7_CR60","doi-asserted-by":"publisher","first-page":"2346","DOI":"10.1016\/j.neucom.2006.04.003","volume":"69","author":"S Lian","year":"2006","unstructured":"Lian S, Sun J, Wang Z (2006) Secure hash function based on neural network. Neurocomputing 69(16\u201318):2346\u20132350. https:\/\/doi.org\/10.1016\/j.neucom.2006.04.003","journal-title":"Neurocomputing"},{"issue":"12","key":"7_CR61","doi-asserted-by":"publisher","first-page":"4948","DOI":"10.1109\/TCAD.2023.3287760","volume":"42","author":"H Lin","year":"2023","unstructured":"Lin H, Wang C, Yu F et al (2023) A triple-memristor hopfield neural network with space multistructure attractors and space initial-offset behaviors. IEEE Trans Comput Aided Des Integr Circuits Syst 42(12):4948\u20134958. https:\/\/doi.org\/10.1109\/TCAD.2023.3287760","journal-title":"IEEE Trans Comput Aided Des Integr Circuits Syst"},{"issue":"18","key":"7_CR62","doi-asserted-by":"publisher","first-page":"27445","DOI":"10.1007\/s11042-021-10979-w","volume":"80","author":"Z Man","year":"2021","unstructured":"Man Z, Li J, Di X et al (2021) A novel image encryption algorithm based on least squares generative adversarial network random number generator. Multimed Tools Appl 80(18):27445\u201327469. https:\/\/doi.org\/10.1007\/s11042-021-10979-w","journal-title":"Multimed Tools Appl"},{"key":"7_CR63","doi-asserted-by":"publisher","unstructured":"Manzoni L, Mariot L (2018) Cellular automata pseudo-random number generatorsand their resistanceto asynchrony. In: Cellular automata. Springer International Publishing, pp 428\u2013437. https:\/\/doi.org\/10.1007\/978-3-319-99813-8_39","DOI":"10.1007\/978-3-319-99813-8_39"},{"key":"7_CR64","doi-asserted-by":"publisher","unstructured":"Mariot L, Jakobovic D, B\u00e4ck T et\u00a0al (2022) Artificial intelligence for the design of symmetric cryptographic primitives. In: Security and artificial intelligence: a crossdisciplinary approach. Springer International Publishing, pp 3\u201324.https:\/\/doi.org\/10.1007\/978-3-030-98795-4_1","DOI":"10.1007\/978-3-030-98795-4_1"},{"key":"7_CR65","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v008.i14","volume":"8","author":"G Marsaglia","year":"2003","unstructured":"Marsaglia G (2003) Xorshift rngs. J Stat Softw 8:1\u20136. https:\/\/doi.org\/10.18637\/jss.v008.i14","journal-title":"J Stat Softw"},{"issue":"1","key":"7_CR66","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1145\/272991.272995","volume":"8","author":"M Matsumoto","year":"1998","unstructured":"Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8(1):3\u201330. https:\/\/doi.org\/10.1145\/272991.272995","journal-title":"ACM Trans Model Comput Simul"},{"key":"7_CR67","doi-asserted-by":"publisher","first-page":"124727","DOI":"10.1109\/ACCESS.2021.3109635","volume":"9","author":"I Meraouche","year":"2021","unstructured":"Meraouche I, Dutta S, Tan H et al (2021) Neural networks-based cryptography: a survey. IEEE Access 9:124727\u2013124740. https:\/\/doi.org\/10.1109\/ACCESS.2021.3109635","journal-title":"IEEE Access"},{"key":"7_CR68","doi-asserted-by":"publisher","first-page":"106220","DOI":"10.1016\/j.engappai.2023.106220","volume":"123","author":"I Meraouche","year":"2023","unstructured":"Meraouche I, Dutta S, Tan H et al (2023) Learning asymmetric encryption using adversarial neural networks. Eng Appl Artif Intell 123:106220. https:\/\/doi.org\/10.1016\/j.engappai.2023.106220","journal-title":"Eng Appl Artif Intell"},{"key":"7_CR69","doi-asserted-by":"publisher","unstructured":"Meraouche I, Dutta S, Sakurai K (2020) 3-party adversarial cryptography. In: Advances in internet, data and web technologies. Springer, Cham, pp 247\u2013258. https:\/\/doi.org\/10.1007\/978-3-030-39746-3_27","DOI":"10.1007\/978-3-030-39746-3_27"},{"key":"7_CR70","doi-asserted-by":"publisher","unstructured":"Millan W, Burnett L, Carter G et\u00a0al (1999) Evolutionary heuristicsfor finding cryptographically strong s-boxes. In: Information and communication security, vol 1726. Springer Berlin Heidelberg, pp 263\u2013274. https:\/\/doi.org\/10.1007\/978-3-540-47942-0_22","DOI":"10.1007\/978-3-540-47942-0_22"},{"key":"7_CR71","doi-asserted-by":"publisher","unstructured":"Millan W, Clark A, Dawson E (1997) An effective genetic algorithm for finding highly nonlinear boolean functions. In: Information and communications security. Springer, pp 149\u2013158. https:\/\/doi.org\/10.1007\/BFb0028471","DOI":"10.1007\/BFb0028471"},{"key":"7_CR72","doi-asserted-by":"publisher","unstructured":"Millan W, Clark A, Dawson E (1998) Heuristic design of cryptographically strong balanced booleanfunctions. In: Advances in cryptology\u2014 EUROCRYPT\u201998. Springer, pp 489\u2013499. https:\/\/doi.org\/10.1007\/BFb0054148","DOI":"10.1007\/BFb0054148"},{"issue":"7540","key":"7_CR73","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1038\/nature14236","volume":"518","author":"V Mnih","year":"2015","unstructured":"Mnih V, Kavukcuoglu K, Silver D et al (2015) Human-level control through deep reinforcement learning. Nature 518(7540):529\u2013533. https:\/\/doi.org\/10.1038\/nature14236","journal-title":"Nature"},{"issue":"3","key":"7_CR74","doi-asserted-by":"publisher","first-page":"39","DOI":"10.3390\/cryptography7030039","volume":"7","author":"A Nitaj","year":"2023","unstructured":"Nitaj A, Rachidi T (2023) Applications of neural network-based AI in cryptography. Cryptography 7(3):39. https:\/\/doi.org\/10.3390\/cryptography7030039","journal-title":"Cryptography"},{"key":"7_CR75","doi-asserted-by":"publisher","unstructured":"Nordin FH, Nagi FH (2008) Layer-recurrent network in identifying a nonlinear system. In: 2008 International conference on control, automation and systems, pp 387\u2013391. https:\/\/doi.org\/10.1109\/ICCAS.2008.4694674","DOI":"10.1109\/ICCAS.2008.4694674"},{"key":"7_CR76","doi-asserted-by":"publisher","unstructured":"Noughabi MNA, Sadeghiyan B (2010) Design of s-boxes based on neural networks. In: 2010 International conference on electronics and information engineering, pp 172\u2013178. https:\/\/doi.org\/10.1109\/ICEIE.2010.5559741","DOI":"10.1109\/ICEIE.2010.5559741"},{"key":"7_CR77","doi-asserted-by":"publisher","unstructured":"Oak R, Rahalkar C, Gujar D (2019) Poster: using generative adversarial networks for secure pseudorandom number generation. In: Proceedings of the 2019 ACM SIGSAC conference on computer and communications security. ACM, London United Kingdom, pp 2597\u20132599. https:\/\/doi.org\/10.1145\/3319535.3363265","DOI":"10.1145\/3319535.3363265"},{"issue":"6","key":"7_CR78","doi-asserted-by":"publisher","first-page":"e0287025","DOI":"10.1371\/journal.pone.0287025","volume":"18","author":"K Okada","year":"2023","unstructured":"Okada K, Endo K, Yasuoka K et al (2023) Learned pseudo-random number generator: Wgan-gp for generating statistically robust random numbers. PLoS ONE 18(6):e0287025. https:\/\/doi.org\/10.1371\/journal.pone.0287025","journal-title":"PLoS ONE"},{"issue":"10","key":"7_CR79","doi-asserted-by":"publisher","first-page":"45","DOI":"10.5815\/ijcnis.2019.10.06","volume":"11","author":"SK Pal","year":"2019","unstructured":"Pal SK, Mishra S (2019) An tpm based approach for generation of secret key. Int J Comput Netw Inf Secur 11(10):45\u201350. https:\/\/doi.org\/10.5815\/ijcnis.2019.10.06","journal-title":"Int J Comput Netw Inf Secur"},{"issue":"7","key":"7_CR80","doi-asserted-by":"publisher","first-page":"3377","DOI":"10.3390\/app12073377","volume":"12","author":"S Park","year":"2022","unstructured":"Park S, Kim K, Kim K et al (2022) Dynamical pseudo-random number generator using reinforcement learning. Appl Sci 12(7):3377. https:\/\/doi.org\/10.3390\/app12073377","journal-title":"Appl Sci"},{"key":"7_CR81","doi-asserted-by":"publisher","first-page":"1122","DOI":"10.1016\/j.procs.2020.03.057","volume":"170","author":"L Pasqualini","year":"2020","unstructured":"Pasqualini L, Parton M (2020a) Pseudo random number generation: a reinforcement learning approach. Procedia Comput Sci 170:1122\u20131127. https:\/\/doi.org\/10.1016\/j.procs.2020.03.057","journal-title":"Procedia Comput Sci"},{"issue":"11","key":"7_CR82","doi-asserted-by":"publisher","first-page":"307","DOI":"10.3390\/a13110307","volume":"13","author":"L Pasqualini","year":"2020","unstructured":"Pasqualini L, Parton M (2020b) Pseudo random number generation through reinforcement learning and recurrent neural networks. Algorithms 13(11):307. https:\/\/doi.org\/10.3390\/a13110307","journal-title":"Algorithms"},{"issue":"4","key":"7_CR83","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1162\/EVCO_a_00191","volume":"24","author":"S Picek","year":"2016","unstructured":"Picek S, Cupic M, Rotim L (2016a) A new cost functionfor evolutionof s-boxes. Evol Comput 24(4):695\u2013718. https:\/\/doi.org\/10.1162\/EVCO_a_00191","journal-title":"Evol Comput"},{"key":"7_CR84","doi-asserted-by":"publisher","unstructured":"Picek S, Mariot L, Yang B et\u00a0al (2017) Design of s-boxes defined with cellular automata rules. In: Proceedings of the computing frontiers conference. Association for Computing Machinery, CF\u201917, pp 409\u2013414.https:\/\/doi.org\/10.1145\/3075564.3079069","DOI":"10.1145\/3075564.3079069"},{"key":"7_CR85","doi-asserted-by":"publisher","unstructured":"Picek S, Miller JF, Jakobovic D et\u00a0al (2015) Cartesian genetic programming approach for generating substitution boxes of different sizes. In: Proceedings of the companion publicationof the 2015 annual conferenceon geneticand evolutionary computation. Association for Computing Machinery, GECCO Companion\u201915, pp 1457\u20131458. https:\/\/doi.org\/10.1145\/2739482.2764698","DOI":"10.1145\/2739482.2764698"},{"key":"7_CR86","doi-asserted-by":"publisher","unstructured":"Picek S, Sisejkovic D, Rozic V et\u00a0al (2016b) Evolving cryptographic pseudorandom number generators. In: Parallel problem solvingfrom nature\u2013 PPSN XIV. Springer International Publishing, pp 613\u2013622https:\/\/doi.org\/10.1007\/978-3-319-45823-6_57","DOI":"10.1007\/978-3-319-45823-6_57"},{"key":"7_CR87","unstructured":"Radford A, Metz L, Chintala S (2015) Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv e-prints"},{"key":"7_CR88","unstructured":"Radford A, Wu J, Child R et\u00a0al (2019) Language models are unsupervised multitask learners. OpenAI Blog. https:\/\/cdn.openai.com\/better-language-models\/language_models_are_unsupervised_multitask_learners.pdf"},{"key":"7_CR89","doi-asserted-by":"crossref","unstructured":"Rivest RL (1991) Cryptography and machine learning. In: International conference on the theory and application of cryptology, Springer, pp 427\u2013439","DOI":"10.1007\/3-540-57332-1_36"},{"key":"7_CR90","unstructured":"Rosulek M (2021) The joy of cryptography. [Online]. https:\/\/joyofcryptography.com\/"},{"issue":"01","key":"7_CR91","doi-asserted-by":"publisher","first-page":"P01009","DOI":"10.1088\/1742-5468\/2005\/01\/P01009","volume":"2005","author":"A Ruttor","year":"2005","unstructured":"Ruttor A, Kinzel W, Kanter I (2005) Neural cryptography with queries. J Stat Mech: Theory Exp 2005(01):P01009. https:\/\/doi.org\/10.1088\/1742-5468\/2005\/01\/P01009","journal-title":"J Stat Mech: Theory Exp"},{"issue":"1","key":"7_CR92","doi-asserted-by":"publisher","first-page":"8214681","DOI":"10.1155\/2019\/8214681","volume":"2019","author":"\u00c9 Salguero Dorokhin","year":"2019","unstructured":"Salguero Dorokhin \u00c9, Fuertes W, Lascano E (2019) On the development of an optimal structure of tree parity machine for the establishment of a cryptographic key. Secur Commun Netw 2019(1):8214681. https:\/\/doi.org\/10.1155\/2019\/8214681","journal-title":"Secur Commun Netw"},{"issue":"1","key":"7_CR93","doi-asserted-by":"publisher","first-page":"44","DOI":"10.11591\/ijai.v8.i1.pp44-53","volume":"8","author":"A Sarkar","year":"2019","unstructured":"Sarkar A (2019) Multilayer neural network synchronized secured session key based encryption in wireless communication. IAES Int J Artif Intell (IJ-AI) 8(1):44\u201353. https:\/\/doi.org\/10.11591\/ijai.v8.i1.pp44-53","journal-title":"IAES Int J Artif Intell (IJ-AI)"},{"key":"7_CR94","unstructured":"Schindler W (1999) Functionality classes and evaluation methodology for deterministic random number generators. Anwendungshinweise and Interpretation (AIS). https:\/\/www.bsi.bund.de\/SharedDocs\/Downloads\/DE\/BSI\/Zertifizierung\/Interpretationen\/AIS_20_Functionality_Classes_Evaluation_Methodology_DRNG_e.pdf?__blob=publicationFile\/"},{"key":"7_CR95","doi-asserted-by":"publisher","unstructured":"Schmidhuber J (2020) Reinforcement learning upside down: don\u2019t predict rewards \u2013 just map them to action. https:\/\/doi.org\/10.48550\/arXiv.1912.02875. arXiv:1912.02875","DOI":"10.48550\/arXiv.1912.02875"},{"issue":"6","key":"7_CR96","doi-asserted-by":"publisher","first-page":"066137","DOI":"10.1103\/PhysRevE.69.066137","volume":"69","author":"LN Shacham","year":"2004","unstructured":"Shacham LN, Klein E, Mislovaty R et al (2004) Cooperating attackers in neural cryptography. Phys Rev E 69(6):066137. https:\/\/doi.org\/10.1103\/PhysRevE.69.066137","journal-title":"Phys Rev E"},{"issue":"4","key":"7_CR97","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","volume":"28","author":"CE Shannon","year":"1949","unstructured":"Shannon CE (1949) Communication theory of secrecy systems. Bell Syst Tech J 28(4):656\u2013715","journal-title":"Bell Syst Tech J"},{"key":"7_CR98","unstructured":"State Cryptography Administration China (2021) Randomness test specification, cryptography industry standard of the p.r. china gm\/t 0005-2021. Technical standard, China Standard Press, [Online]. https:\/\/www.chinesestandard.net\/pdf\/BOOK.aspx\/GMT0005-2021"},{"issue":"1","key":"7_CR99","doi-asserted-by":"publisher","first-page":"1423","DOI":"10.1109\/TNNLS.2022.3180197","volume":"35","author":"M Stypi\u0144ski","year":"2024","unstructured":"Stypi\u0144ski M, Niemiec M (2024a) Synchronization of tree parity machines using nonbinary input vectors. IEEE Trans Neural Netw Learn Syst 35(1):1423\u20131429. https:\/\/doi.org\/10.1109\/TNNLS.2022.3180197","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7_CR100","doi-asserted-by":"publisher","unstructured":"Stypi\u0144ski M, Niemiec M (2024b) Weight equalization algorithm for tree parity machine. https:\/\/doi.org\/10.48550\/arXiv.2406.00802. arXiv:2406.00802","DOI":"10.48550\/arXiv.2406.00802"},{"key":"7_CR101","volume-title":"Reinforcement learning: an introduction","author":"RS Sutton","year":"2018","unstructured":"Sutton RS, Barto AG (2018) Reinforcement learning: an introduction, 2nd edn. Bradford Books, Cambridge, MA","edition":"2"},{"key":"7_CR102","doi-asserted-by":"publisher","unstructured":"Tirdad K, Sadeghian A (2010) Hopfield neural networks as pseudo random number generators. In: 2010 Annual meeting of the north american fuzzy information processing society. IEEE, Toronto, Canada, pp 1\u20136. https:\/\/doi.org\/10.1109\/NAFIPS.2010.5548182","DOI":"10.1109\/NAFIPS.2010.5548182"},{"key":"7_CR103","unstructured":"Vaswani A, Shazeer N, Parmar N et\u00a0al (2017) Attention is all you need. In: Proceedings of the 31st international conference on neural information processing systems. Curran Associates Inc., Red Hook, NY, USA, NIPS\u201917, pp 6000\u20136010. https:\/\/dl.acm.org\/doi\/10.5555\/3295222.3295349"},{"key":"7_CR104","doi-asserted-by":"publisher","first-page":"100480","DOI":"10.1016\/j.eij.2024.100480","volume":"26","author":"A Waheed","year":"2024","unstructured":"Waheed A, Subhan F, Mohd Su\u2019ud M et al (2024) Molding robust s-box design based on linear fractional transformation and multilayer perceptron: applications to multimedia security. Egyptian Inf J 26:100480. https:\/\/doi.org\/10.1016\/j.eij.2024.100480","journal-title":"Egyptian Inf J"},{"key":"7_CR105","unstructured":"Walker J (2008) Ent: a pseudorandom number sequence test program. [Online]. http:\/\/www.fourmilab.ch\/random\/"},{"key":"7_CR106","doi-asserted-by":"publisher","unstructured":"Wang Yh, Shen Zd, Zhang Hg (2006) Pseudo random number generator based on hopfield neural network. In: 2006 International conference on machine learning and cybernetics. IEEE, Dalian, China, pp 2810\u20132813.https:\/\/doi.org\/10.1109\/ICMLC.2006.259003","DOI":"10.1109\/ICMLC.2006.259003"},{"key":"7_CR107","doi-asserted-by":"publisher","unstructured":"Wang Y, Wang G, Zhang H (2010) Random number generator based on hopfield neural network and sha-2 (512). In: Advancing computing, communication, control and management, vol 56. Springer Berlin Heidelberg, Berlin, Heidelberg, p 198\u2013205. https:\/\/doi.org\/10.1007\/978-3-642-05173-9_26","DOI":"10.1007\/978-3-642-05173-9_26"},{"key":"7_CR108","doi-asserted-by":"publisher","unstructured":"Wu H (2008) The stream cipher hc-128. In: New stream cipher designs. Springer, Berlin, Heidelberg, p 39\u201347. https:\/\/doi.org\/10.1007\/978-3-540-68351-3_4","DOI":"10.1007\/978-3-540-68351-3_4"},{"key":"7_CR109","unstructured":"Wu X, Han Y, Zhang M et\u00a0al (2023a) Non-deterministic symmetric encryption communication system based on generative adversarial networks. China Communications, pp 1\u201312. http:\/\/www.cic-chinacommunications.cn\/EN\/10.23919\/JCC.ja.2022-0629"},{"key":"7_CR110","doi-asserted-by":"publisher","unstructured":"Wu X, Han Y, Zhu S et\u00a0al (2023b) Learned pseudo-random number generator based on generative adversarial networks. In: International conference on frontiers in cyber security. Springer, pp 517\u2013530.https:\/\/doi.org\/10.1007\/978-981-99-9331-4_34","DOI":"10.1007\/978-981-99-9331-4_34"},{"key":"7_CR111","doi-asserted-by":"publisher","unstructured":"Yang B, Ro\u017ei\u0107 V, Gruji\u0107 M et\u00a0al (2017) On-chip jitter measurement for true random number generators. In: 2017 Asian Hardware Oriented Security and Trust Symposium (AsianHOST), pp 91\u201396.https:\/\/doi.org\/10.1109\/AsianHOST.2017.8354001","DOI":"10.1109\/AsianHOST.2017.8354001"},{"issue":"2","key":"7_CR112","doi-asserted-by":"publisher","first-page":"177","DOI":"10.14311\/NNW.2014.24.011","volume":"24","author":"A Yayik","year":"2014","unstructured":"Yayik A, Kutlu Y (2014) Neural network based cryptography. Neural Netw World 24(2):177\u2013192. https:\/\/doi.org\/10.14311\/NNW.2014.24.011","journal-title":"Neural Netw World"},{"key":"7_CR113","doi-asserted-by":"publisher","unstructured":"Yedroudj M, Comby F, Chaumont M (2020) Steganography using a 3-player game. J Vis Commun Image Represent 72:102910. https:\/\/doi.org\/10.1016\/j.jvcir.2020.102910","DOI":"10.1016\/j.jvcir.2020.102910"},{"key":"7_CR114","doi-asserted-by":"publisher","unstructured":"Zhang X, Chen F, Chen B et\u00a0al (2015) A new scheme for implementing s-box based on neural network. In: 2015 International Conference on Computational Science and Computational Intelligence (CSCI), pp 571\u2013576. https:\/\/doi.org\/10.1109\/CSCI.2015.9","DOI":"10.1109\/CSCI.2015.9"},{"issue":"2","key":"7_CR115","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.32604\/cmc.2023.041187","volume":"76","author":"R Zhang","year":"2023","unstructured":"Zhang R, Shu R, Wei Y et al (2023) A novel s-box generation methodology based on the optimized gan model. Computers, Materials and Continua 76(2):1911\u20131927. https:\/\/doi.org\/10.32604\/cmc.2023.041187","journal-title":"Computers, Materials and Continua"},{"issue":"1","key":"7_CR116","doi-asserted-by":"publisher","first-page":"166","DOI":"10.3390\/e25010166","volume":"25","author":"W Zhao","year":"2023","unstructured":"Zhao W, Chang Z, Ma C et al (2023) A pseudorandom number generator based on the chaotic map and quantum random walks. Entropy 25(1):166. https:\/\/doi.org\/10.3390\/e25010166","journal-title":"Entropy"},{"key":"7_CR117","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.cose.2018.07.018","volume":"80","author":"L Zhou","year":"2019","unstructured":"Zhou L, Chen J, Zhang Y et al (2019) Security analysis and new models on the intelligent symmetric key encryption. Comput Secur 80:14\u201324. https:\/\/doi.org\/10.1016\/j.cose.2018.07.018","journal-title":"Comput Secur"}],"container-title":["Journal of King Saud University Computer and Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-025-00007-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44443-025-00007-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-025-00007-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T11:45:35Z","timestamp":1748605535000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44443-025-00007-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,7]]},"references-count":117,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["7"],"URL":"https:\/\/doi.org\/10.1007\/s44443-025-00007-4","relation":{},"ISSN":["1319-1578","2213-1248"],"issn-type":[{"value":"1319-1578","type":"print"},{"value":"2213-1248","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,7]]},"assertion":[{"value":"27 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"18"}}