Introduction to algebraic approaches for solving isogeny path-finding problems (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)
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- FUKASAKU, Ryoya
- Faculty of Mathematics, Kyushu University
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- IKEMATSU, Yasuhiko
- Institute of Mathematics for Industry, Kyushu University
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- KUDO, Momonari
- Department of Mathematical Informatics, The University of Tokyo
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- YASUDA, Masaya
- Department of Mathematics, Rikkyo University
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- YOKOYAMA, Kazuhiro
- Department of Mathematics, Rikkyo University
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説明
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.
収録刊行物
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- 数理解析研究所講究録別冊
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数理解析研究所講究録別冊 B90 169-184, 2022-06
Research Institute for Mathematical Sciences, Kyoto University
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詳細情報 詳細情報について
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- CRID
- 1050012003719916288
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- NII書誌ID
- AA12196120
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- HANDLE
- 2433/276280
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- ISSN
- 18816193
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
