Jacobian coordinates on genus 2 curves
| dc.contributor.author | Hüseyin Hişil | |
| dc.contributor.author | Craig Costello | |
| dc.contributor.author | Hisil, Huseyin | |
| dc.contributor.author | Costello, Craig | |
| dc.contributor.editor | P. Sarkar , T. Iwata | |
| dc.date.accessioned | 2025-10-06T17:52:35Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | This paper presents a new projective coordinate system and new explicit algorithms which together boost the speed of arithmetic in the divisor class group of genus 2 curves. The proposed formulas generalise the use of Jacobian coordinates on elliptic curves and their application improves the speed of performing cryptographic scalar multiplications in Jacobians of genus 2 curves over prime fields by an approximate factor of 1.25x. For example on a single core of an Intel Core i7-3770M (Ivy Bridge) we show that replacing the previous best formulas with our new set improves the cost of generic scalar multiplications from 243000 to 195000 cycles and drops the cost of specialised GLV-style scalar multiplications from 166000 to 129000 cycles. © 2020 Elsevier B.V. All rights reserved. | |
| dc.description.sponsorship | Academia Sinica, International Association for Cryptologic Research (IACR), Ministry of Economic Affairs, Ministry of Education, Ministry of Science and Technology, National Sun Yat-sen University | |
| dc.identifier.doi | 10.1007/978-3-662-45611-8_18 | |
| dc.identifier.isbn | 9789819698936, 9789819698042, 9789819698110, 9789819698905, 9789819512324, 9783032026019, 9783032008909, 9783031915802, 9789819698141, 9783031984136 | |
| dc.identifier.isbn | 9783662456101 | |
| dc.identifier.isbn | 9783662456118 | |
| dc.identifier.issn | 16113349, 03029743 | |
| dc.identifier.issn | 0933-2790 | |
| dc.identifier.issn | 1432-1378 | |
| dc.identifier.issn | 1611-3349 | |
| dc.identifier.issn | 0302-9743 | |
| dc.identifier.scopus | 2-s2.0-84916618742 | |
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| dc.identifier.uri | https://gcris.yasar.edu.tr/handle/123456789/10020 | |
| dc.identifier.uri | https://doi.org/10.1007/978-3-662-45611-8_18 | |
| dc.language.iso | English | |
| dc.publisher | Springer Verlag | |
| dc.relation.ispartof | 20th International Conference on the Theory and Application of Cryptology and Information Security ASIACRYPT 2014 | |
| dc.relation.ispartofseries | Lecture Notes in Computer Science | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.source | Lecture Notes in Computer Science | |
| dc.subject | Explicit Formulas, Genus 2, Hyperelliptic Curves, Jacobian Coordinates, Scalar Multiplication, Geometry, Security Of Data, Explicit Formula, Genus 2, Hyper-elliptic Curves, Jacobian Coordinate, Scalar Multiplication, Cryptography | |
| dc.subject | Geometry, Security of data, Explicit formula, Genus 2, Hyper-elliptic curves, Jacobian coordinate, Scalar multiplication, Cryptography | |
| dc.subject | Genus 2 | |
| dc.subject | Scalar Multiplication | |
| dc.subject | Explicit Formulas | |
| dc.subject | Hyperelliptic Curves | |
| dc.subject | Jacobian Coordinates | |
| dc.title | Jacobian coordinates on genus 2 curves | |
| dc.type | Conference Object | |
| dspace.entity.type | Publication | |
| gdc.author.id | Costello, Craig/0000-0001-5423-7714 | |
| gdc.author.id | HISIL, HUSEYIN/0000-0002-1019-2187 | |
| gdc.author.scopusid | 34869404400 | |
| gdc.author.scopusid | 13408968300 | |
| gdc.author.wosid | HISIL, HUSEYIN/L-9151-2013 | |
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| gdc.description.department | ||
| gdc.description.departmenttemp | [Hisil, Huseyin] Yasar Univ, Izmir, Turkey; [Costello, Craig] Microsoft Res, Redmond, WA USA | |
| gdc.description.endpage | 600 | |
| gdc.description.publicationcategory | Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı | |
| gdc.description.startpage | 572 | |
| gdc.description.volume | 30 | |
| gdc.description.woscitationindex | Conference Proceedings Citation Index - Science | |
| gdc.identifier.openalex | W101238618 | |
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| gdc.oaire.keywords | Computational aspects of algebraic curves | |
| gdc.oaire.keywords | Jacobian coordinates | |
| gdc.oaire.keywords | genus 2 | |
| gdc.oaire.keywords | Applications to coding theory and cryptography of arithmetic geometry | |
| gdc.oaire.keywords | Hyperelliptic curves | |
| gdc.oaire.keywords | 620 | |
| gdc.oaire.keywords | 510 | |
| gdc.oaire.keywords | hyperelliptic curves | |
| gdc.oaire.keywords | explicit formulas | |
| gdc.oaire.keywords | Explicit formulas | |
| gdc.oaire.keywords | Cryptography | |
| gdc.oaire.keywords | scalar multiplication | |
| gdc.oaire.keywords | Scalar multiplication | |
| gdc.oaire.keywords | Genus 2 | |
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| gdc.oaire.sciencefields | 01 natural sciences | |
| gdc.oaire.sciencefields | 0101 mathematics | |
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| person.identifier.scopus-author-id | Hişil- Hüseyin (13408968300), Costello- Craig (34869404400) | |
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