{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:18:29Z","timestamp":1760145509444,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T00:00:00Z","timestamp":1722988800000},"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 our paper, we explore the consequences of replacing the commutative group operation used in Lai\u2013Massey structures with a quasigroup operation. We introduce four quasigroup versions of the Lai\u2013Massey structure and prove that for quasigroups isotopic with a group G, the complexity of launching a differential attack against these variants of the Lai\u2013Massey structure is equivalent to attacking an alternative structure based on G. Then, we provide the conditions needed for correct decryption and further refine the resulting structure. The emerging structure is both intriguing and novel, and we hope that it will form the basis for future secure block ciphers based on non-commutative groups. In the case of commutative groups, we show that the resulting structure reduces to the classic Lai\u2013Massey structure.<\/jats:p>","DOI":"10.3390\/cryptography8030035","type":"journal-article","created":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T07:01:25Z","timestamp":1723100485000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Note on the Quasigroup of Lai\u2013Massey Structures"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3953-2744","authenticated-orcid":false,"given":"George","family":"Te\u015feleanu","sequence":"first","affiliation":[{"name":"Advanced Technologies Institute, 10 Dinu Vintil\u0103, 021101 Bucharest, Romania"},{"name":"Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei, 010702 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,7]]},"reference":[{"key":"ref_1","unstructured":"Vaudenay, S. 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