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There have remained two weak points on the protocol: one is that the protocol is indistinguishable against adaptive chosen ciphertext attack (IND-CCA) in a slightly restricted sense, what they call IND-rCCA secure, and the other is that the conditions imposed on groups and hashing schemes are too strict to make the protocol practical. In this article, we propose an IND-CCA secure protocol that resolves those problems. The key idea is to employ some specific semidirect product as platform groups, so that we can achieve the exact IND-CCA security from concise conditions on groups and hashing schemes. Our protocol is not dependent on any computational assumptions on abelian subgroups.<\/jats:p>","DOI":"10.1515\/jmc-2022-0018","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T07:10:38Z","timestamp":1679382638000},"source":"Crossref","is-referenced-by-count":0,"title":["A construction of encryption protocols over some semidirect products"],"prefix":"10.1515","volume":"17","author":[{"given":"Shuji","family":"Isobe","sequence":"first","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University , Sendai 980-8576 , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eisuke","family":"Koizumi","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University , Sendai 980-8576 , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"2025120600280476053_j_jmc-2022-0018_ref_001","doi-asserted-by":"crossref","unstructured":"Anshel I, Anshel M, Fisher B, Goldfeld D. 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