{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:27Z","timestamp":1747189707273,"version":"3.40.5"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> Let [Formula: see text] be a finite set of finitary operation symbols and let [Formula: see text] be a nontrivial variety of [Formula: see text]-algebras. Assume that for some set [Formula: see text] of group operation symbols, all [Formula: see text]-algebras in [Formula: see text] are groups under the operations associated with the symbols in\u00a0[Formula: see text]. In other words, [Formula: see text] is assumed to be a nontrivial variety of expanded groups. In particular, [Formula: see text] can be a nontrivial variety of groups or rings. Our main result is that there are no post-quantum weakly pseudo-free families in [Formula: see text], even in the worst-case setting and\/or the black-box model. In this paper, we restrict ourselves to families [Formula: see text] of computational and black-box [Formula: see text]-algebras (where [Formula: see text]) such that for every [Formula: see text], each element of [Formula: see text] is represented by a unique bit string of length polynomial in the length of\u00a0d. In our main result, we use straight-line programs to represent nontrivial relations between elements of [Formula: see text]-algebras. Note that under certain conditions, this result depends on the classification of finite simple groups. Also, we define and study some types of post-quantum weak pseudo-freeness for families of computational and black-box [Formula: see text]-algebras. <\/jats:p>","DOI":"10.1142\/s0218196724500188","type":"journal-article","created":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T15:07:17Z","timestamp":1712329637000},"page":"471-490","source":"Crossref","is-referenced-by-count":0,"title":["There are no post-quantum weakly pseudo-free families in any nontrivial variety of expanded groups"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3960-3867","authenticated-orcid":false,"given":"Mikhail","family":"Anokhin","sequence":"first","affiliation":[{"name":"Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, 1-52, Leninskiye Gory, Moscow 119991, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,5,17]]},"reference":[{"key":"S0218196724500188BIB001","doi-asserted-by":"publisher","DOI":"10.1515\/gcc-2013-0003"},{"key":"S0218196724500188BIB002","doi-asserted-by":"publisher","DOI":"10.1515\/jmc-2020-0014"},{"key":"S0218196724500188BIB003","doi-asserted-by":"publisher","DOI":"10.1515\/jmc-2020-0055"},{"key":"S0218196724500188BIB005","first-page":"229","volume-title":"25th Annual Symp. 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