{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:52:31Z","timestamp":1753894351405,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T00:00:00Z","timestamp":1720483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper we analyze computational properties of the Diophantine problem\n(and its search variant) for spherical equations $\\prod_{i=1}^m z_i^{-1} c_i\nz_i = 1$ (and its variants) over the class of finite metabelian groups\n$G_{p,n}=\\mathbb{Z}_p^n \\rtimes \\mathbb{Z}_p^\\ast$, where $n\\in\\mathbb{N}$ and\n$p$ is prime. We prove that the problem of finding solutions for certain\nconstrained spherical equations is computationally hard on average (assuming\nthat some lattice approximation problem is hard in the worst case).<\/jats:p>","DOI":"10.46298\/jgcc.2024.16.1.13555","type":"journal-article","created":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T11:25:05Z","timestamp":1720524305000},"source":"Crossref","is-referenced-by-count":0,"title":["Constrained inhomogeneous spherical equations: average-case hardness"],"prefix":"10.46298","volume":"Volume 16, Issue 1","author":[{"given":"Alexander","family":"Ushakov","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,7,9]]},"container-title":["journal of Groups, complexity, cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/gcc.episciences.org\/13555\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/gcc.episciences.org\/13555\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T11:25:06Z","timestamp":1720524306000},"score":1,"resource":{"primary":{"URL":"https:\/\/gcc.episciences.org\/13555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/jgcc.2024.16.1.13555","relation":{"is-same-as":[{"id-type":"arxiv","id":"2405.03591","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2405.03591","asserted-by":"subject"}]},"ISSN":["1869-6104"],"issn-type":[{"type":"electronic","value":"1869-6104"}],"subject":[],"published":{"date-parts":[[2024,7,9]]},"article-number":"13555"}}