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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<front><div type="abstract" xml: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.</div>
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<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>
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<ChapterTitle Language="En">The Semi-Generic Group Model and Applications to Pairing-Based Cryptography</ChapterTitle>
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<FamilyName>Jager</FamilyName>
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<Contact><Email>tibor.jager@rub.de</Email>
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<Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Andy</GivenName>
<FamilyName>Rupp</FamilyName>
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<Contact><Email>andy.rupp@rub.de</Email>
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<Affiliation ID="Aff17"><OrgDivision>Horst Görtz Institute for IT Security</OrgDivision>
<OrgName>Ruhr-University Bochum</OrgName>
<OrgAddress><Country>Germany</Country>
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<Affiliation ID="Aff18"><OrgName>University of Trier</OrgName>
<OrgAddress><Country>Germany</Country>
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<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>
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<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>
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<subTitle>16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings</subTitle>
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