Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques
Identifieur interne : 005578 ( Hal/Corpus ); précédent : 005577; suivant : 005579Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques
Auteurs : Nicolas EstibalsSource :
Descripteurs français
- mix :
Abstract
Pairings are cryptographic primitives which are now used in numerous protocols. Computing and implementing them efficiently is then an interesting challenge relying on an algorithmic and arithmetic study of those mathematical functions. More precisely, pairings are bilinear maps defined over elliptic and hyperelliptic curves. Among those, we restrict our study to supersingular curves, as they allow both symmetric pairings and efficient algorithm for pairing computation. We propose an unified framework for the construction of algorithms computing pairings and we apply it to the design of a novel algorithm for a pairing over a genus-2 characteristic-2 hyperelliptic curve. The computations involved in our algorithms require the implementation of rapid arithmetic for finite fields of small characteristic. Since multiplication is the critical operation, we present an algorithm for the exhaustive search of multiplication formulae. Finally, we apply all the previous methods to the design and implementation of different hardware accelerators for the computation of cryptographic pairings over various curves.
Url:
Links to Exploration step
Hal:tel-00924743Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="fr">Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques</title><author><name sortKey="Estibals, Nicolas" sort="Estibals, Nicolas" uniqKey="Estibals N" first="Nicolas" last="Estibals">Nicolas Estibals</name><affiliation><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></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:tel-00924743</idno><idno type="halId">tel-00924743</idno><idno type="halUri">https://tel.archives-ouvertes.fr/tel-00924743</idno><idno type="url">https://tel.archives-ouvertes.fr/tel-00924743</idno><date when="2013-10-30">2013-10-30</date><idno type="wicri:Area/Hal/Corpus">005578</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="fr">Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques</title><author><name sortKey="Estibals, Nicolas" sort="Estibals, Nicolas" uniqKey="Estibals N" first="Nicolas" last="Estibals">Nicolas Estibals</name><affiliation><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></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="fr"><term>architecture des ordinateurs</term><term>architecture des ordinateurs.</term><term>arithmétique</term><term>couplage</term><term>cryptographie</term><term>opérateur matériel</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Pairings are cryptographic primitives which are now used in numerous protocols. Computing and implementing them efficiently is then an interesting challenge relying on an algorithmic and arithmetic study of those mathematical functions. More precisely, pairings are bilinear maps defined over elliptic and hyperelliptic curves. Among those, we restrict our study to supersingular curves, as they allow both symmetric pairings and efficient algorithm for pairing computation. We propose an unified framework for the construction of algorithms computing pairings and we apply it to the design of a novel algorithm for a pairing over a genus-2 characteristic-2 hyperelliptic curve. The computations involved in our algorithms require the implementation of rapid arithmetic for finite fields of small characteristic. Since multiplication is the critical operation, we present an algorithm for the exhaustive search of multiplication formulae. Finally, we apply all the previous methods to the design and implementation of different hardware accelerators for the computation of cryptographic pairings over various curves.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="fr">Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques</title><author role="aut"><persName><forename type="first">Nicolas</forename><surname>Estibals</surname></persName><email>Nicolas.Estibals@inria.fr</email><ptr type="url" target="http://people.irisa.fr/Nicolas.Estibals/"></ptr><idno type="halauthor">962476</idno><affiliation ref="#struct-119560"></affiliation></author><editor role="depositor"><persName><forename>Nicolas</forename><surname>Estibals</surname></persName><email>Nicolas.Estibals@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2014-01-07 10:40:58</date><date type="whenModified">2015-12-16 01:09:21</date><date type="whenReleased">2014-01-07 11:10:25</date><date type="whenProduced">2013-10-30</date><date type="whenEndEmbargoed">2014-01-07</date><ref type="file" target="https://tel.archives-ouvertes.fr/tel-00924743/document"><date notBefore="2014-01-07"></date></ref><ref type="file" n="1" target="https://tel.archives-ouvertes.fr/tel-00924743/file/thesis-Nicolas.Estibals.pdf"><date notBefore="2014-01-07"></date></ref></edition><respStmt><resp>contributor</resp><name key="190185"><persName><forename>Nicolas</forename><surname>Estibals</surname></persName><email>Nicolas.Estibals@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">tel-00924743</idno><idno type="halUri">https://tel.archives-ouvertes.fr/tel-00924743</idno><idno type="halBibtex">estibals:tel-00924743</idno><idno type="halRefHtml">Cryptographie et sécurité [cs.CR]. Université de Lorraine, 2013. Français</idno><idno type="halRef">Cryptographie et sécurité [cs.CR]. Université de Lorraine, 2013. Français</idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA-ACGI" p="LORIA">Algorithmique, calcul, image et géométrie</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="LORIA-ALGO-TEST5">LORIA-ALGO-TEST5 </idno><idno type="stamp" n="INRIA2">INRIA 2</idno></seriesStmt><notesStmt></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="fr">Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques</title><author role="aut"><persName><forename type="first">Nicolas</forename><surname>Estibals</surname></persName><email>Nicolas.Estibals@inria.fr</email><ptr type="url" target="http://people.irisa.fr/Nicolas.Estibals/"></ptr><idno type="halAuthorId">962476</idno><affiliation ref="#struct-119560"></affiliation></author></analytic><monogr><imprint><date type="dateDefended">2013-10-30</date></imprint><authority type="institution">Université de Lorraine</authority><authority type="supervisor">Jérémie Detrey, Pierrick Gaudry</authority></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="fr">French</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">architecture des ordinateurs</term><term xml:lang="fr">cryptographie</term><term xml:lang="fr">couplage</term><term xml:lang="fr">opérateur matériel</term><term xml:lang="fr">arithmétique</term><term xml:lang="fr">architecture des ordinateurs.</term></keywords><classCode scheme="halDomain" n="info.info-cr">Computer Science [cs]/Cryptography and Security [cs.CR]</classCode><classCode scheme="halDomain" n="info.info-ao">Computer Science [cs]/Computer Arithmetic</classCode><classCode scheme="halTypology" n="THESE">Theses</classCode></textClass><abstract xml:lang="en">Pairings are cryptographic primitives which are now used in numerous protocols. Computing and implementing them efficiently is then an interesting challenge relying on an algorithmic and arithmetic study of those mathematical functions. More precisely, pairings are bilinear maps defined over elliptic and hyperelliptic curves. Among those, we restrict our study to supersingular curves, as they allow both symmetric pairings and efficient algorithm for pairing computation. We propose an unified framework for the construction of algorithms computing pairings and we apply it to the design of a novel algorithm for a pairing over a genus-2 characteristic-2 hyperelliptic curve. The computations involved in our algorithms require the implementation of rapid arithmetic for finite fields of small characteristic. Since multiplication is the critical operation, we present an algorithm for the exhaustive search of multiplication formulae. Finally, we apply all the previous methods to the design and implementation of different hardware accelerators for the computation of cryptographic pairings over various curves.</abstract><abstract xml:lang="fr">Les couplages sont des primitives cryptographiques qui interviennent désormais dans de nombreux protocoles. Dès lors, il est nécessaire de s'intéresser à leur calcul et à leur implémentation efficace. Pour ce faire, nous nous reposons sur une étude algorithmique et arithmétique de ces fonctions mathématiques. Les couplages sont des applications bilinéaires définies sur des courbes algébriques, plus particulièrement, dans le cas qui nous intéresse, des courbes elliptiques et hyperelliptiques. Nous avons choisi de nous concentrer sur une sous-famille de celles-ci : les courbes supersingulières dont les propriétés permettent d'obtenir à la fois des couplages symétriques et des algorithmes efficaces pour leur calcul. Nous décrivons alors une approche unifiée permettant d'établir une large variété d'algorithmes calculant des couplages. Nous l'appliquons notamment à la construc- tion d'un nouvel algorithme pour le calcul de couplages sur des courbes supersin- gulières de genre 2 et de caractéristique 2. Les calculs nécessaires aux couplages que nous décrivons s'appuient sur l'implé- mentation d'une arithmétique rapide pour les corps finis de petite caractéristique : la multiplication est l'opération critique qu'il convient d'optimiser. Nous présen- tons donc un algorithme de recherche exhaustive de formules de multiplication. Enfin, nous appliquons toutes les méthodes précédentes à la conception et l'im- plémentation de différents accélérateurs matériels pour le calcul de couplages sur différentes courbes dont les architectures ont été optimisées soit pour leur rapidité, soit pour leur compacité.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 005578 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Corpus/biblio.hfd -nk 005578 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Hal
|étape= Corpus
|type= RBID
|clé= Hal:tel-00924743
|texte= Algorithmes et arithmétique pour l'implémentation de couplages cryptographiques
}}
| This area was generated with Dilib version V0.6.33. |  |