{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:07Z","timestamp":1760241127987,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,28]],"date-time":"2019-11-28T00:00:00Z","timestamp":1574899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In cryptography, the property of randomness in pseudo-random generators is very important to avoid any pattern in output sequences, to provide security against attacks, privacy and anonymity. In this article, the randomness of the family of sequences obtained from the generalized self-shrinking generator is analyzed. Moreover, the characteristics, generalities and relationship between the t-modified self-shrinking generator and the generalized self-shrinking generator are presented. We find that the t-modified self-shrunken sequences can be generated from a generalized self-shrinking generator. Then, an in-depth analysis of randomness focused on the generalized sequences by means of complete and powerful batteries of statistical tests and graphical tools is done, providing a useful vision of the behaviour of these sequences and proving that they are suitable to be used in cryptography.<\/jats:p>","DOI":"10.3390\/sym11121460","type":"journal-article","created":{"date-parts":[[2019,11,28]],"date-time":"2019-11-28T10:54:10Z","timestamp":1574938450000},"page":"1460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Randomness Analysis for the Generalized Self-Shrinking Sequences"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0225-5106","authenticated-orcid":false,"given":"Sara D.","family":"Cardell","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e3o Cient\u00edfica, UNICAMP, 13083-859 Campinas-SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1497-6456","authenticated-orcid":false,"given":"Ver\u00f3nica","family":"Requena","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Alicante, 03690 Alicante, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8261-3550","authenticated-orcid":false,"given":"Amparo","family":"F\u00faster-Sabater","sequence":"additional","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n, CSIC, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4422-5004","authenticated-orcid":false,"given":"Amalia B.","family":"Or\u00fae","sequence":"additional","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n, CSIC, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bhowmick, A., Sinha, N., Arjunan, R.V., and Kishore, B. 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[2nd ed.]."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/12\/1460\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:38:24Z","timestamp":1760189904000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/12\/1460"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,28]]},"references-count":44,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["sym11121460"],"URL":"https:\/\/doi.org\/10.3390\/sym11121460","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,11,28]]}}}