Jacobian Coordinates on Genus 2 Curves
| dc.contributor.author | Hüseyin Hişil | |
| dc.contributor.author | Craig Costello | |
| dc.date.accessioned | 2025-10-06T17:51:59Z | |
| dc.date.issued | 2017 | |
| 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 generalize 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 i7-3770 (Ivy Bridge) we show that replacing the previous best formulas with our new set improves the cost of generic scalar multiplications from 239000 to 192000 cycles and drops the cost of specialized GLV-style scalar multiplications from 155000 to 123000 cycles. © 2017 Elsevier B.V. All rights reserved. | |
| dc.identifier.doi | 10.1007/s00145-016-9227-7 | |
| dc.identifier.issn | 14321378, 09332790 | |
| dc.identifier.issn | 0933-2790 | |
| dc.identifier.issn | 1432-1378 | |
| dc.identifier.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84961162912&doi=10.1007%2Fs00145-016-9227-7&partnerID=40&md5=ad63556ac2ad5e2b81b575130692da89 | |
| dc.identifier.uri | https://gcris.yasar.edu.tr/handle/123456789/9691 | |
| dc.language.iso | English | |
| dc.publisher | Springer New York LLC barbara.b.bertram@gsk.com | |
| dc.relation.ispartof | Journal of Cryptology | |
| dc.source | Journal of Cryptology | |
| dc.subject | Explicit Formulas, Genus 2, Hyperelliptic Curves, Jacobian Coordinates, Scalar Multiplication, Algorithms, Explicit Formula, Genus 2, Hyper-elliptic Curves, Jacobian Coordinate, Scalar Multiplication, Geometry | |
| dc.subject | Algorithms, Explicit formula, Genus 2, Hyper-elliptic curves, Jacobian coordinate, Scalar multiplication, Geometry | |
| dc.title | Jacobian Coordinates on Genus 2 Curves | |
| dc.type | Article | |
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| gdc.description.endpage | 600 | |
| gdc.description.startpage | 572 | |
| gdc.description.volume | 30 | |
| gdc.identifier.openalex | W2330347957 | |
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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 | |
| gdc.oaire.popularity | 6.678898E-9 | |
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| gdc.oaire.sciencefields | 0102 computer and information sciences | |
| 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) | |
| publicationissue.issueNumber | 2 | |
| publicationvolume.volumeNumber | 30 | |
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