On Kummer lines with full rational 2-torsion and their usage in cryptography
| dc.contributor.author | Hüseyin Hişil | |
| dc.contributor.author | Joost Renes | |
| dc.date.accessioned | 2025-10-06T17:51:12Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | A paper by Karati and Sarkar at Asiacrypt'17 has pointed out the potential for Kummer lines in genus 1 by observing that their SIMD-friendly arithmetic is competitive with the status quo. A more recent preprint explores the connection with (twisted) Edwards curves. In this article we extend this work and significantly simplify the treatment of Karati and Sarkar. We show that their Kummer line is the x-line of a Montgomery curve translated by a point of order two and exhibit a natural isomorphism to the y-line of a twisted Edwards curve. Moreover we show that the Kummer line presented by Gaudry and Lubicz can be obtained via the action of a point of order two on the y-line of an Edwards curve. The maps connecting these curves and lines are all very simple. As a result a cryptographic implementation can use the arithmetic that is optimal for its instruction set at negligible cost. © 2019 Elsevier B.V. All rights reserved. | |
| dc.identifier.doi | 10.1145/3361680 | |
| dc.identifier.issn | 15577295, 00983500 | |
| dc.identifier.issn | 0098-3500 | |
| dc.identifier.issn | 1557-7295 | |
| dc.identifier.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85076712395&doi=10.1145%2F3361680&partnerID=40&md5=79bd0131ea0d8dc7a65dc3720f6df844 | |
| dc.identifier.uri | https://gcris.yasar.edu.tr/handle/123456789/9337 | |
| dc.language.iso | English | |
| dc.publisher | Association for Computing Machinery acmhelp@acm.org | |
| dc.relation.ispartof | ACM Transactions on Mathematical Software | |
| dc.source | ACM Transactions on Mathematical Software | |
| dc.subject | Digital Signatures, Edwards Curves, Kummer Lines, Montgomery Curves, Montgomery Ladder, Computer Software, Electronic Document Identification Systems, Software Engineering, Cryptographic Implementation, Edwards Curves, Instruction Set, Kummer Lines, Montgomery, Status Quo, Cryptography | |
| dc.subject | Computer software, Electronic document identification systems, Software engineering, Cryptographic implementation, Edwards curves, Instruction set, Kummer lines, Montgomery, Status quo, Cryptography | |
| dc.title | On Kummer lines with full rational 2-torsion and their usage in cryptography | |
| dc.type | Article | |
| dspace.entity.type | Publication | |
| gdc.bip.impulseclass | C5 | |
| gdc.bip.influenceclass | C5 | |
| gdc.bip.popularityclass | C4 | |
| gdc.coar.type | text::journal::journal article | |
| gdc.collaboration.industrial | false | |
| gdc.description.endpage | 17 | |
| gdc.description.startpage | 1 | |
| gdc.description.volume | 45 | |
| gdc.identifier.openalex | W2899515059 | |
| gdc.index.type | Scopus | |
| gdc.oaire.diamondjournal | false | |
| gdc.oaire.impulse | 1.0 | |
| gdc.oaire.influence | 2.975326E-9 | |
| gdc.oaire.isgreen | true | |
| gdc.oaire.keywords | Edwards curves | |
| gdc.oaire.keywords | Montgomery curves | |
| gdc.oaire.keywords | Cryptography | |
| gdc.oaire.keywords | Kummer lines | |
| gdc.oaire.keywords | digital signatures | |
| gdc.oaire.keywords | Applications to coding theory and cryptography of arithmetic geometry | |
| gdc.oaire.keywords | Digital Security | |
| gdc.oaire.keywords | Software, source code, etc. for problems pertaining to information and communication theory | |
| gdc.oaire.keywords | Montgomery ladder | |
| gdc.oaire.popularity | 6.356244E-9 | |
| gdc.oaire.publicfunded | false | |
| gdc.oaire.sciencefields | 0202 electrical engineering, electronic engineering, information engineering | |
| gdc.oaire.sciencefields | 0102 computer and information sciences | |
| gdc.oaire.sciencefields | 02 engineering and technology | |
| gdc.oaire.sciencefields | 01 natural sciences | |
| gdc.openalex.collaboration | International | |
| gdc.openalex.fwci | 0.0 | |
| gdc.openalex.normalizedpercentile | 0.01 | |
| gdc.opencitations.count | 7 | |
| gdc.plumx.crossrefcites | 7 | |
| gdc.plumx.mendeley | 13 | |
| gdc.plumx.scopuscites | 8 | |
| person.identifier.scopus-author-id | Hişil- Hüseyin (13408968300), Renes- Joost (57190299759) | |
| project.funder.name | The second author is partially supported by the Technology Foundation STW (project 13499—TYPHOON & ASPASIA) from the Dutch government. Authors’ addresses: H. Hisil Yasar University Selcuk Yasar Campus Room U110 Engineering Faculty Computer Engineering Department Universite Caddesi No 35-37 Agacli Yol Bornova Izmir 35100 Turkey, email: huseyin.hisil@yasar.edu.tr, J. Renes Radboud University Room 3.11 Faculty of Science University of Nijmegen Postbus 9010 6500GL Nijmegen The Netherland, email: j.renes@cs.ru.nl. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise or republish to post on servers or to redistribute to lists requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. © 2019 Association for Computing Machinery. 0098-3500/2019/12-ART39 $15.00 https://doi.org/10.1145/3361680 | |
| publicationissue.issueNumber | 4 | |
| publicationvolume.volumeNumber | 45 | |
| relation.isOrgUnitOfPublication | ac5ddece-c76d-476d-ab30-e4d3029dee37 | |
| relation.isOrgUnitOfPublication.latestForDiscovery | ac5ddece-c76d-476d-ab30-e4d3029dee37 |