InforLorV4, PascalFrancis, Curation, bibRecord, 000793

FACTORIZATION WITH GENUS 2 CURVES

Identifieur interne : 000793 ( PascalFrancis/Curation ); précédent : 000792; suivant : 000794

FACTORIZATION WITH GENUS 2 CURVES

Auteurs : Romain Cosset [France]

Source :

Mathematics of computation [ 0025-5718 ] ; 2010.

RBID : Pascal:10-0177404

Descripteurs français

Pascal (Inist)
- Courbe elliptique, Méthode factorisation, Courbe hyperelliptique, Surface, Complexité algorithme, Implémentation, Analyse numérique, Calcul scientifique, 11G07, 14H52.
Wicri :
- topic : Calcul scientifique.

English descriptors

KwdEn :
- Algorithm complexity, Elliptic curve, Factorization method, Hyperelliptic curve, Implementation, Numerical analysis, Scientific computation, Surface.

Abstract

The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring large numbers.

A01	`01`	`1`		`@0 0025-5718`
A02	`01`			`@0 MCMPAF`
A03		`1`		`@0 Math. comput.`
A05				`@2 79`
A06				`@2 270`
A08	`01`	`1`	`ENG`	`@1 FACTORIZATION WITH GENUS 2 CURVES`
A11	`01`	`1`		`@1 COSSET (Romain)`
A14	`01`			`@1 LORIA, CAMPUS SCIENTIFIQUE - BP 239 @2 54506 VANDOEUVRE-LÈS-NANCY @3 FRA @Z 1 aut.`
A20				`@1 1191-1208`
A21				`@1 2010`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 5227 @5 354000189654270260`
A44				`@0 0000 @1 © 2010 INIST-CNRS. All rights reserved.`
A45				`@0 13 ref.`
A47	`01`	`1`		`@0 10-0177404`
A60				`@1 P`
A61				`@0 A`
A64	`01`	`1`		`@0 Mathematics of computation`
A66	`01`			`@0 USA`
C01	`01`		`ENG`	`@0 The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring large numbers.`
C02	`01`	`X`		`@0 001A02I02`
C02	`02`	`X`		`@0 001A02I01`
C02	`03`	`X`		`@0 001A02C02`
C02	`04`	`X`		`@0 001A02C05`
C03	`01`	`X`	`FRE`	`@0 Courbe elliptique @5 17`
C03	`01`	`X`	`ENG`	`@0 Elliptic curve @5 17`
C03	`01`	`X`	`SPA`	`@0 Curva eliptica @5 17`
C03	`02`	`X`	`FRE`	`@0 Méthode factorisation @5 18`
C03	`02`	`X`	`ENG`	`@0 Factorization method @5 18`
C03	`02`	`X`	`SPA`	`@0 Método factorización @5 18`
C03	`03`	`X`	`FRE`	`@0 Courbe hyperelliptique @5 19`
C03	`03`	`X`	`ENG`	`@0 Hyperelliptic curve @5 19`
C03	`03`	`X`	`SPA`	`@0 Curvo elíptico @5 19`
C03	`04`	`X`	`FRE`	`@0 Surface @5 20`
C03	`04`	`X`	`ENG`	`@0 Surface @5 20`
C03	`04`	`X`	`SPA`	`@0 Superficie @5 20`
C03	`05`	`X`	`FRE`	`@0 Complexité algorithme @5 21`
C03	`05`	`X`	`ENG`	`@0 Algorithm complexity @5 21`
C03	`05`	`X`	`SPA`	`@0 Complejidad algoritmo @5 21`
C03	`06`	`X`	`FRE`	`@0 Implémentation @5 22`
C03	`06`	`X`	`ENG`	`@0 Implementation @5 22`
C03	`06`	`X`	`SPA`	`@0 Implementación @5 22`
C03	`07`	`X`	`FRE`	`@0 Analyse numérique @5 23`
C03	`07`	`X`	`ENG`	`@0 Numerical analysis @5 23`
C03	`07`	`X`	`SPA`	`@0 Análisis numérico @5 23`
C03	`08`	`X`	`FRE`	`@0 Calcul scientifique @5 24`
C03	`08`	`X`	`ENG`	`@0 Scientific computation @5 24`
C03	`08`	`X`	`SPA`	`@0 Computación científica @5 24`
C03	`09`	`X`	`FRE`	`@0 11G07 @4 INC @5 70`
C03	`10`	`X`	`FRE`	`@0 14H52 @4 INC @5 71`
N21				`@1 116`
N44	`01`			`@1 OTO`
N82				`@1 OTO`

Links toward previous steps (curation, corpus...)

to stream PascalFrancis, to step Corpus: Pour aller vers cette notice dans l'étape Curation :000225

Links to Exploration step

Pascal:10-0177404

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">FACTORIZATION WITH GENUS 2 CURVES</title>
<author><name sortKey="Cosset, Romain" sort="Cosset, Romain" uniqKey="Cosset R" first="Romain" last="Cosset">Romain Cosset</name>
<affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LORIA, CAMPUS SCIENTIFIQUE - BP 239</s1>
<s2>54506 VANDOEUVRE-LÈS-NANCY</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>France</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">INIST</idno>
<idno type="inist">10-0177404</idno>
<date when="2010">2010</date>
<idno type="stanalyst">PASCAL 10-0177404 INIST</idno>
<idno type="RBID">Pascal:10-0177404</idno>
<idno type="wicri:Area/PascalFrancis/Corpus">000225</idno>
<idno type="wicri:Area/PascalFrancis/Curation">000793</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">FACTORIZATION WITH GENUS 2 CURVES</title>
<author><name sortKey="Cosset, Romain" sort="Cosset, Romain" uniqKey="Cosset R" first="Romain" last="Cosset">Romain Cosset</name>
<affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LORIA, CAMPUS SCIENTIFIQUE - BP 239</s1>
<s2>54506 VANDOEUVRE-LÈS-NANCY</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>France</country>
</affiliation>
</author>
</analytic>
<series><title level="j" type="main">Mathematics of computation</title>
<title level="j" type="abbreviated">Math. comput.</title>
<idno type="ISSN">0025-5718</idno>
<imprint><date when="2010">2010</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><title level="j" type="main">Mathematics of computation</title>
<title level="j" type="abbreviated">Math. comput.</title>
<idno type="ISSN">0025-5718</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithm complexity</term>
<term>Elliptic curve</term>
<term>Factorization method</term>
<term>Hyperelliptic curve</term>
<term>Implementation</term>
<term>Numerical analysis</term>
<term>Scientific computation</term>
<term>Surface</term>
</keywords>
<keywords scheme="Pascal" xml:lang="fr"><term>Courbe elliptique</term>
<term>Méthode factorisation</term>
<term>Courbe hyperelliptique</term>
<term>Surface</term>
<term>Complexité algorithme</term>
<term>Implémentation</term>
<term>Analyse numérique</term>
<term>Calcul scientifique</term>
<term>11G07</term>
<term>14H52</term>
</keywords>
<keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Calcul scientifique</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring large numbers.</div>
</front>
</TEI>
<inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0025-5718</s0>
</fA01>
<fA02 i1="01"><s0>MCMPAF</s0>
</fA02>
<fA03 i2="1"><s0>Math. comput.</s0>
</fA03>
<fA05><s2>79</s2>
</fA05>
<fA06><s2>270</s2>
</fA06>
<fA08 i1="01" i2="1" l="ENG"><s1>FACTORIZATION WITH GENUS 2 CURVES</s1>
</fA08>
<fA11 i1="01" i2="1"><s1>COSSET (Romain)</s1>
</fA11>
<fA14 i1="01"><s1>LORIA, CAMPUS SCIENTIFIQUE - BP 239</s1>
<s2>54506 VANDOEUVRE-LÈS-NANCY</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</fA14>
<fA20><s1>1191-1208</s1>
</fA20>
<fA21><s1>2010</s1>
</fA21>
<fA23 i1="01"><s0>ENG</s0>
</fA23>
<fA43 i1="01"><s1>INIST</s1>
<s2>5227</s2>
<s5>354000189654270260</s5>
</fA43>
<fA44><s0>0000</s0>
<s1>© 2010 INIST-CNRS. All rights reserved.</s1>
</fA44>
<fA45><s0>13 ref.</s0>
</fA45>
<fA47 i1="01" i2="1"><s0>10-0177404</s0>
</fA47>
<fA60><s1>P</s1>
</fA60>
<fA61><s0>A</s0>
</fA61>
<fA64 i1="01" i2="1"><s0>Mathematics of computation</s0>
</fA64>
<fA66 i1="01"><s0>USA</s0>
</fA66>
<fC01 i1="01" l="ENG"><s0>The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring large numbers.</s0>
</fC01>
<fC02 i1="01" i2="X"><s0>001A02I02</s0>
</fC02>
<fC02 i1="02" i2="X"><s0>001A02I01</s0>
</fC02>
<fC02 i1="03" i2="X"><s0>001A02C02</s0>
</fC02>
<fC02 i1="04" i2="X"><s0>001A02C05</s0>
</fC02>
<fC03 i1="01" i2="X" l="FRE"><s0>Courbe elliptique</s0>
<s5>17</s5>
</fC03>
<fC03 i1="01" i2="X" l="ENG"><s0>Elliptic curve</s0>
<s5>17</s5>
</fC03>
<fC03 i1="01" i2="X" l="SPA"><s0>Curva eliptica</s0>
<s5>17</s5>
</fC03>
<fC03 i1="02" i2="X" l="FRE"><s0>Méthode factorisation</s0>
<s5>18</s5>
</fC03>
<fC03 i1="02" i2="X" l="ENG"><s0>Factorization method</s0>
<s5>18</s5>
</fC03>
<fC03 i1="02" i2="X" l="SPA"><s0>Método factorización</s0>
<s5>18</s5>
</fC03>
<fC03 i1="03" i2="X" l="FRE"><s0>Courbe hyperelliptique</s0>
<s5>19</s5>
</fC03>
<fC03 i1="03" i2="X" l="ENG"><s0>Hyperelliptic curve</s0>
<s5>19</s5>
</fC03>
<fC03 i1="03" i2="X" l="SPA"><s0>Curvo elíptico</s0>
<s5>19</s5>
</fC03>
<fC03 i1="04" i2="X" l="FRE"><s0>Surface</s0>
<s5>20</s5>
</fC03>
<fC03 i1="04" i2="X" l="ENG"><s0>Surface</s0>
<s5>20</s5>
</fC03>
<fC03 i1="04" i2="X" l="SPA"><s0>Superficie</s0>
<s5>20</s5>
</fC03>
<fC03 i1="05" i2="X" l="FRE"><s0>Complexité algorithme</s0>
<s5>21</s5>
</fC03>
<fC03 i1="05" i2="X" l="ENG"><s0>Algorithm complexity</s0>
<s5>21</s5>
</fC03>
<fC03 i1="05" i2="X" l="SPA"><s0>Complejidad algoritmo</s0>
<s5>21</s5>
</fC03>
<fC03 i1="06" i2="X" l="FRE"><s0>Implémentation</s0>
<s5>22</s5>
</fC03>
<fC03 i1="06" i2="X" l="ENG"><s0>Implementation</s0>
<s5>22</s5>
</fC03>
<fC03 i1="06" i2="X" l="SPA"><s0>Implementación</s0>
<s5>22</s5>
</fC03>
<fC03 i1="07" i2="X" l="FRE"><s0>Analyse numérique</s0>
<s5>23</s5>
</fC03>
<fC03 i1="07" i2="X" l="ENG"><s0>Numerical analysis</s0>
<s5>23</s5>
</fC03>
<fC03 i1="07" i2="X" l="SPA"><s0>Análisis numérico</s0>
<s5>23</s5>
</fC03>
<fC03 i1="08" i2="X" l="FRE"><s0>Calcul scientifique</s0>
<s5>24</s5>
</fC03>
<fC03 i1="08" i2="X" l="ENG"><s0>Scientific computation</s0>
<s5>24</s5>
</fC03>
<fC03 i1="08" i2="X" l="SPA"><s0>Computación científica</s0>
<s5>24</s5>
</fC03>
<fC03 i1="09" i2="X" l="FRE"><s0>11G07</s0>
<s4>INC</s4>
<s5>70</s5>
</fC03>
<fC03 i1="10" i2="X" l="FRE"><s0>14H52</s0>
<s4>INC</s4>
<s5>71</s5>
</fC03>
<fN21><s1>116</s1>
</fN21>
<fN44 i1="01"><s1>OTO</s1>
</fN44>
<fN82><s1>OTO</s1>
</fN82>
</pA>
</standard>
</inist>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/PascalFrancis/Curation

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000793 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/PascalFrancis/Curation/biblio.hfd -nk 000793 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    PascalFrancis
   |étape=   Curation
   |type=    RBID
   |clé=     Pascal:10-0177404
   |texte=   FACTORIZATION WITH GENUS 2 CURVES
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur la recherche en informatique en Lorraine

FACTORIZATION WITH GENUS 2 CURVES

FACTORIZATION WITH GENUS 2 CURVES

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri