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dc.contributor.author | FUKASAKU, Ryoya | en |
dc.contributor.author | IKEMATSU, Yasuhiko | en |
dc.contributor.author | KUDO, Momonari | en |
dc.contributor.author | YASUDA, Masaya | en |
dc.contributor.author | YOKOYAMA, Kazuhiro | en |
dc.date.accessioned | 2022-09-14T08:23:09Z | - |
dc.date.available | 2022-09-14T08:23:09Z | - |
dc.date.issued | 2022-06 | - |
dc.identifier.uri | http://hdl.handle.net/2433/276280 | - |
dc.description.abstract | The isogeny path-finding is a computational problem that finds an isogeny connecting two given isogenous elliptic curves. The hardness of the isogeny path-finding problem supports the fundamental security of isogeny-based cryptosystems. In this paper, we introduce an algebraic approach for solving the isogeny path-finding problem. The basic idea is to reduce the isogeny problem to a system of algebraic equations using modular polynomials, and to solve the system by Gröbner basis computation. We report running time of the algebraic approach for solving the isogeny path-finding problem of 3-power isogeny degrees on supersingular elliptic curves. This is a brief summary of [16] with implementation codes. | en |
dc.language.iso | eng | - |
dc.publisher | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.publisher.alternative | 京都大学数理解析研究所 | ja |
dc.rights | © 2022 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved. Printed in Japan. | en |
dc.subject | 14G50 | en |
dc.subject | 94A60 | en |
dc.subject | Elliptic curves | en |
dc.subject | Isogenies | en |
dc.subject | Isogeny problems | en |
dc.subject | Gröbner basis computation | en |
dc.subject.ndc | 410 | - |
dc.title | Introduction to algebraic approaches for solving isogeny path-finding problems (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties) | en |
dc.type | departmental bulletin paper | - |
dc.type.niitype | Departmental Bulletin Paper | - |
dc.identifier.ncid | AA12196120 | - |
dc.identifier.jtitle | 数理解析研究所講究録別冊 | ja |
dc.identifier.volume | B90 | - |
dc.identifier.spage | 169 | - |
dc.identifier.epage | 184 | - |
dc.textversion | publisher | - |
dc.sortkey | 11 | - |
dc.address | Faculty of Mathematics, Kyushu University | en |
dc.address | Institute of Mathematics for Industry, Kyushu University | en |
dc.address | Department of Mathematical Informatics, The University of Tokyo | en |
dc.address | Department of Mathematics, Rikkyo University | en |
dc.address | Department of Mathematics, Rikkyo University | en |
dcterms.accessRights | open access | - |
datacite.awardNumber | 19K22847 | - |
datacite.awardNumber | 20K14301 | - |
datacite.awardNumber.uri | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19K22847/ | - |
datacite.awardNumber.uri | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20K14301/ | - |
dc.identifier.pissn | 1881-6193 | - |
dc.identifier.jtitle-alternative | RIMS Kokyuroku Bessatsu | en |
jpcoar.funderName | 日本学術振興会 | ja |
jpcoar.funderName | 日本学術振興会 | ja |
jpcoar.awardTitle | 同種写像暗号に対する数理的技法による解読法の探求と計算量評価 | ja |
jpcoar.awardTitle | 計算代数手法に基づく正標数の代数曲線に関する研究の深化と暗号応用への展望 | ja |
出現コレクション: | B90 Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties |
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