2022 Fiscal Year Final Research Report
Exploration for mathematical attacks against isogeny-based cryptography and their complexity analysis
| Project/Area Number |
19K22847
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Review Section |
Medium-sized Section 60:Information science, computer engineering, and related fields
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| Research Institution | Rikkyo University (2020-2022)
Kyushu University (2019) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
高島 克幸 早稲田大学, 教育・総合科学学術院, 教授 (70723964)
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| Project Period (FY) |
2019-06-28 – 2023-03-31
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| Keywords | 同種写像暗号 / 楕円曲線 / 同種写像問題 / Deuring対応 / 耐量子計算機暗号 / 超特異楕円曲線 / 自己準同型環 / 四元数環 |
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| Outline of Final Research Achievements |
Isogeny-based cryptography is one of the candidates for quantum-safe cryptography. In this research, we developed several mathematical attacks against isogeny problems that support the security of isogeny-based cryptography. We also analyzed their computational complexity based on implementation results. Specifically, we reduced the general isogeny problem to a system of algebraic equations, and solved the system using Groebner basis calculation algorithms. We also reported the running time for breaking SIKE by our method. Furthermore, we succeeded in speeding up the constructive Deuring correspondence calculation for supersingular elliptic curves over finite fields. We also developed and implemented an algorithm for computing the endomorphism ring of a supersingular elliptic curve, which is equivalent to solving the isogeny path-finding problem.
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| Free Research Field |
暗号数理
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では, 耐量子計算機暗号候補の1つである同種写像暗号の安全性を支える同種写像計算問題に対して, 代数的手法に基づく解読実験によって多角的に安全性解析を行った．今回得られた解読手法と解析結果は, 同種写像暗号における暗号方式として安全なパラメータの選択時に活用することができる．特に, 本研究による多角的な安全性解析は, 同種写像暗号がどの程度安全か評価するための学術的データを与えるため, 耐量子計算機暗号としての同種写像暗号の標準化活動への貢献が期待できる．
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