{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T12:55:45Z","timestamp":1782996945971,"version":"3.54.5"},"reference-count":26,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T00:00:00Z","timestamp":1607990400000},"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>The construction of substitute box (S-box) has always been an important research direction in cryptography. This paper proposes a new S-box generation method and advanced design based on combined chaotic system. Firstly, our paper proposes a new combined chaotic system and analyze its dynamic behavior. Next, we construct S-box by combining the generated pseudo-random sequence with the linear congruence random number generator, and the standard mapping is introduced to scramble the initial S-box. Then, the S-box optimization method based on advanced genetic algorithm is proposed in this paper. We design adaptive of S-box coding, selection operator, crossover operator and mutation operator to avoid the shortcomings of low calculation efficiency and non-convergence of optimization results in traditional genetic algorithm. Finally, through a lot of security analysis experiments and comparison with other papers, the optimized S-box has better cryptography characteristics and can resist linear attacks and differential attacks.<\/jats:p>","DOI":"10.3390\/sym12122087","type":"journal-article","created":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T21:11:02Z","timestamp":1608066662000},"page":"2087","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["A New S-Box Generation Method and Advanced Design Based on Combined Chaotic System"],"prefix":"10.3390","volume":"12","author":[{"given":"Ding","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaojun","family":"Tong","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information, Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF00203967","article-title":"The structured design of cryptographically good S-boxes","volume":"3","author":"Adams","year":"1990","journal-title":"J. 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