{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T19:37:59Z","timestamp":1772048279080,"version":"3.50.1"},"reference-count":56,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T00:00:00Z","timestamp":1543708800000},"content-version":"vor","delay-in-days":335,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>This paper proposes a novel method of constructing strong substitution\u2010boxes (S\u2010boxes) of order <jats:italic>n<\/jats:italic> (4 \u2264 <jats:italic>n<\/jats:italic> \u2264 8) based on a recent optimization algorithm known as sine\u2010cosine algorithm (SCA). The paper also proposes a new 1D chaotic map, which owns enhanced dynamics compared to conventional chaotic map, for generating initial population of S\u2010boxes and facilitating the optimization mechanism of SCA. The proposed method applies the SCA with enhanced chaotic map to explore and exploit the search space for obtaining optimized S\u2010boxes on the basis of maximization of nonlinearity as fitness function. The S\u2010box construction involves three phases such as initialization of population, optimization, and adjustment. The simulation and performance analyses are done using standard measures of nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, and autocorrelation function. The obtained experimental results are compared with some immediate optimization\u2010based and other S\u2010boxes to show the strength of proposed method for constructing bijective S\u2010boxes of salient cryptographic features.<\/jats:p>","DOI":"10.1155\/2018\/9389065","type":"journal-article","created":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T23:34:57Z","timestamp":1543793697000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":85,"title":["Sine\u2010Cosine Optimization\u2010Based Bijective Substitution\u2010Boxes Construction Using Enhanced Dynamics of Chaotic Map"],"prefix":"10.1155","volume":"2018","author":[{"given":"Amer Awad","family":"Alzaidi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4915-9325","authenticated-orcid":false,"given":"Musheer","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hussam S.","family":"Ahmed","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eesa Al","family":"Solami","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,12,2]]},"reference":[{"key":"e_1_2_9_1_2","volume-title":"An Introduction to Cryptography","author":"Mollin R. 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