<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01257075</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-04T01:29:27+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="fr">Théorie des nombres et cryptographie</title>
            <author role="aut">
              <persName>
                <forename type="first">David</forename>
                <surname>Kohel</surname>
              </persName>
              <email type="md5">f33b0fbe54786438c87a483ad4f067fa</email>
              <email type="domain">univ-amu.fr</email>
              <idno type="idhal" notation="string">drkohel</idno>
              <idno type="idhal" notation="numeric">6821</idno>
              <idno type="halauthorid" notation="string">3155-6821</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-5828-7786</idno>
              <idno type="IDREF">https://www.idref.fr/070142726</idno>
              <affiliation ref="#struct-241321"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Igor E.</forename>
                <surname>Shparlinski</surname>
              </persName>
              <idno type="halauthorid">982500-0</idno>
              <affiliation ref="#struct-74661"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>David</forename>
                <surname>Kohel</surname>
              </persName>
              <email type="md5">f33b0fbe54786438c87a483ad4f067fa</email>
              <email type="domain">univ-amu.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-01-15 16:55:10</date>
              <date type="whenModified">2024-04-26 16:42:58</date>
              <date type="whenReleased">2016-01-18 10:20:56</date>
              <date type="whenProduced">2014-06-20</date>
              <date type="whenEndEmbargoed">2016-01-15</date>
              <ref type="file" target="https://hal.science/hal-01257075v1/document">
                <date notBefore="2016-01-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01257075v1/file/NT-Crypto.fr.pdf" id="file-1257075-1336652">
                <date notBefore="2016-01-15"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="330384">
                <persName>
                  <forename>David</forename>
                  <surname>Kohel</surname>
                </persName>
                <email type="md5">f33b0fbe54786438c87a483ad4f067fa</email>
                <email type="domain">univ-amu.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01257075</idno>
            <idno type="halUri">https://hal.science/hal-01257075</idno>
            <idno type="halBibtex">kohel:hal-01257075</idno>
            <idno type="halRefHtml">&lt;i&gt;Arithmétique et dynamique. Chaires Jean Morlet 2014, SMF Journée Annuelle&lt;/i&gt;, 27, &lt;a target="_blank" href="http://smf.emath.fr/content/journ%C3%A9e-annuelle-2014-paris"&gt;&lt;/a&gt;, pp.1-23, 2014</idno>
            <idno type="halRef">Arithmétique et dynamique. Chaires Jean Morlet 2014, SMF Journée Annuelle, 27, , pp.1-23, 2014</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1257075-1336652"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="I2M-2014-" corresp="I2M">Institut de Mathématiques de Marseille 2014-</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
            <note type="popular" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="fr">Théorie des nombres et cryptographie</title>
                <author role="aut">
                  <persName>
                    <forename type="first">David</forename>
                    <surname>Kohel</surname>
                  </persName>
                  <email type="md5">f33b0fbe54786438c87a483ad4f067fa</email>
                  <email type="domain">univ-amu.fr</email>
                  <idno type="idhal" notation="string">drkohel</idno>
                  <idno type="idhal" notation="numeric">6821</idno>
                  <idno type="halauthorid" notation="string">3155-6821</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-5828-7786</idno>
                  <idno type="IDREF">https://www.idref.fr/070142726</idno>
                  <affiliation ref="#struct-241321"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Igor E.</forename>
                    <surname>Shparlinski</surname>
                  </persName>
                  <idno type="halauthorid">982500-0</idno>
                  <affiliation ref="#struct-74661"/>
                </author>
              </analytic>
              <monogr>
                <title level="m">Arithmétique et dynamique. Chaires Jean Morlet 2014, SMF Journée Annuelle</title>
                <imprint>
                  <biblScope unit="volume">27</biblScope>
                  <biblScope unit="pp">1-23</biblScope>
                  <date type="datePub">2014-06-20</date>
                </imprint>
              </monogr>
              <ref type="publisher">http://smf.emath.fr/content/journ%C3%A9e-annuelle-2014-paris</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="fr">French</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="fr">théorie des nombres</term>
                <term xml:lang="fr"> cryptographie</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-nt">Mathematics [math]/Number Theory [math.NT]</classCode>
              <classCode scheme="halDomain" n="math.math-it">Mathematics [math]/Information Theory [math.IT]</classCode>
              <classCode scheme="halTypology" n="COUV">Book sections</classCode>
              <classCode scheme="halOldTypology" n="COUV">Book sections</classCode>
              <classCode scheme="halTreeTypology" n="COUV">Book sections</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p> Modern cryptographic constructions are based on constructions from number theory, but many of the links go deeper than typically realized. The development of modern cryptography runs in parallel to developments and central questions in number theory. After recalling some of the constructions used in modern public key cryptography, based on modular arithmetic, finite fields, lattices and elliptic curves, we describe some of their number theoretic origins. The first concerns the Riemann hypothesis and associated questions of distributions of prime numbers and smooth numbers, and of distributions of divisors of integers. Next we consider the origins of elliptic curve cryptography, beginning from Hasse's theorem, the conjectures of Weil, and Schoof's algorithm. Finally we mention the context of Mordell's theorem and the conjectures of Birch and Swinnerton-Dyer. In conclusion we consider the future prospects of these cryptosystems.</p>
            </abstract>
            <abstract xml:lang="fr">
              <p> Des constructions en cryptographie moderne sont basées sur la théorie des nombres. Toutefois, les liens entre ces deux domaines sont plus profonds qu'il n'y paraît. Le développement de la cryptographie moderne a eu lieu en parallele avec des developpements et des questions centrales en théorie des nombres. Après des rappels de constructions en cryptographie à clef publique, à base de l'arithmétique modulaire, des corps finis, des réseaux et des courbes elliptiques, nous décrivons quelques unes de ces racines en théorie des nombres. La première concerne l'hypothèse de Riemann et les questions associées sur la distribution des nombres premiers et des nombres friables, et des distributions des diviseurs d'entiers. Puis on considère les origines de la cryptographie à base de courbes elliptiques, en commençant par le théorème de Hasse, les conjectures de Weil, et l'algorithme de Schoof. Finalement on se place dans le contexte du théorème de Mordell et de la conjecture de Birch et Swinnerton-Dyer. En conclusion on considère les perspectives d'avenir pour ces cryptosystèmes.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-241321" status="VALID">
          <idno type="RNSR">201420768T</idno>
          <idno type="ROR">042h2y225</idno>
          <orgName>Institut de Mathématiques de Marseille</orgName>
          <orgName type="acronym">I2M</orgName>
          <date type="start">2014</date>
          <desc>
            <address>
              <addrLine>Centre de Mathématiques et Informatique (CMI)Technopôle Château-Gombert39, rue Frédéric Joliot Curie13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.i2m.univ-amu.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7373" active="#struct-198056" type="direct"/>
            <relation name="UMR7373" active="#struct-300415" type="direct"/>
            <relation name="UMR7373" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-74661" status="VALID">
          <idno type="ROR">https://ror.org/03r8z3t63</idno>
          <orgName>University of New South Wales [Sydney]</orgName>
          <orgName type="acronym">UNSW</orgName>
          <desc>
            <address>
              <addrLine>High StKensington, Sydney, NSW 2052</addrLine>
              <country key="AU"/>
            </address>
            <ref type="url">http://www.unsw.edu.au/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</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"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>