InforLorV4, Main, Exploration, bibRecord, 000683

Root optimization of polynomials in the number field sieve

Identifieur interne : 000683 ( Main/Exploration ); précédent : 000682; suivant : 000684

Root optimization of polynomials in the number field sieve

Auteurs : Shi Bai [Nouvelle-Zélande] ; Richard Brent [Australie] ; Emmanuel Thomé [France]

Source :

Mathematics of Computation [ 0025-5718 ] ; 2015.

RBID : Hal:hal-00919367

Abstract

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.

Url:

https://hal.inria.fr/hal-00919367

DOI: 10.1090/S0025-5718-2015-02926-3

Affiliations:

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

to stream Hal, to step Corpus: 004274
to stream Hal, to step Curation: 004274
to stream Hal, to step Checkpoint: 000670
to stream Main, to step Merge: 000684
to stream Main, to step Curation: 000683

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Root optimization of polynomials in the number field sieve</title>
<author><name sortKey="Bai, Shi" sort="Bai, Shi" uniqKey="Bai S" first="Shi" last="Bai">Shi Bai</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-395297" status="INCOMING"><orgName>Department of Mathematics</orgName>
<desc><address><country key="NZ"></country>
</address>
</desc>
<listRelation><relation active="#struct-133271" type="direct"></relation>
<relation active="#struct-160272" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-133271" type="direct"><org type="laboratory" xml:id="struct-133271" status="VALID"><orgName>Department of Mathematics [Auckland]</orgName>
<desc><address><addrLine>Department of Mathematics University of Auckland Private Bag 92019 Auckland Mail Centre Auckland 1142 NEW ZEALAND</addrLine>
<country key="NZ"></country>
</address>
<ref type="url">http://www.math.auckland.ac.nz/</ref>
</desc>
<listRelation><relation active="#struct-160272" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-160272" type="indirect"><org type="institution" xml:id="struct-160272" status="VALID"><orgName>University of Auckland [Auckland]</orgName>
<desc><address><addrLine>Private Bag 92019 Auckland 1142</addrLine>
<country key="NZ"></country>
</address>
<ref type="url">https://www.auckland.ac.nz/en.html</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Nouvelle-Zélande</country>
</affiliation>
</author>
<author><name sortKey="Brent, Richard" sort="Brent, Richard" uniqKey="Brent R" first="Richard" last="Brent">Richard Brent</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-47047" status="VALID"><orgName>Mathematical Sciences Institute</orgName>
<orgName type="acronym">MSI</orgName>
<desc><address><addrLine>Bldg 27 - The Australian National University - ACT 0200 - Australia</addrLine>
<country key="AU"></country>
</address>
</desc>
<listRelation><relation active="#struct-74662" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-74662" type="direct"><org type="institution" xml:id="struct-74662" status="VALID"><orgName>Australian National University</orgName>
<orgName type="acronym">ANU</orgName>
<desc><address><addrLine>The Australian National University Canberra ACT 0200 Australia</addrLine>
<country key="AU"></country>
</address>
<ref type="url">http://www.anu.edu.au/index.php</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Australie</country>
</affiliation>
</author>
<author><name sortKey="Thome, Emmanuel" sort="Thome, Emmanuel" uniqKey="Thome E" first="Emmanuel" last="Thomé">Emmanuel Thomé</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-119560" status="VALID"><idno type="RNSR">201020971F</idno>
<orgName>Cryptology, Arithmetic: Hardware and Software</orgName>
<orgName type="acronym">CARAMEL</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/caramel</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-00919367</idno>
<idno type="halId">hal-00919367</idno>
<idno type="halUri">https://hal.inria.fr/hal-00919367</idno>
<idno type="url">https://hal.inria.fr/hal-00919367</idno>
<idno type="doi">10.1090/S0025-5718-2015-02926-3 </idno>
<date when="2015">2015</date>
<idno type="wicri:Area/Hal/Corpus">004274</idno>
<idno type="wicri:Area/Hal/Curation">004274</idno>
<idno type="wicri:Area/Hal/Checkpoint">000670</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000670</idno>
<idno type="wicri:doubleKey">0025-5718:2015:Bai S:root:optimization:of</idno>
<idno type="wicri:Area/Main/Merge">000684</idno>
<idno type="wicri:Area/Main/Curation">000683</idno>
<idno type="wicri:Area/Main/Exploration">000683</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Root optimization of polynomials in the number field sieve</title>
<author><name sortKey="Bai, Shi" sort="Bai, Shi" uniqKey="Bai S" first="Shi" last="Bai">Shi Bai</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-395297" status="INCOMING"><orgName>Department of Mathematics</orgName>
<desc><address><country key="NZ"></country>
</address>
</desc>
<listRelation><relation active="#struct-133271" type="direct"></relation>
<relation active="#struct-160272" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-133271" type="direct"><org type="laboratory" xml:id="struct-133271" status="VALID"><orgName>Department of Mathematics [Auckland]</orgName>
<desc><address><addrLine>Department of Mathematics University of Auckland Private Bag 92019 Auckland Mail Centre Auckland 1142 NEW ZEALAND</addrLine>
<country key="NZ"></country>
</address>
<ref type="url">http://www.math.auckland.ac.nz/</ref>
</desc>
<listRelation><relation active="#struct-160272" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-160272" type="indirect"><org type="institution" xml:id="struct-160272" status="VALID"><orgName>University of Auckland [Auckland]</orgName>
<desc><address><addrLine>Private Bag 92019 Auckland 1142</addrLine>
<country key="NZ"></country>
</address>
<ref type="url">https://www.auckland.ac.nz/en.html</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Nouvelle-Zélande</country>
</affiliation>
</author>
<author><name sortKey="Brent, Richard" sort="Brent, Richard" uniqKey="Brent R" first="Richard" last="Brent">Richard Brent</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-47047" status="VALID"><orgName>Mathematical Sciences Institute</orgName>
<orgName type="acronym">MSI</orgName>
<desc><address><addrLine>Bldg 27 - The Australian National University - ACT 0200 - Australia</addrLine>
<country key="AU"></country>
</address>
</desc>
<listRelation><relation active="#struct-74662" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-74662" type="direct"><org type="institution" xml:id="struct-74662" status="VALID"><orgName>Australian National University</orgName>
<orgName type="acronym">ANU</orgName>
<desc><address><addrLine>The Australian National University Canberra ACT 0200 Australia</addrLine>
<country key="AU"></country>
</address>
<ref type="url">http://www.anu.edu.au/index.php</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Australie</country>
</affiliation>
</author>
<author><name sortKey="Thome, Emmanuel" sort="Thome, Emmanuel" uniqKey="Thome E" first="Emmanuel" last="Thomé">Emmanuel Thomé</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-119560" status="VALID"><idno type="RNSR">201020971F</idno>
<orgName>Cryptology, Arithmetic: Hardware and Software</orgName>
<orgName type="acronym">CARAMEL</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/caramel</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1090/S0025-5718-2015-02926-3 </idno>
<series><title level="j">Mathematics of Computation</title>
<idno type="ISSN">0025-5718</idno>
<imprint><date type="datePub">2015</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.</div>
</front>
</TEI>
<affiliations><list><country><li>Australie</li>
<li>France</li>
<li>Nouvelle-Zélande</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="Nouvelle-Zélande"><noRegion><name sortKey="Bai, Shi" sort="Bai, Shi" uniqKey="Bai S" first="Shi" last="Bai">Shi Bai</name>
</noRegion>
</country>
<country name="Australie"><noRegion><name sortKey="Brent, Richard" sort="Brent, Richard" uniqKey="Brent R" first="Richard" last="Brent">Richard Brent</name>
</noRegion>
</country>
<country name="France"><region name="Grand Est"><name sortKey="Thome, Emmanuel" sort="Thome, Emmanuel" uniqKey="Thome E" first="Emmanuel" last="Thomé">Emmanuel Thomé</name>
</region>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000683 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000683 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     Hal:hal-00919367
   |texte=   Root optimization of polynomials in the number field sieve
}}

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

Root optimization of polynomials in the number field sieve

Root optimization of polynomials in the number field sieve

Source :

Abstract

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

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri