{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T20:42:41Z","timestamp":1779914561444,"version":"3.53.1"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T00:00:00Z","timestamp":1582848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the Hindmarsh\u2013Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan\u2013Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh\u2013Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests.<\/jats:p>","DOI":"10.3390\/s20051326","type":"journal-article","created":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T03:13:28Z","timestamp":1583205208000},"page":"1326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":70,"title":["Chaotic Image Encryption Using Hopfield and Hindmarsh\u2013Rose Neurons Implemented on FPGA"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7187-4686","authenticated-orcid":false,"given":"Esteban","family":"Tlelo-Cuautle","sequence":"first","affiliation":[{"name":"Department of Electronics, INAOE, Puebla 72840, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan Daniel","family":"D\u00edaz-Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Department of Electronics, INAOE, Puebla 72840, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Astrid Maritza","family":"Gonz\u00e1lez-Zapata","sequence":"additional","affiliation":[{"name":"Department of Electronics, INAOE, Puebla 72840, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, UESTC, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Walter Daniel","family":"Le\u00f3n-Salas","sequence":"additional","affiliation":[{"name":"School of Engineering Technology, Purdue University, 401 N. Grant St., West Lafayette, IN 47907, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8682-2280","authenticated-orcid":false,"given":"Francisco V.","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Instituto de Microelectr\u00f3nica de Sevilla, CSIC and Universidad de Sevilla, 41092 Sevilla, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Omar","family":"Guill\u00e9n-Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Department of Electronics, INAOE, Puebla 72840, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0380-0233","authenticated-orcid":false,"given":"Israel","family":"Cruz-Vega","sequence":"additional","affiliation":[{"name":"Department of Electronics, INAOE, Puebla 72840, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s13319-017-0148-5","article-title":"A Survey of Image Encryption Algorithms","volume":"8","author":"Kumari","year":"2017","journal-title":"3D Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","article-title":"Neural networks and physical systems with emergent collective computational abilities","volume":"79","author":"Hopfield","year":"1982","journal-title":"Proc. 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