Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures
Identifieur interne : 000039 ( Pmc/Checkpoint ); précédent : 000038; suivant : 000040Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures
Auteurs : Maocai Wang [République populaire de Chine] ; Guangming Dai [République populaire de Chine] ; Kim-Kwang Raymond Choo [République populaire de Chine, États-Unis] ; Prem Prakash Jayaraman [Australie] ; Rajiv Ranjan [Royaume-Uni]Source :
- PLoS ONE [ 1932-6203 ] ; 2016.
Abstract
Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user’s public key based on the user’s identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al.
Url:
DOI: 10.1371/journal.pone.0161857
PubMed: 27564373
PubMed Central: 5001717
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type="wicri:Area/Pmc/Checkpoint">000039</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures</title><author><name sortKey="Wang, Maocai" sort="Wang, Maocai" uniqKey="Wang M" first="Maocai" last="Wang">Maocai Wang</name><affiliation wicri:level="1"><nlm:aff id="aff001"><addr-line>School of Computer, China University of Geosciences, Wuhan, Hubei, China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>School of Computer, China University of Geosciences, Wuhan, Hubei</wicri:regionArea><wicri:noRegion>Hubei</wicri:noRegion></affiliation><affiliation wicri:level="1"><nlm:aff id="aff002"><addr-line>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei, China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei</wicri:regionArea><wicri:noRegion>Hubei</wicri:noRegion></affiliation></author><author><name sortKey="Dai, Guangming" sort="Dai, Guangming" uniqKey="Dai G" first="Guangming" last="Dai">Guangming Dai</name><affiliation wicri:level="1"><nlm:aff id="aff001"><addr-line>School of Computer, China University of Geosciences, Wuhan, Hubei, China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>School of Computer, China University of Geosciences, Wuhan, Hubei</wicri:regionArea><wicri:noRegion>Hubei</wicri:noRegion></affiliation><affiliation wicri:level="1"><nlm:aff id="aff002"><addr-line>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei, China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei</wicri:regionArea><wicri:noRegion>Hubei</wicri:noRegion></affiliation></author><author><name sortKey="Choo, Kim Kwang Raymond" sort="Choo, Kim Kwang Raymond" uniqKey="Choo K" first="Kim-Kwang Raymond" last="Choo">Kim-Kwang Raymond Choo</name><affiliation wicri:level="1"><nlm:aff id="aff001"><addr-line>School of Computer, China University of Geosciences, Wuhan, Hubei, China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>School of Computer, China University of Geosciences, Wuhan, Hubei</wicri:regionArea><wicri:noRegion>Hubei</wicri:noRegion></affiliation><affiliation wicri:level="1"><nlm:aff id="aff002"><addr-line>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei, China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei</wicri:regionArea><wicri:noRegion>Hubei</wicri:noRegion></affiliation><affiliation wicri:level="2"><nlm:aff id="aff003"><addr-line>Department of Information Systems and Cyber Security, University of Texas at San Antonio, San Antonio, Texas, United States of America</addr-line></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea>Department of Information Systems and Cyber Security, University of Texas at San Antonio, San Antonio, Texas</wicri:regionArea><placeName><region type="state">Texas</region></placeName></affiliation></author><author><name sortKey="Jayaraman, Prem Prakash" sort="Jayaraman, Prem Prakash" uniqKey="Jayaraman P" first="Prem Prakash" last="Jayaraman">Prem Prakash Jayaraman</name><affiliation wicri:level="1"><nlm:aff id="aff004"><addr-line>RMIT University, Melbourne, Australia</addr-line></nlm:aff><country xml:lang="fr">Australie</country><wicri:regionArea>RMIT University, Melbourne</wicri:regionArea><wicri:noRegion>Melbourne</wicri:noRegion></affiliation></author><author><name sortKey="Ranjan, Rajiv" sort="Ranjan, Rajiv" uniqKey="Ranjan R" first="Rajiv" last="Ranjan">Rajiv Ranjan</name><affiliation wicri:level="1"><nlm:aff id="aff005"><addr-line>University of Newcastle, Newcastle, United Kingdom</addr-line></nlm:aff><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>University of Newcastle, Newcastle</wicri:regionArea><wicri:noRegion>Newcastle</wicri:noRegion></affiliation></author></analytic><series><title level="j">PLoS ONE</title><idno type="eISSN">1932-6203</idno><imprint><date when="2016">2016</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user’s public key based on the user’s identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Dong, Mx" uniqKey="Dong M">MX Dong</name></author><author><name sortKey="Ota, K" uniqKey="Ota K">K Ota</name></author><author><name sortKey="Laurence, T" uniqKey="Laurence T">T Laurence</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author><author><name sortKey="Tao, J" uniqKey="Tao J">J. Tao</name></author><author><name sortKey="Ranjan, R" uniqKey="Ranjan R">R. Ranjan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kepler, D" uniqKey="Kepler D">D Kepler</name></author><author><name sortKey="Heasley, P" uniqKey="Heasley P">P Heasley</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhao, J" uniqKey="Zhao J">J. Zhao</name></author><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author><author><name sortKey="Tao, J" uniqKey="Tao J">J. Tao</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chen, D" uniqKey="Chen D">D. Chen</name></author><author><name sortKey="Liu, Z" uniqKey="Liu Z">Z. Liu</name></author><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author><author><name sortKey="Kurze, T" uniqKey="Kurze T">T. Kurze</name></author><author><name sortKey="Tao, J" uniqKey="Tao J">J. Tao</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author><author><name sortKey="Fu, C" uniqKey="Fu C">C Fu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhang, W" uniqKey="Zhang W">W. Zhang</name></author><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author><author><name sortKey="Liu, D" uniqKey="Liu D">D. Liu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name></author><author><name sortKey="Chen, D" uniqKey="Chen D">D. Chen</name></author><author><name sortKey="Hu, Y" uniqKey="Hu Y">Y. Hu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Raymond, C" uniqKey="Raymond C">C Raymond</name></author><author><name sortKey="Kaur, H" uniqKey="Kaur H">H Kaur</name></author><author><name sortKey="Tao, X" uniqKey="Tao X">X Tao</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Raymond Choo, K" uniqKey="Raymond Choo K">K Raymond Choo</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Raymond Choo, K" uniqKey="Raymond Choo K">K Raymond Choo</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Dong, M" uniqKey="Dong M">M Dong</name></author><author><name sortKey="Ota, K" uniqKey="Ota K">K Ota</name></author><author><name sortKey="Laurence, T" uniqKey="Laurence T">T Laurence</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dong, M" uniqKey="Dong M">M Dong</name></author><author><name sortKey="Li, H" uniqKey="Li H">H Li</name></author><author><name sortKey="Ota, K" uniqKey="Ota K">K Ota</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mao, W" uniqKey="Mao W">W Mao</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Joye, M" uniqKey="Joye M">M. Joye</name></author><author><name sortKey="Neven, G" uniqKey="Neven G">G Neven</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Moody, D" uniqKey="Moody D">D. Moody</name></author><author><name sortKey="Peralta, R" uniqKey="Peralta R">R. Peralta</name></author><author><name sortKey="Perlner, R" uniqKey="Perlner R">R. Perlner</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Rahuman, A" uniqKey="Rahuman A">A Rahuman</name></author><author><name sortKey="Athisha, G" uniqKey="Athisha G">G Athisha</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dai, G" uniqKey="Dai G">G Dai</name></author><author><name sortKey="Wang, M" uniqKey="Wang M">M Wang</name></author><author><name sortKey="Peng, L" uniqKey="Peng L">L Peng</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Miller, V" uniqKey="Miller V">V Miller</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Barreto, P" uniqKey="Barreto P">P Barreto</name></author><author><name sortKey="Galbraith, S" uniqKey="Galbraith S">S Galbraith</name></author><author><name sortKey="Eigeartaigh, C" uniqKey="Eigeartaigh C">C Eigeartaigh</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Barreto, P" uniqKey="Barreto P">P Barreto</name></author><author><name sortKey="Galbraith, S" uniqKey="Galbraith S">S Galbraith</name></author><author><name sortKey="Eigeartaigh, C" uniqKey="Eigeartaigh C">C Eigeartaigh</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Miyaji, A" uniqKey="Miyaji A">A Miyaji</name></author><author><name sortKey="Nakabayashi, M" uniqKey="Nakabayashi M">M Nakabayashi</name></author><author><name sortKey="Takano, S" uniqKey="Takano S">S Takano</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Menezes, A" uniqKey="Menezes A">A Menezes</name></author><author><name sortKey="Okamoto, T" uniqKey="Okamoto T">T Okamoto</name></author><author><name sortKey="Vanstone, S" uniqKey="Vanstone S">S Vanstone</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Brezing, F" uniqKey="Brezing F">F Brezing</name></author><author><name sortKey="Weng, A" uniqKey="Weng A">A Weng</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Pollard, J" uniqKey="Pollard J">J Pollard</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Frey G And Ruck, H" uniqKey="Frey G And Ruck H">H Frey G and Ruck</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Perera, C" uniqKey="Perera C">C Perera</name></author><author><name sortKey="Ranjan, R" uniqKey="Ranjan R">R Ranjan</name></author><author><name sortKey="Wang, L" uniqKey="Wang L">L Wang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kolodziej, J" uniqKey="Kolodziej J">J Kolodziej</name></author><author><name sortKey="Khan, S" uniqKey="Khan S">S Khan</name></author><author><name sortKey="Wang, L" uniqKey="Wang L">L Wang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wei, J" uniqKey="Wei J">J Wei</name></author><author><name sortKey="Cai, W" uniqKey="Cai W">W Cai</name></author><author><name sortKey="Wang, L" uniqKey="Wang L">L Wang</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">PLoS One</journal-id><journal-id journal-id-type="iso-abbrev">PLoS ONE</journal-id><journal-id journal-id-type="publisher-id">plos</journal-id><journal-id journal-id-type="pmc">plosone</journal-id><journal-title-group><journal-title>PLoS ONE</journal-title></journal-title-group><issn pub-type="epub">1932-6203</issn><publisher><publisher-name>Public Library of Science</publisher-name><publisher-loc>San Francisco, CA USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">27564373</article-id><article-id pub-id-type="pmc">5001717</article-id><article-id pub-id-type="publisher-id">PONE-D-16-13711</article-id><article-id pub-id-type="doi">10.1371/journal.pone.0161857</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Physical Sciences</subject><subj-group><subject>Mathematics</subject><subj-group><subject>Algebra</subject><subj-group><subject>Algebraic Geometry</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Physical Sciences</subject><subj-group><subject>Mathematics</subject><subj-group><subject>Applied Mathematics</subject><subj-group><subject>Algorithms</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Research and Analysis Methods</subject><subj-group><subject>Simulation and Modeling</subject><subj-group><subject>Algorithms</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Computer and Information Sciences</subject><subj-group><subject>Cryptography</subject></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Physical Sciences</subject><subj-group><subject>Mathematics</subject><subj-group><subject>Cryptography</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Social Sciences</subject><subj-group><subject>Political Science</subject><subj-group><subject>National Security</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Engineering and Technology</subject><subj-group><subject>Equipment</subject></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Engineering and Technology</subject><subj-group><subject>Equipment</subject><subj-group><subject>Safety Equipment</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Medicine and Health Sciences</subject><subj-group><subject>Public and Occupational Health</subject><subj-group><subject>Safety</subject><subj-group><subject>Safety Equipment</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Computer and Information Sciences</subject><subj-group><subject>Information Technology</subject><subj-group><subject>Databases</subject></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v3"><subject>Research and Analysis Methods</subject><subj-group><subject>Database and Informatics Methods</subject></subj-group></subj-group></article-categories><title-group><article-title>Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures</article-title><alt-title alt-title-type="running-head">Constructing Pairing-Friendly EC under Embedding Degree 1 for Securing Critical Infrastructures</alt-title></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="false">http://orcid.org/0000-0002-5495-6417</contrib-id><name><surname>Wang</surname><given-names>Maocai</given-names></name><xref ref-type="aff" rid="aff001"><sup>1</sup></xref><xref ref-type="aff" rid="aff002"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Dai</surname><given-names>Guangming</given-names></name><xref ref-type="aff" rid="aff001"><sup>1</sup></xref><xref ref-type="aff" rid="aff002"><sup>2</sup></xref><xref ref-type="corresp" rid="cor001">*</xref></contrib><contrib contrib-type="author" equal-contrib="yes"><name><surname>Choo</surname><given-names>Kim-Kwang Raymond</given-names></name><xref ref-type="aff" rid="aff001"><sup>1</sup></xref><xref ref-type="aff" rid="aff002"><sup>2</sup></xref><xref ref-type="aff" rid="aff003"><sup>3</sup></xref></contrib><contrib contrib-type="author" equal-contrib="yes"><name><surname>Jayaraman</surname><given-names>Prem Prakash</given-names></name><xref ref-type="aff" rid="aff004"><sup>4</sup></xref></contrib><contrib contrib-type="author" equal-contrib="yes"><name><surname>Ranjan</surname><given-names>Rajiv</given-names></name><xref ref-type="aff" rid="aff005"><sup>5</sup></xref></contrib></contrib-group><aff id="aff001"><label>1</label><addr-line>School of Computer, China University of Geosciences, Wuhan, Hubei, China</addr-line></aff><aff id="aff002"><label>2</label><addr-line>Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, Hubei, China</addr-line></aff><aff id="aff003"><label>3</label><addr-line>Department of Information Systems and Cyber Security, University of Texas at San Antonio, San Antonio, Texas, United States of America</addr-line></aff><aff id="aff004"><label>4</label><addr-line>RMIT University, Melbourne, Australia</addr-line></aff><aff id="aff005"><label>5</label><addr-line>University of Newcastle, Newcastle, United Kingdom</addr-line></aff><contrib-group><contrib contrib-type="editor"><name><surname>Shi</surname><given-names>Yongtang</given-names></name><role>Editor</role><xref ref-type="aff" rid="edit1"></xref></contrib></contrib-group><aff id="edit1"><addr-line>Nankai University, CHINA</addr-line></aff><author-notes><fn fn-type="COI-statement" id="coi001"><p><bold>Competing Interests: </bold>The authors have declared that no competing interests exist.</p></fn><fn fn-type="con"><p><list list-type="simple"><list-item><p><bold>Conceptualization:</bold> MCW GMD.</p></list-item><list-item><p><bold>Data curation:</bold> MCW KRC.</p></list-item><list-item><p><bold>Formal analysis:</bold> MCW RR.</p></list-item><list-item><p><bold>Funding acquisition:</bold> MCW GMD.</p></list-item><list-item><p><bold>Investigation:</bold> MCW.</p></list-item><list-item><p><bold>Methodology:</bold> MCW GMD.</p></list-item><list-item><p><bold>Project administration:</bold> MCW.</p></list-item><list-item><p><bold>Resources:</bold> MCW.</p></list-item><list-item><p><bold>Software:</bold> MCW GMD.</p></list-item><list-item><p><bold>Supervision:</bold> GMD.</p></list-item><list-item><p><bold>Validation:</bold> MCW GMD PPJ.</p></list-item><list-item><p><bold>Visualization:</bold> PPJ RR.</p></list-item><list-item><p><bold>Writing – original draft:</bold> MCW KRC.</p></list-item><list-item><p><bold>Writing – review & editing:</bold> MCW RR.</p></list-item></list></p></fn><corresp id="cor001">* E-mail: <email>cugdgm@126.com</email></corresp></author-notes><pub-date pub-type="collection"><year>2016</year></pub-date><pub-date pub-type="epub"><day>26</day><month>8</month><year>2016</year></pub-date><volume>11</volume><issue>8</issue><elocation-id>e0161857</elocation-id><history><date date-type="received"><day>5</day><month>4</month><year>2016</year></date><date date-type="accepted"><day>13</day><month>8</month><year>2016</year></date></history><permissions><copyright-statement>© 2016 Wang et al</copyright-statement><copyright-year>2016</copyright-year><copyright-holder>Wang et al</copyright-holder><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><license-p>This is an open access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="pone.0161857.pdf"></self-uri><abstract><p>Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user’s public key based on the user’s identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al.</p></abstract><funding-group><award-group id="award001"><funding-source><institution-wrap><institution-id institution-id-type="funder-id">http://dx.doi.org/10.13039/501100001809</institution-id><institution>National Natural Science Foundation of China</institution></institution-wrap></funding-source><award-id>41571403</award-id><principal-award-recipient><contrib-id contrib-id-type="orcid" authenticated="false">http://orcid.org/0000-0002-5495-6417</contrib-id><name><surname>Wang</surname><given-names>Maocai</given-names></name></principal-award-recipient></award-group><award-group id="award002"><funding-source><institution-wrap><institution-id institution-id-type="funder-id">http://dx.doi.org/10.13039/501100002858</institution-id><institution>China Postdoctoral Science Foundation</institution></institution-wrap></funding-source><award-id>2012T50681</award-id><principal-award-recipient><contrib-id contrib-id-type="orcid" authenticated="false">http://orcid.org/0000-0002-5495-6417</contrib-id><name><surname>Wang</surname><given-names>Maocai</given-names></name></principal-award-recipient></award-group><award-group id="award003"><funding-source><institution-wrap><institution-id institution-id-type="funder-id">http://dx.doi.org/10.13039/501100002858</institution-id><institution>China Postdoctoral Science Foundation</institution></institution-wrap></funding-source><award-id>2011M501260</award-id><principal-award-recipient><contrib-id contrib-id-type="orcid" authenticated="false">http://orcid.org/0000-0002-5495-6417</contrib-id><name><surname>Wang</surname><given-names>Maocai</given-names></name></principal-award-recipient></award-group><award-group id="award004"><funding-source><institution-wrap><institution-id institution-id-type="funder-id">http://dx.doi.org/10.13039/501100001809</institution-id><institution>National Natural Science Foundation of China</institution></institution-wrap></funding-source><award-id>61472375</award-id><principal-award-recipient><name><surname>Dai</surname><given-names>Guangming</given-names></name></principal-award-recipient></award-group><funding-statement>This work was supported by National Natural Science Foundation of China (Grant No. 41571403 and 61472375, <ext-link ext-link-type="uri" xlink:href="http://www.nsfc.gov.cn/">http://www.nsfc.gov.cn/</ext-link>) and China Postdoctoral Science Foundation (Grant No. 2012T50681 and 2011M501260, <ext-link ext-link-type="uri" xlink:href="http://www.chinapostdoctor.org.cn">www.chinapostdoctor.org.cn</ext-link>). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.</funding-statement></funding-group><counts><fig-count count="1"></fig-count><table-count count="3"></table-count><page-count count="13"></page-count></counts><custom-meta-group><custom-meta id="data-availability"><meta-name>Data Availability</meta-name><meta-value>All relevant data are within the paper and its Supporting Information files.</meta-value></custom-meta></custom-meta-group></article-meta><notes><title>Data Availability</title><p>All relevant data are within the paper and its Supporting Information files.</p></notes></front></pmc><affiliations><list><country><li>Australie</li><li>Royaume-Uni</li><li>République populaire de Chine</li><li>États-Unis</li></country><region><li>Texas</li></region></list><tree><country name="République populaire de Chine"><noRegion><name sortKey="Wang, Maocai" sort="Wang, Maocai" uniqKey="Wang M" first="Maocai" last="Wang">Maocai Wang</name></noRegion><name sortKey="Choo, Kim Kwang Raymond" sort="Choo, Kim Kwang Raymond" uniqKey="Choo K" first="Kim-Kwang Raymond" last="Choo">Kim-Kwang Raymond Choo</name><name sortKey="Choo, Kim Kwang Raymond" sort="Choo, Kim Kwang Raymond" uniqKey="Choo K" first="Kim-Kwang Raymond" last="Choo">Kim-Kwang Raymond Choo</name><name sortKey="Dai, Guangming" sort="Dai, Guangming" uniqKey="Dai G" first="Guangming" last="Dai">Guangming Dai</name><name sortKey="Dai, Guangming" sort="Dai, Guangming" uniqKey="Dai G" first="Guangming" last="Dai">Guangming Dai</name><name sortKey="Wang, Maocai" sort="Wang, Maocai" uniqKey="Wang M" first="Maocai" last="Wang">Maocai Wang</name></country><country name="États-Unis"><region name="Texas"><name sortKey="Choo, Kim Kwang Raymond" sort="Choo, Kim Kwang Raymond" uniqKey="Choo K" first="Kim-Kwang Raymond" last="Choo">Kim-Kwang Raymond Choo</name></region></country><country name="Australie"><noRegion><name sortKey="Jayaraman, Prem Prakash" sort="Jayaraman, Prem Prakash" uniqKey="Jayaraman P" first="Prem Prakash" last="Jayaraman">Prem Prakash Jayaraman</name></noRegion></country><country name="Royaume-Uni"><noRegion><name sortKey="Ranjan, Rajiv" sort="Ranjan, Rajiv" uniqKey="Ranjan R" first="Rajiv" last="Ranjan">Rajiv Ranjan</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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