{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:28:28Z","timestamp":1771673308660,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T00:00:00Z","timestamp":1558310400000},"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>In substitution\u2013permutation network as a cryptosystem, substitution boxes play the role of the only nonlinear part. It would be easy for adversaries to compromise the security of the system without them. 8-bit S-boxes are the most used cryptographic components. So far, cryptographers were constructing 8-bit S-boxes used in cryptographic primitives by exhaustive search of permutations of order 256. However, now for cryptographic techniques with 8-bit S-boxes as confusion layers, researchers are trying to reduce the size of S-box by working with a small unit of data. The aim is to make the techniques compact, fast and elegant. The novelty of this research is the construction of S-box on the elements of the multiplicative subgroup of the Galois field instead of the entire Galois field. The sturdiness of the proposed S-box against algebraic attacks was hashed out by employing the renowned analyses, including balance, nonlinearity, strict avalanche criterion, and approximation probabilities. Furthermore, the statistical strength of the S-box was tested by the majority logic criterion. The fallouts show that the S-box is appropriate for applications for secure data communications. The S-box was also used for watermarking of grayscale images with good outcomes.<\/jats:p>","DOI":"10.3390\/cryptography3020013","type":"journal-article","created":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T11:05:07Z","timestamp":1558350307000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["S-Box on Subgroup of Galois Field"],"prefix":"10.3390","volume":"3","author":[{"given":"Tariq","family":"Shah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan"}]},{"given":"Ayesha","family":"Qureshi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Farwa, S., Shah, T., Muhammad, N., Bibi, N., Jahangir, A., and Arshad, S. 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