{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T01:37:54Z","timestamp":1773884274963,"version":"3.50.1"},"reference-count":19,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,7,15]],"date-time":"2018-07-15T00:00:00Z","timestamp":1531612800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002701","name":"Ministry of Education","doi-asserted-by":"publisher","award":["NRF-2017R1A2B4011599"],"award-info":[{"award-number":["NRF-2017R1A2B4011599"]}],"id":[{"id":"10.13039\/501100002701","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2018,7,15]]},"abstract":"<jats:p>The isogeny-based cryptosystem is the most recent category in the field of postquantum cryptography. However, it is widely studied due to short key sizes and compatibility with the current elliptic curve primitives. The main building blocks when implementing the isogeny-based cryptosystem are isogeny computations and point operations. From isogeny construction perspective, since the cryptosystem moves along the isogeny graph, isogeny formula cannot be optimized for specific coefficients of elliptic curves. Therefore, Montgomery curves are used in the literature, due to the efficient point operation on an arbitrary elliptic curve. In this paper, we propose formulas for computing 3 and 4 isogenies on twisted Edwards curves. Additionally, we further optimize our isogeny formulas on Edwards curves and compare the computational cost of Montgomery curves. We also present the implementation results of our isogeny computations and demonstrate that isogenies on Edwards curves are as efficient as those on Montgomery curves.<\/jats:p>","DOI":"10.1155\/2018\/5747642","type":"journal-article","created":{"date-parts":[[2018,7,15]],"date-time":"2018-07-15T19:32:20Z","timestamp":1531683140000},"page":"1-11","source":"Crossref","is-referenced-by-count":13,"title":["Efficient Isogeny Computations on Twisted Edwards Curves"],"prefix":"10.1155","volume":"2018","author":[{"given":"Suhri","family":"Kim","sequence":"first","affiliation":[{"name":"Center for Information Security Technologies (CIST), Korea University, Seoul, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kisoon","family":"Yoon","sequence":"additional","affiliation":[{"name":"NSHC Inc., Uiwang, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jihoon","family":"Kwon","sequence":"additional","affiliation":[{"name":"Center for Information Security Technologies (CIST), Korea University, Seoul, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7506-4023","authenticated-orcid":true,"given":"Seokhie","family":"Hong","sequence":"additional","affiliation":[{"name":"Center for Information Security Technologies (CIST), Korea University, Seoul, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2253-492X","authenticated-orcid":true,"given":"Young-Ho","family":"Park","sequence":"additional","affiliation":[{"name":"Sejong Cyber University, Seoul, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"20","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598347011"},{"key":"11","volume":"291","year":"2006","journal-title":"IACR Cryptology ePrint Archive"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2010.4.215"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1515\/jmc-2012-0016"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25405-5_2"},{"key":"8","first-page":"679","volume-title":"Efficient compression of sidh public keys","year":"2017"},{"key":"3","volume":"672","year":"2016","journal-title":"IACR Cryptology ePrint Archive"},{"key":"16","first-page":"88","volume-title":"Neon-sidh: efficient implementation of supersingular isogeny diffie-hellman key exchange protocol on arm","year":"2016"},{"key":"10","first-page":"572","volume-title":"Efficient algorithms for supersingular isogeny diffie-hellman","year":"2016"},{"key":"12","first-page":"3","volume-title":"Identification protocols and signature schemes based on supersingular isogeny problems","year":"2017"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70972-7_9"},{"key":"4","first-page":"389","volume-title":"Twisted Edwards curves","volume":"5023","year":"2008"},{"key":"7","first-page":"303","volume-title":"A simple and compact algorithm for sidh with arbitrary degree isogenies","year":"2017"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3036"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-46588-1_17"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157015000017"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1515\/JMC.2009.022"},{"key":"23","first-page":"238","volume":"273","year":"1971","journal-title":"Comptes Rendus Mathematique Academie des Sciences, Paris"},{"key":"14","first-page":"104","volume-title":"Timing attacks on implementations of diffie-hellman, rsa, dss, and other systems","year":"1996"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/5747642.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/5747642.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/5747642.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,2]],"date-time":"2019-04-02T23:28:25Z","timestamp":1554247705000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2018\/5747642\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,15]]},"references-count":19,"alternative-id":["5747642","5747642"],"URL":"https:\/\/doi.org\/10.1155\/2018\/5747642","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"value":"1939-0114","type":"print"},{"value":"1939-0122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,15]]}}}