{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T21:11:11Z","timestamp":1779916271290,"version":"3.53.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,6,14]],"date-time":"2025-06-14T00:00:00Z","timestamp":1749859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>Among the multiple important properties that characterize strong S-boxes for symmetric cryptography and are used in their designs, this study focuses on two: the non-linearity property, a classical security metric, and the confusion coefficient variance property, a statistical proxy for side channel resistance under the Hamming weight leakage model. Given an S-box, two sets can be created: the set of affine-shifted S-boxes, where S-boxes have the same non-linearity value, and the set of Hamming weight classes, where S-boxes have the same confusion coefficient variance value. The inherent values of these two properties ensure resistance to cryptographic attacks; however, if the value of one property increases, it will imply a decrease in the value of the other property. In view of the aforementioned fact, attaining a trade-off becomes a complex undertaking. The impetus for this research stems from the following hypothesis: if an initial S-box already exhibits a trade-off, it would be advantageous to employ a method that generates new S-boxes while preserving the balance. A thorough review of the extant literature reveals the absence of any methodology that encompasses the aforementioned elements. The present paper proposes a novel methodology for generating an affine-shifted subset of S-boxes, ensuring that the resulting subset possesses the same confusion coefficient variance value. We provide insights on the optimal search strategy to optimize non-linearity and confusion coefficient variance. The proposed methodology guarantees the preservation of constant values on the designated. It is possible to incorporate these properties into a comprehensive design scheme, in which case the remaining S-box properties are to be examined. We also demonstrate that, despite the fact that this subset contains S-boxes with the theoretical resistance to side channel attacks under the Hamming weight model, the S-boxes are in different Hamming weight classes.<\/jats:p>","DOI":"10.3390\/cryptography9020045","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T06:40:27Z","timestamp":1750056027000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7064-232X","authenticated-orcid":false,"given":"Ismel","family":"Mart\u00ednez-D\u00edaz","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Lleida, Jaume II, 69, 25001 Lleida, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6104-9671","authenticated-orcid":false,"given":"Carlos Miguel","family":"Leg\u00f3n-P\u00e9rez","sequence":"additional","affiliation":[{"name":"Instituto Superior Tecnol\u00f3gico Internacional San Luis (ITSAL), Canonigo Ramos y Avenida La Prensa, Riobamba 060101, Ecuador"},{"name":"Instituto de Criptograf\u00eda, Facultad de Matem\u00e1tica y Computaci\u00f3n, Universidad de la Habana, Calle J No. 556 Entre 25 y 27, Ciudad de La Habana 10400, Cuba"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7793-896X","authenticated-orcid":false,"given":"Guillermo","family":"Sosa-G\u00f3mez","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan 45010, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,14]]},"reference":[{"key":"ref_1","unstructured":"Van Tilborg, H.C., and Jajodia, S. 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