<?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-01287981</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="2026-05-20T03:14:54+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants</title>
            <author role="aut">
              <persName>
                <forename type="first">Luk</forename>
                <surname>Bettale</surname>
              </persName>
              <email type="md5">c04ec4f6072b597867078fd34501104a</email>
              <email type="domain">lip6.fr</email>
              <idno type="idhal" notation="numeric">966118</idno>
              <idno type="halauthorid" notation="string">684396-966118</idno>
              <affiliation ref="#struct-2438"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-Charles</forename>
                <surname>Faugère</surname>
              </persName>
              <email type="md5">424972c8b3e59f15dec87335bdbaf554</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">faugere</idno>
              <idno type="idhal" notation="numeric">19366</idno>
              <idno type="halauthorid" notation="string">2141-19366</idno>
              <idno type="IDREF">https://www.idref.fr/090173449</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/COI-0285-2022</idno>
              <affiliation ref="#struct-2438"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Ludovic</forename>
                <surname>Perret</surname>
              </persName>
              <email type="md5">d1e76a35cfabf006008b7e9391c5bc7d</email>
              <email type="domain">lip6.fr</email>
              <idno type="idhal" notation="numeric">935330</idno>
              <idno type="halauthorid" notation="string">143637-935330</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/JPN-3539-2023</idno>
              <idno type="ISNI">http://isni.org/isni/0000000359243421</idno>
              <idno type="VIAF">https://viaf.org/viaf/217378925</idno>
              <idno type="IDREF">https://www.idref.fr/123278864</idno>
              <affiliation ref="#struct-2438"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Lip6</forename>
                <surname>Publications</surname>
              </persName>
              <email type="md5">48f930374cf1d03f2eafeaae16bb5814</email>
              <email type="domain">lip6.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-03-14 14:15:50</date>
              <date type="whenModified">2025-02-26 15:24:03</date>
              <date type="whenReleased">2016-03-14 14:15:50</date>
              <date type="whenProduced">2011-03</date>
              <ref type="externalLink" target="https://link.springer.com/content/pdf/10.1007%2F978-3-642-19379-8_27.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="196566">
                <persName>
                  <forename>Lip6</forename>
                  <surname>Publications</surname>
                </persName>
                <email type="md5">48f930374cf1d03f2eafeaae16bb5814</email>
                <email type="domain">lip6.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01287981</idno>
            <idno type="halUri">https://hal.science/hal-01287981</idno>
            <idno type="halBibtex">bettale:hal-01287981</idno>
            <idno type="halRefHtml">&lt;i&gt;Public Key Cryptography - PKC 2011&lt;/i&gt;, Mar 2011, Taormina, Italy. pp.441-458, &lt;a target="_blank" href="https://dx.doi.org/10.1007/978-3-642-19379-8_27"&gt;&amp;#x27E8;10.1007/978-3-642-19379-8_27&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Public Key Cryptography - PKC 2011, Mar 2011, Taormina, Italy. pp.441-458, &amp;#x27E8;10.1007/978-3-642-19379-8_27&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UPMC" corresp="SORBONNE-UNIVERSITE">Université Pierre et Marie Curie</idno>
            <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-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="LIP6" corresp="SORBONNE-UNIVERSITE">Laboratoire d'Informatique de Paris 6</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="UPMC_POLE_1" corresp="UPMC">UPMC Pôle 1</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Luk</forename>
                    <surname>Bettale</surname>
                  </persName>
                  <email type="md5">c04ec4f6072b597867078fd34501104a</email>
                  <email type="domain">lip6.fr</email>
                  <idno type="idhal" notation="numeric">966118</idno>
                  <idno type="halauthorid" notation="string">684396-966118</idno>
                  <affiliation ref="#struct-2438"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-Charles</forename>
                    <surname>Faugère</surname>
                  </persName>
                  <email type="md5">424972c8b3e59f15dec87335bdbaf554</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">faugere</idno>
                  <idno type="idhal" notation="numeric">19366</idno>
                  <idno type="halauthorid" notation="string">2141-19366</idno>
                  <idno type="IDREF">https://www.idref.fr/090173449</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/COI-0285-2022</idno>
                  <affiliation ref="#struct-2438"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Ludovic</forename>
                    <surname>Perret</surname>
                  </persName>
                  <email type="md5">d1e76a35cfabf006008b7e9391c5bc7d</email>
                  <email type="domain">lip6.fr</email>
                  <idno type="idhal" notation="numeric">935330</idno>
                  <idno type="halauthorid" notation="string">143637-935330</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/JPN-3539-2023</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000359243421</idno>
                  <idno type="VIAF">https://viaf.org/viaf/217378925</idno>
                  <idno type="IDREF">https://www.idref.fr/123278864</idno>
                  <affiliation ref="#struct-2438"/>
                </author>
              </analytic>
              <monogr>
                <title level="m">Public Key Cryptography - PKC 2011</title>
                <meeting>
                  <title>Public Key Cryptography - PKC 2011</title>
                  <date type="start">2011-03</date>
                  <settlement>Taormina</settlement>
                  <country key="IT">Italy</country>
                </meeting>
                <imprint>
                  <publisher>Springer Berlin / Heidelberg</publisher>
                  <biblScope unit="serie">Lecture Notes in Computer Science</biblScope>
                  <biblScope unit="volume">6571</biblScope>
                  <biblScope unit="pp">441-458</biblScope>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/978-3-642-19379-8_27</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info">Computer Science [cs]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We investigate the security of a generalization of HFE (multivariate and odd-characteristic variants). First, we propose an improved version of the basic Kipnis-Shamir key recovery attack against HFE. Second, we generalize the Kipnis-Shamir attack to Multi-HFE. The attack reduces to solve a MinRank problem directly on the public key. This leads to an improvement of a factor corresponding to the square of the degree of the extension field. We used recent results on MinRank to show that our attack is polynomial in the degree of the extension field. It appears that multi-HFE is less secure than original HFE for equal-sized keys. Finally, adaptations of our attack overcome several variants (i.e. minus modifier and embedding). As a proof of concept, we have practically broken the most conservative parameters given by Chen, Chen, Ding, Werner and Yang in 9 days for 256 bits security. All in all, our results give a more precise picture on the (in)security of several variants of HFE proposed these last years.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-2438" status="OLD">
          <idno type="RNSR">200518334L</idno>
          <orgName>Solvers for Algebraic Systems and Applications</orgName>
          <orgName type="acronym">SALSA</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-233" type="direct"/>
            <relation active="#struct-93591" type="indirect"/>
            <relation name="UMR7606" active="#struct-441569" type="indirect"/>
            <relation active="#struct-86790" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-233" status="OLD">
          <idno type="RNSR">199712651U</idno>
          <idno type="ROR">https://ror.org/05krcen59</idno>
          <orgName>Laboratoire d'Informatique de Paris 6</orgName>
          <orgName type="acronym">LIP6</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 Place JUSSIEU 75252 PARIS CEDEX 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lip6.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93591" type="direct"/>
            <relation name="UMR7606" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93591" status="OLD">
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Université Pierre et Marie Curie - Paris 6</orgName>
          <orgName type="acronym">UPMC</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 place Jussieu - 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.upmc.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>
        <org type="laboratory" xml:id="struct-86790" status="OLD">
          <orgName>Inria Paris-Rocquencourt</orgName>
          <date type="end">2016-03-30</date>
          <desc>
            <address>
              <addrLine>INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris-rocquencourt</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <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"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>