{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T16:46:07Z","timestamp":1764002767269,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,23]],"date-time":"2024-10-23T00:00:00Z","timestamp":1729641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004173","name":"Autonomous Metropolitan University\u2014Iztapalapa","doi-asserted-by":"publisher","award":["12704013","SIP-20240745"],"award-info":[{"award-number":["12704013","SIP-20240745"]}],"id":[{"id":"10.13039\/501100004173","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003069","name":"Instituto Polit\u00e9cnico Nacional","doi-asserted-by":"publisher","award":["12704013","SIP-20240745"],"award-info":[{"award-number":["12704013","SIP-20240745"]}],"id":[{"id":"10.13039\/501100003069","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Certain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps. In particular, we introduce a Bernoulli chaotic map that utilizes function transformations and constraints on its control parameter, covering complementary regions of the phase space. This approach allows the generation of chaotic number sequences with a wide coverage of phase space, thereby increasing the uncertainty in the number sequence generation process. Moreover, by incorporating a scaling factor and a sine function, we develop a robust chaotic map, called the Sine-Multiple Modified Bernoulli Chaotic Map (SM-MBCM), which ensures a high degree of randomness, validated through statistical mechanics analysis tools. Using the SM-MBCM, we propose a chaotic PRNG (CPRNG) and evaluate its quality through correlation coefficient analysis, key sensitivity tests, statistical and entropy analysis, key space evaluation, linear complexity analysis, and performance tests. Furthermore, we present an FPGA-based implementation scheme that leverages equivalent MBCM variants to optimize the electronic implementation process. Finally, we compare the proposed system with existing designs in terms of throughput and key space.<\/jats:p>","DOI":"10.3390\/info15110667","type":"journal-article","created":{"date-parts":[[2024,10,23]],"date-time":"2024-10-23T12:04:22Z","timestamp":1729685062000},"page":"667","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Enhanced Chaotic Pseudorandom Number Generation Using Multiple Bernoulli Maps with Field Programmable Gate Array Optimizations"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5193-2014","authenticated-orcid":false,"given":"Leonardo","family":"Palacios-Luengas","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Autonomous Metropolitan University (UAM), Iztapalapa, Mexico City 09340, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4701-1447","authenticated-orcid":false,"given":"Reyna Carolina","family":"Medina-Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Autonomous Metropolitan University (UAM), Iztapalapa, Mexico City 09340, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5355-5830","authenticated-orcid":false,"given":"Ricardo","family":"Marcel\u00edn-Jim\u00e9nez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Autonomous Metropolitan University (UAM), Iztapalapa, Mexico City 09340, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1696-3349","authenticated-orcid":false,"given":"Enrique","family":"Rodriguez-Colina","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Autonomous Metropolitan University (UAM), Iztapalapa, Mexico City 09340, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5550-8819","authenticated-orcid":false,"given":"Francisco R.","family":"Castillo-Soria","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, Autonomous University of San Luis Potos\u00ed, San Luis Potos\u00ed 78290, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6210-4097","authenticated-orcid":false,"given":"Rub\u00e9n","family":"V\u00e1zquez-Medina","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, CICATA, Quer\u00e9taro 76090, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36667","DOI":"10.1109\/ACCESS.2019.2906292","article-title":"Novel medical image encryption scheme based on chaos and DNA encoding","volume":"7","author":"Belazi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100421","DOI":"10.1016\/j.prime.2024.100421","article-title":"A relative investigation of one-dimensional chaotic maps intended for light-weight cryptography in smart grid","volume":"7","author":"Soni","year":"2024","journal-title":"e-Prime Adv. 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