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Ensuring resistance to these attacks is critical for the security of block ciphers. In this paper, we investigate the relationship between differential\/linear clustering effect and the number of active S-boxes in the intermediate rounds. Our findings indicate that an increase in the number of active S-boxes in the intermediate rounds does not inherently lead to an evident improvement in EDP\/ELP. Instead, the EDP\/ELP remains stable once the number of active S-boxes exceeds a certain threshold. We apply our method to four lightweight SPN primitives including GIFT-64, PRESENT, RECTANGLE and KNOT-256. For GIFT-64, RECTANGLE, and KNOT-256, we obtain improvements in the best known linear propagation results, while our other results are consistent with the best known results.<\/jats:p>","DOI":"10.1186\/s42400-025-00427-9","type":"journal-article","created":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T01:02:37Z","timestamp":1770166957000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On relationship between differential\/linear clustering effects and the number of active S-boxes in block ciphers"],"prefix":"10.1186","volume":"9","author":[{"given":"Ting","family":"Peng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wentao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingsui","family":"Weng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,4]]},"reference":[{"key":"427_CR1","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1007\/978-3-642-37682-5_26","volume-title":"Information security and cryptology\u2014ICISC 2012","author":"MA Abdelraheem","year":"2013","unstructured":"Abdelraheem MA (2013) Estimating the probabilities of low-weight differential and linear approximations on present-like ciphers. 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