The Semi-Generic Group Model and Applications to Pairing-Based Cryptography
Identifieur interne : 001B50 ( Istex/Corpus ); précédent : 001B49; suivant : 001B51The Semi-Generic Group Model and Applications to Pairing-Based Cryptography
Auteurs : Tibor Jager ; Andy RuppSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Abstract
Abstract: In pairing-based cryptography the Generic Group Model (GGM) is used frequently to provide evidence towards newly introduced hardness assumptions. Unfortunately, the GGM does not reflect many known properties of bilinear group settings and thus hardness results in this model are of limited significance. This paper proposes a novel computational model for pairing-based cryptography, called the Semi-Generic Group Model (SGGM), that is closer to the standard model and allows to make more meaningful security guarantees. In fact, the best algorithms currently known for solving pairing-based problems are semi-generic in nature. We demonstrate the usefulness of our new model by applying it to study several important assumptions (BDDH, Co-DH). Furthermore, we develop master theorems facilitating an easy analysis of other (future) assumptions. These master theorems imply that (unless there are better algorithms than the semi-generic ones) great parts of the zoo of novel assumptions over bilinear groups are reducible to just two (more or less) standard assumptions over finite fields. Finally, we examine the appropriateness of the SGGM as a tool for analyzing the security of practical cryptosystems without random oracles by applying it to the BLS signature scheme.
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DOI: 10.1007/978-3-642-17373-8_31
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Unfortunately, the GGM does not reflect many known properties of bilinear group settings and thus hardness results in this model are of limited significance. This paper proposes a novel computational model for pairing-based cryptography, called the Semi-Generic Group Model (SGGM), that is closer to the standard model and allows to make more meaningful security guarantees. In fact, the best algorithms currently known for solving pairing-based problems are semi-generic in nature. We demonstrate the usefulness of our new model by applying it to study several important assumptions (BDDH, Co-DH). Furthermore, we develop master theorems facilitating an easy analysis of other (future) assumptions. These master theorems imply that (unless there are better algorithms than the semi-generic ones) great parts of the zoo of novel assumptions over bilinear groups are reducible to just two (more or less) standard assumptions over finite fields. Finally, we examine the appropriateness of the SGGM as a tool for analyzing the security of practical cryptosystems without random oracles by applying it to the BLS signature scheme.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Tibor Jager</name><affiliations><json:string>Horst Görtz Institute for IT Security, Ruhr-University Bochum, Germany</json:string><json:string>E-mail: tibor.jager@rub.de</json:string></affiliations></json:item><json:item><name>Andy Rupp</name><affiliations><json:string>University of Trier, Germany</json:string><json:string>E-mail: andy.rupp@rub.de</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: In pairing-based cryptography the Generic Group Model (GGM) is used frequently to provide evidence towards newly introduced hardness assumptions. Unfortunately, the GGM does not reflect many known properties of bilinear group settings and thus hardness results in this model are of limited significance. This paper proposes a novel computational model for pairing-based cryptography, called the Semi-Generic Group Model (SGGM), that is closer to the standard model and allows to make more meaningful security guarantees. In fact, the best algorithms currently known for solving pairing-based problems are semi-generic in nature. We demonstrate the usefulness of our new model by applying it to study several important assumptions (BDDH, Co-DH). Furthermore, we develop master theorems facilitating an easy analysis of other (future) assumptions. These master theorems imply that (unless there are better algorithms than the semi-generic ones) great parts of the zoo of novel assumptions over bilinear groups are reducible to just two (more or less) standard assumptions over finite fields. Finally, we examine the appropriateness of the SGGM as a tool for analyzing the security of practical cryptosystems without random oracles by applying it to the BLS signature scheme.</abstract><qualityIndicators><score>8.756</score><pdfVersion>1.6</pdfVersion><pdfPageSize>429.725 x 659.895 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1282</abstractCharCount><pdfWordCount>9435</pdfWordCount><pdfCharCount>44928</pdfCharCount><pdfPageCount>18</pdfPageCount><abstractWordCount>188</abstractWordCount></qualityIndicators><title>The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</title><chapterId><json:string>31</json:string><json:string>Chap31</json:string></chapterId><refBibs><json:item><host><author></author><title>The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</title></host></json:item><json:item><author><json:item><name>D Aggarwal</name></json:item><json:item><name>U Maurer</name></json:item></author><host><pages><last>53</last><first>36</first></pages><author></author><title>EUROCRYPT 2009</title><publicationDate>2010</publicationDate></host><title>Breaking RSA generically is equivalent to factoring</title><publicationDate>2010</publicationDate></json:item><json:item><author><json:item><name>M Bellare</name></json:item><json:item><name>P Rogaway</name></json:item></author><host><pages><last>73</last><first>62</first></pages><author></author><title>ACM Conference on Computer and Communications Security</title><publicationDate>1993</publicationDate></host><title>Random oracles are practical: A paradigm for designing efficient protocols</title><publicationDate>1993</publicationDate></json:item><json:item><host><author><json:item><name>D Boneh</name></json:item></author><title>Number-theoretic assumptions. 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Kleinberg</name><affiliations><json:string>Cornell University, Ithaca, NY, USA</json:string></affiliations></json:item><json:item><name>Friedemann Mattern</name><affiliations><json:string>ETH Zurich, Zurich, Switzerland</json:string></affiliations></json:item><json:item><name>John C. Mitchell</name><affiliations><json:string>Stanford University, Stanford, CA, USA</json:string></affiliations></json:item><json:item><name>Moni Naor</name><affiliations><json:string>Weizmann Institute of Science, Rehovot, Israel</json:string></affiliations></json:item><json:item><name>Oscar Nierstrasz</name><affiliations><json:string>University of Bern, Bern, Switzerland</json:string></affiliations></json:item><json:item><name>C. Pandu Rangan</name><affiliations><json:string>Indian Institute of Technology, Madras, India</json:string></affiliations></json:item><json:item><name>Bernhard Steffen</name><affiliations><json:string>University of Dortmund, Dortmund, Germany</json:string></affiliations></json:item><json:item><name>Madhu Sudan</name><affiliations><json:string>Massachusetts Institute of Technology, MA, USA</json:string></affiliations></json:item><json:item><name>Demetri Terzopoulos</name><affiliations><json:string>University of California, Los Angeles, CA, USA</json:string></affiliations></json:item><json:item><name>Doug Tygar</name><affiliations><json:string>University of California, Berkeley, CA, USA</json:string></affiliations></json:item><json:item><name>Moshe Y. Vardi</name><affiliations><json:string>Rice University, Houston, TX, USA</json:string></affiliations></json:item><json:item><name>Gerhard Weikum</name><affiliations><json:string>Max-Planck Institute of Computer Science, Saarbrücken, Germany</json:string></affiliations></json:item></editor><issn><json:string>0302-9743</json:string></issn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Lecture Notes in Computer Science</title><copyrightDate>2010</copyrightDate></serie><host><editor><json:item><name>Masayuki Abe</name><affiliations><json:string>, 3-9-11 Midori-cho, Musashino-shi, 180-8585, Tokyo, Japan</json:string><json:string>E-mail: abe.masyuki@lab.ntt.co.jp</json:string></affiliations></json:item></editor><subject><json:item><value>Computer Science</value></json:item><json:item><value>Computer Science</value></json:item><json:item><value>Data Encryption</value></json:item><json:item><value>Algorithm Analysis and Problem Complexity</value></json:item><json:item><value>Management of Computing and Information Systems</value></json:item><json:item><value>Discrete Mathematics in Computer Science</value></json:item><json:item><value>Systems and Data Security</value></json:item><json:item><value>Applications of Mathematics</value></json:item></subject><isbn><json:string>978-3-642-17372-1</json:string></isbn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Advances in Cryptology - ASIACRYPT 2010</title><bookId><json:string>978-3-642-17373-8</json:string></bookId><volume>6477</volume><pages><last>556</last><first>539</first></pages><issn><json:string>0302-9743</json:string></issn><genre><json:string>book-series</json:string></genre><eisbn><json:string>978-3-642-17373-8</json:string></eisbn><copyrightDate>2010</copyrightDate><doi><json:string>10.1007/978-3-642-17373-8</json:string></doi></host><publicationDate>2010</publicationDate><copyrightDate>2010</copyrightDate><doi><json:string>10.1007/978-3-642-17373-8_31</json:string></doi><id>C6933B744AB20C89601B013A19C06E2208B4C82B</id><score>0.70506346</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/C6933B744AB20C89601B013A19C06E2208B4C82B/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/C6933B744AB20C89601B013A19C06E2208B4C82B/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/C6933B744AB20C89601B013A19C06E2208B4C82B/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><availability><p>International Association for Cryptologic Research, 2010</p></availability><date>2010</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</title><author xml:id="author-1"><persName><forename type="first">Tibor</forename><surname>Jager</surname></persName><email>tibor.jager@rub.de</email><affiliation>Horst Görtz Institute for IT Security, Ruhr-University Bochum, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Andy</forename><surname>Rupp</surname></persName><email>andy.rupp@rub.de</email><affiliation>University of Trier, Germany</affiliation></author></analytic><monogr><title level="m">Advances in Cryptology - ASIACRYPT 2010</title><title level="m" type="sub">16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings</title><idno type="pISBN">978-3-642-17372-1</idno><idno type="eISBN">978-3-642-17373-8</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/978-3-642-17373-8</idno><idno type="book-ID">978-3-642-17373-8</idno><idno type="book-title-ID">215167</idno><idno type="book-sequence-number">6477</idno><idno type="book-volume-number">6477</idno><idno type="book-chapter-count">35</idno><editor><persName><forename type="first">Masayuki</forename><surname>Abe</surname></persName><email>abe.masyuki@lab.ntt.co.jp</email><affiliation>, 3-9-11 Midori-cho, Musashino-shi, 180-8585, Tokyo, Japan</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2010"></date><biblScope unit="volume">6477</biblScope><biblScope unit="page" from="539">539</biblScope><biblScope unit="page" to="556">556</biblScope></imprint></monogr><series><title level="s">Lecture Notes in Computer Science</title><editor><persName><forename type="first">David</forename><surname>Hutchison</surname></persName><affiliation>Lancaster University, Lancaster, UK</affiliation></editor><editor><persName><forename type="first">Takeo</forename><surname>Kanade</surname></persName><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation></editor><editor><persName><forename type="first">Josef</forename><surname>Kittler</surname></persName><affiliation>University of Surrey, Guildford, UK</affiliation></editor><editor><persName><forename type="first">Jon</forename><forename type="first">M.</forename><surname>Kleinberg</surname></persName><affiliation>Cornell University, Ithaca, NY, USA</affiliation></editor><editor><persName><forename type="first">Friedemann</forename><surname>Mattern</surname></persName><affiliation>ETH Zurich, Zurich, Switzerland</affiliation></editor><editor><persName><forename type="first">John</forename><forename type="first">C.</forename><surname>Mitchell</surname></persName><affiliation>Stanford University, Stanford, CA, USA</affiliation></editor><editor><persName><forename type="first">Moni</forename><surname>Naor</surname></persName><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation></editor><editor><persName><forename type="first">Oscar</forename><surname>Nierstrasz</surname></persName><affiliation>University of Bern, Bern, Switzerland</affiliation></editor><editor><persName><forename type="first">C.</forename><surname>Pandu Rangan</surname></persName><affiliation>Indian Institute of Technology, Madras, India</affiliation></editor><editor><persName><forename type="first">Bernhard</forename><surname>Steffen</surname></persName><affiliation>University of Dortmund, Dortmund, Germany</affiliation></editor><editor><persName><forename type="first">Madhu</forename><surname>Sudan</surname></persName><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation></editor><editor><persName><forename type="first">Demetri</forename><surname>Terzopoulos</surname></persName><affiliation>University of California, Los Angeles, CA, USA</affiliation></editor><editor><persName><forename type="first">Doug</forename><surname>Tygar</surname></persName><affiliation>University of California, Berkeley, CA, USA</affiliation></editor><editor><persName><forename type="first">Moshe</forename><forename type="first">Y.</forename><surname>Vardi</surname></persName><affiliation>Rice University, Houston, TX, USA</affiliation></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation></editor><biblScope><date>2010</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">C6933B744AB20C89601B013A19C06E2208B4C82B</idno><idno type="DOI">10.1007/978-3-642-17373-8_31</idno><idno type="ChapterID">31</idno><idno type="ChapterID">Chap31</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: In pairing-based cryptography the Generic Group Model (GGM) is used frequently to provide evidence towards newly introduced hardness assumptions. Unfortunately, the GGM does not reflect many known properties of bilinear group settings and thus hardness results in this model are of limited significance. This paper proposes a novel computational model for pairing-based cryptography, called the Semi-Generic Group Model (SGGM), that is closer to the standard model and allows to make more meaningful security guarantees. In fact, the best algorithms currently known for solving pairing-based problems are semi-generic in nature. We demonstrate the usefulness of our new model by applying it to study several important assumptions (BDDH, Co-DH). Furthermore, we develop master theorems facilitating an easy analysis of other (future) assumptions. These master theorems imply that (unless there are better algorithms than the semi-generic ones) great parts of the zoo of novel assumptions over bilinear groups are reducible to just two (more or less) standard assumptions over finite fields. Finally, we examine the appropriateness of the SGGM as a tool for analyzing the security of practical cryptosystems without random oracles by applying it to the BLS signature scheme.</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>I</label><label>I15033</label><label>I16021</label><label>I24067</label><label>I17028</label><label>I14050</label><label>M13003</label><item><term>Computer Science</term></item><item><term>Data Encryption</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Management of Computing and Information Systems</term></item><item><term>Discrete Mathematics in Computer Science</term></item><item><term>Systems and Data Security</term></item><item><term>Applications of 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University</OrgName><OrgAddress><City>Lancaster</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Carnegie Mellon University</OrgName><OrgAddress><City>Pittsburgh</City><State>PA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>University of Surrey</OrgName><OrgAddress><City>Guildford</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgName>Cornell University</OrgName><OrgAddress><City>Ithaca</City><State>NY</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgName>ETH Zurich</OrgName><OrgAddress><City>Zurich</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Stanford University</OrgName><OrgAddress><City>Stanford</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Weizmann Institute of Science</OrgName><OrgAddress><City>Rehovot</City><Country>Israel</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>University of Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>University of California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-642-17373-8</BookID><BookTitle>Advances in Cryptology - ASIACRYPT 2010</BookTitle><BookSubTitle>16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings</BookSubTitle><BookVolumeNumber>6477</BookVolumeNumber><BookSequenceNumber>6477</BookSequenceNumber><BookDOI>10.1007/978-3-642-17373-8</BookDOI><BookTitleID>215167</BookTitleID><BookPrintISBN>978-3-642-17372-1</BookPrintISBN><BookElectronicISBN>978-3-642-17373-8</BookElectronicISBN><BookChapterCount>35</BookChapterCount><BookCopyright><CopyrightHolderName>International Association for Cryptologic Research</CopyrightHolderName><CopyrightYear>2010</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I15033" Priority="1" Type="Secondary">Data Encryption</BookSubject><BookSubject Code="I16021" Priority="2" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I24067" Priority="3" Type="Secondary">Management of Computing and Information Systems</BookSubject><BookSubject Code="I17028" Priority="4" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I14050" Priority="5" Type="Secondary">Systems and Data Security</BookSubject><BookSubject Code="M13003" Priority="6" Type="Secondary">Applications of Mathematics</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Masayuki</GivenName><FamilyName>Abe</FamilyName></EditorName><Contact><Email>abe.masyuki@lab.ntt.co.jp</Email></Contact></Editor><Affiliation ID="Aff16"><OrgName> </OrgName><OrgAddress><Street>3-9-11 Midori-cho, Musashino-shi</Street><Postcode>180-8585</Postcode><City>Tokyo</City><Country>Japan</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part10"><PartInfo TocLevels="0"><PartID>10</PartID><PartSequenceNumber>10</PartSequenceNumber><PartTitle>Models, Notions, and Assumptions</PartTitle><PartChapterCount>3</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Advances in Cryptology - ASIACRYPT 2010</BookTitle></PartContext></PartInfo><Chapter ID="Chap31" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>31</ChapterID><ChapterDOI>10.1007/978-3-642-17373-8_31</ChapterDOI><ChapterSequenceNumber>31</ChapterSequenceNumber><ChapterTitle Language="En">The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</ChapterTitle><ChapterFirstPage>539</ChapterFirstPage><ChapterLastPage>556</ChapterLastPage><ChapterCopyright><CopyrightHolderName>International Association for Cryptologic Research</CopyrightHolderName><CopyrightYear>2010</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>10</PartID><BookID>978-3-642-17373-8</BookID><BookTitle>Advances in Cryptology - ASIACRYPT 2010</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff17"><AuthorName DisplayOrder="Western"><GivenName>Tibor</GivenName><FamilyName>Jager</FamilyName></AuthorName><Contact><Email>tibor.jager@rub.de</Email></Contact></Author><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Andy</GivenName><FamilyName>Rupp</FamilyName></AuthorName><Contact><Email>andy.rupp@rub.de</Email></Contact></Author><Affiliation ID="Aff17"><OrgDivision>Horst Görtz Institute for IT Security</OrgDivision><OrgName>Ruhr-University Bochum</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgName>University of Trier</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>In pairing-based cryptography the Generic Group Model (GGM) is used frequently to provide evidence towards newly introduced hardness assumptions. Unfortunately, the GGM does not reflect many known properties of bilinear group settings and thus hardness results in this model are of limited significance. This paper proposes a novel computational model for pairing-based cryptography, called the Semi-Generic Group Model (SGGM), that is closer to the standard model and allows to make more meaningful security guarantees. In fact, <Emphasis Type="Italic">the best algorithms currently known for solving pairing-based problems are semi-generic</Emphasis> in nature. We demonstrate the usefulness of our new model by applying it to study several important assumptions (BDDH, Co-DH). Furthermore, we develop master theorems facilitating an easy analysis of other (future) assumptions. These master theorems imply that (unless there are better algorithms than the semi-generic ones) great parts of the zoo of novel assumptions over bilinear groups are reducible to just <Emphasis Type="Italic">two</Emphasis> (more or less) standard assumptions over finite fields. Finally, we examine the appropriateness of the SGGM as a tool for analyzing the security of <Emphasis Type="Italic">practical</Emphasis> cryptosystems without random oracles by applying it to the BLS signature scheme.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Restricted models of computation</Keyword><Keyword>generic groups</Keyword><Keyword>semi-generic group model</Keyword><Keyword>cryptographic assumptions</Keyword><Keyword>master theorems</Keyword><Keyword>provable security</Keyword><Keyword>pairing-based cryptography</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>This is an extended abstract, see [20] for the full version. This research has been supported by the European Community (FP7/2007-2013) under grant agreement number ICT-2007-216646 - European Network of Excellence in Cryptology II (ECRYPT II).</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</title></titleInfo><name type="personal"><namePart type="given">Tibor</namePart><namePart type="family">Jager</namePart><affiliation>Horst Görtz Institute for IT Security, Ruhr-University Bochum, Germany</affiliation><affiliation>E-mail: tibor.jager@rub.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Andy</namePart><namePart type="family">Rupp</namePart><affiliation>University of Trier, Germany</affiliation><affiliation>E-mail: andy.rupp@rub.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2010</dateIssued><copyrightDate encoding="w3cdtf">2010</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: In pairing-based cryptography the Generic Group Model (GGM) is used frequently to provide evidence towards newly introduced hardness assumptions. Unfortunately, the GGM does not reflect many known properties of bilinear group settings and thus hardness results in this model are of limited significance. This paper proposes a novel computational model for pairing-based cryptography, called the Semi-Generic Group Model (SGGM), that is closer to the standard model and allows to make more meaningful security guarantees. In fact, the best algorithms currently known for solving pairing-based problems are semi-generic in nature. We demonstrate the usefulness of our new model by applying it to study several important assumptions (BDDH, Co-DH). Furthermore, we develop master theorems facilitating an easy analysis of other (future) assumptions. These master theorems imply that (unless there are better algorithms than the semi-generic ones) great parts of the zoo of novel assumptions over bilinear groups are reducible to just two (more or less) standard assumptions over finite fields. Finally, we examine the appropriateness of the SGGM as a tool for analyzing the security of practical cryptosystems without random oracles by applying it to the BLS signature scheme.</abstract><relatedItem type="host"><titleInfo><title>Advances in Cryptology - ASIACRYPT 2010</title><subTitle>16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Masayuki</namePart><namePart type="family">Abe</namePart><affiliation> , 3-9-11 Midori-cho, Musashino-shi, 180-8585, Tokyo, Japan</affiliation><affiliation>E-mail: abe.masyuki@lab.ntt.co.jp</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2010</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I15033">Data Encryption</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I24067">Management of Computing and Information Systems</topic><topic authority="SpringerSubjectCodes" authorityURI="I17028">Discrete Mathematics in Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I14050">Systems and Data Security</topic><topic authority="SpringerSubjectCodes" authorityURI="M13003">Applications of Mathematics</topic></subject><identifier type="DOI">10.1007/978-3-642-17373-8</identifier><identifier type="ISBN">978-3-642-17372-1</identifier><identifier type="eISBN">978-3-642-17373-8</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">215167</identifier><identifier type="BookID">978-3-642-17373-8</identifier><identifier type="BookChapterCount">35</identifier><identifier type="BookVolumeNumber">6477</identifier><identifier type="BookSequenceNumber">6477</identifier><identifier type="PartChapterCount">3</identifier><part><date>2010</date><detail type="part"><title>Models, Notions, and Assumptions</title></detail><detail type="volume"><number>6477</number><caption>vol.</caption></detail><extent unit="pages"><start>539</start><end>556</end></extent></part><recordInfo><recordOrigin>International Association for Cryptologic Research, 2010</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart type="family">Hutchison</namePart><affiliation>Lancaster University, Lancaster, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Takeo</namePart><namePart type="family">Kanade</namePart><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moni</namePart><namePart type="family">Naor</namePart><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart type="family">Nierstrasz</namePart><affiliation>University of Bern, Bern, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu Rangan</namePart><affiliation>Indian Institute of Technology, Madras, India</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Steffen</namePart><affiliation>University of Dortmund, Dortmund, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Madhu</namePart><namePart type="family">Sudan</namePart><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Demetri</namePart><namePart type="family">Terzopoulos</namePart><affiliation>University of California, Los Angeles, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Doug</namePart><namePart type="family">Tygar</namePart><affiliation>University of California, Berkeley, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moshe</namePart><namePart type="given">Y.</namePart><namePart type="family">Vardi</namePart><affiliation>Rice University, Houston, TX, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Weikum</namePart><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2010</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>International Association for Cryptologic Research, 2010</recordOrigin></recordInfo></relatedItem><identifier type="istex">C6933B744AB20C89601B013A19C06E2208B4C82B</identifier><identifier type="DOI">10.1007/978-3-642-17373-8_31</identifier><identifier type="ChapterID">31</identifier><identifier type="ChapterID">Chap31</identifier><accessCondition type="use and reproduction" contentType="copyright">International Association for Cryptologic Research, 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