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タイトル: | Introduction to algebraic approaches for solving isogeny path-finding problems (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties) |
著者: | FUKASAKU, Ryoya IKEMATSU, Yasuhiko KUDO, Momonari YASUDA, Masaya YOKOYAMA, Kazuhiro |
キーワード: | 14G50 94A60 Elliptic curves Isogenies Isogeny problems Gröbner basis computation |
発行日: | Jun-2022 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B90 |
開始ページ: | 169 |
終了ページ: | 184 |
抄録: | 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. |
著作権等: | © 2022 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved. Printed in Japan. |
URI: | http://hdl.handle.net/2433/276280 |
出現コレクション: | B90 Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties |
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