{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T15:49:21Z","timestamp":1781797761167,"version":"3.54.5"},"reference-count":42,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2019,11,18]],"date-time":"2019-11-18T00:00:00Z","timestamp":1574035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61602408"],"award-info":[{"award-number":["61602408"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61572435"],"award-info":[{"award-number":["61572435"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Zhejiang Science and Technology Research","award":["2017C01091"],"award-info":[{"award-number":["2017C01091"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LY19F020005"],"award-info":[{"award-number":["LY19F020005"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LY18F020026"],"award-info":[{"award-number":["LY18F020026"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LZ18F020003"],"award-info":[{"award-number":["LZ18F020003"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LZ16F020001"],"award-info":[{"award-number":["LZ16F020001"]}]},{"name":"Shandong Province Foundation","award":["ZR2017MF035"],"award-info":[{"award-number":["ZR2017MF035"]}]},{"name":"Open Foundation of State Key Laboratory of Networking and Switching Technology","award":["SKLNST-2016-2-19"],"award-info":[{"award-number":["SKLNST-2016-2-19"]}]},{"name":"Open Foundation of State Key Laboratory of Networking and Switching Technology","award":["SKLNST-2016-1-05"],"award-info":[{"award-number":["SKLNST-2016-1-05"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>With the development of Lie theory, Lie groups have attained profound significance in several branches of Mathematics and Physics. In Lie theory, the matrix exponential plays a crucial role between Lie groups and Lie algebras. Meanwhile, as the finite analogue of Lie groups, finite groups of Lie type have potential applications in cryptography due to their unique mathematical structures. In this paper, we first put forward a novel idea of designing cryptosystems based on Lie theory. First of all, combing with discrete logarithm problem and group factorization problem, we proposed several new intractable assumptions based on the matrix exponential in finite groups of Lie type. Subsequently, in analog with Boyen\u2019s scheme (Asiacrypt 2007), we designed a public-key encryption scheme based on the non-abelian factorization problem in finite groups of Lie type. Finally, our proposal was proved to be indistinguishable against adaptively chosen-ciphertext attack in the random oracle model. It is encouraging that our scheme also has the potential to resist against Shor\u2019s quantum algorithm attack.<\/jats:p>","DOI":"10.1093\/comjnl\/bxz068","type":"journal-article","created":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T07:09:50Z","timestamp":1559372990000},"source":"Crossref","is-referenced-by-count":2,"title":["A Miniature CCA Public Key Encryption Scheme Based on Non-abelian Factorization Problem in Finite Groups of Lie Type"],"prefix":"10.1093","author":[{"given":"Haibo","family":"Hong","sequence":"first","affiliation":[{"name":"School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou, 310018 P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Licheng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876 P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou, 310018 P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianhua","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Information and Electric Engineering, Ludong University, Yantai, 264025, P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haseeb","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Computer Science, National Textile University, Faisalabad, 37610 Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guiyi","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou, 310018 P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mande","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou, 310018 P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yixian","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876 P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,11,18]]},"reference":[{"key":"2019111802201988500_ref1","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","article-title":"New directions in cryptography","volume":"22","author":"Diffie","year":"1976","journal-title":"IEEE Trans. Inf. 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