Updated on 2025/09/05

写真b

 
YASUDA Masaya
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Doctoral Program in Mathematics
Graduate School of Science Master's Program in Mathematics
Title*
Professor
Degree
博士（数理科学） （ 東京大学 ）
Contact information
Mail Address
Research Interests

  • 格子基底簡約

  • 準同型暗号

  • 楕円曲線暗号

  • 格子暗号

  • 暗号数理

    • Campus Career*
    • 4 2022 - Present 
      College of Science   Department of Mathematics   Professor
    • 4 2022 - Present 
      Graduate School of Science   Master's Program in Mathematics   Professor
    • 4 2022 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Professor
    • 4 2020 - 3 2022 
      College of Science   Department of Mathematics   Associate Professor
    • 4 2020 - 3 2022 
      Graduate School of Science   Master's Program in Mathematics   Associate Professor
    • 4 2020 - 3 2022 
      Graduate School of Science   Doctoral Program in Mathematics   Associate Professor

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    Profile
    数学に関係する数理暗号の解読法の探索や安全性解析について研究しています。具体的には、楕円曲線暗号の安全性を支える楕円曲線離散対数問題や、格子暗号の安全性を支える最短ベクトル問題などの格子問題の代数的なアプローチによる解読法について興味を持っています。また、暗号化したまま加算や乗算が可能な準同型暗号のプライバシー保護データ利活用分野への応用にも取り組んでいます。
     

    Research Areas

    • Informatics / Information security  / 暗号解析

    • Natural Science / Algebra

    Research History

    • 4 2022 - Present 
      Rikkyo University

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    • 4 2020 - Present 
      Kyushu University   Institute of Mathematics for Industry   Guest Professor

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    • 4 2020 - 3 2022 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Associate Professor

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    • 4 2020 - 3 2022 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Associate Professor

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    • 4 2015 - 3 2020 
      Kyushu University

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    • 9 2007 - 3 2015 
      株式会社富士通研究所   セキュアコンピューティング研究部   研究員

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    • 4 2007 - 8 2007 
      東京大学大学院   数理科学研究科   研究生

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    Education

    • 4 2004 - 3 2007 
      東京大学大学院   数理科学研究科 博士課程

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    • 4 2002 - 3 2004 
      東京大学大学院   数理科学研究科 修士課程

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    • 4 1998 - 3 2002 
      Kyoto University   Faculty of Science

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    Committee Memberships

    • 2017 - Present 
      電子情報通信学会   英文論文誌小特集号編集委員会 編集委員

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      Committee type：Academic society

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    • 2016 - Present 
      電子情報通信学会   情報セキュリティ研究会（ISEC）の専門委員

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      Committee type：Academic society

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    • 2013 - Present 
      CRYPTREC暗号技術調査WG（暗号解析評価）における委員

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      Committee type：Academic society

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    Awards

    • 2013  
      暗号と情報セキュリティシンポジウム（SCIS2012）イノベーション論文賞 
       
      安田雅哉

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    Papers

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    Misc.

    • 有限体上の楕円曲線の積によるAbel曲⾯のBrauer群の位数計算

      片山瑛, 安田雅哉

      ⽇本応⽤数理学会第21回研究部会連合発表会   3 2025

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      Authorship：Last author   Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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    • FALCONの安全性証明に向けたマスキング実装の改良

      片山瑛, 中邑聡史, 安田雅哉

      2025年暗号と情報セキュリティシンポジウム（SCIS2025）4A2-5   1 2025

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      Authorship：Last author   Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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    • 自己双対型PotBKZ基底簡約の提案とBKZとの比較

      佐藤新, 安田雅哉

      2025年暗号と情報セキュリティシンポジウム（SCIS2025）2D2-1   1 2025

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      Authorship：Last author   Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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    • 同種写像問題に対する攻撃法の比較：自己準同型環計算による攻撃 vs. 中間一致攻撃

      神戸祐太, 片山瑛, 相川勇輔, 石原侑樹, 安田 雅哉, 横山和弘

      2025年暗号と情報セキュリティシンポジウム（SCIS2025）1D1-5   1 2025

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      Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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    • Schoofアルゴリズムによる超特異楕円曲線の自己準同型写像のトレース計算の高速化

      小峰 和樹, 片山瑛, 安田雅哉

      2025年暗号と情報セキュリティシンポジウム（SCIS2025）1D1-4   1 2025

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    • 同種写像グラフ上のサイクル探索による同種写像求解法の高効率化

      神戸祐太, 片山瑛, 相川勇輔, 石原侑樹, 安田雅哉, 横山和弘

      2024年暗号と情報セキュリティシンポジウム（SCIS2024）   1 2024

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      Language：Japanese  

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    • 近似最近ベクトル探索と埋め込み法を用いた格子による素因数分解法の実装報告

      佐藤新, Auzemery Aurelien, 片山瑛, 安田雅哉

      2024年暗号と情報セキュリティシンポジウム（SCIS2024）   1 2024

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    • FALCON におけるマスキング実装の提案

      片山瑛, 中邑聡史, 上野真奈, 安田雅哉

      2024年暗号と情報セキュリティシンポジウム（SCIS2024）   1 2024

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    • ハイブリッドStreaming法によるCRYSTALS-Dilithiumのリソース最適化

      高橋康, 西田直央, 海上勇二, 豊永三朗, 池松泰彦, 縫田光司, 安田雅哉

      2024年暗号と情報セキュリティシンポジウム（SCIS2024）   1 2024

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    • CSIDHにおける同値な秘密鍵の探索と秘密鍵空間の解析

      高橋康, 安田雅哉

      2023年コンピュータセキュリティシンポジウム（CSS 2023）   11 2023

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      Authorship：Last author   Language：Japanese   Publishing type：Internal/External technical report, pre-print, etc.  

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    • Solving the supersingular isogeny problem over Fp via the Deuring correspondence Peer-reviewed

      Yuta Kambe, Akira Katayama, Yusuke Aikawa, Yuki Ishihara, Masaya Yasuda, Kazuhiro Yokoyama

      5-th International Workshop on Mathematical Cryptology (MathCrypt 2023)   8 2023

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      Authorship：Corresponding author   Language：English   Publishing type：Meeting report  

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    • 有限体上の通常楕円曲線の自己準同型環の生成元計算

      片山瑛, 安田雅哉

      日本応用数理学会第19回研究部会連合発表会 「数論アルゴリズムとその応用」   3 2023

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    • 超特異楕円曲線の自己準同型環計算の実装報告

      神戸祐太, 片山瑛, 相川勇輔, 石原侑樹, 安田雅哉, 横山和弘

      2023年暗号と情報セキュリティシンポジウム（SCIS2023）   1 2023

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    • 探索Module-LWE問題に対する格子攻撃の実験報告

      中邑聡史, 片山瑛, 安田雅哉

      2023年暗号と情報セキュリティシンポジウム（SCIS2023）   1 2023

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      Authorship：Last author   Language：Japanese   Publishing type：Meeting report  

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    • 構成的Deuring対応の計算可能性について

      神戸祐太, 安田雅哉, 横山和弘

      日本応用数理学会2022年度年会「数論アルゴリズムとその応用」（JANT）セッション   9 2022

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    • ρ法による超特異同種写像グラフにおけるサイクル探索

      神戸祐太, 片山瑛, 相川勇輔, 安田雅哉, 横山和弘

      日本応用数理学会2022年度年会「数論アルゴリズムとその応用」（JANT）セッション   9 2022

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    • 有限体上の楕円曲線の積によるアーベル曲面のブラウアー群の位数計算

      片山瑛, 安田雅哉

      日本応用数理学会2022年度年会「数論アルゴリズムとその応用」（JANT）セッション   9 2022

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      Authorship：Last author   Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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    • NTRU格子の拡張と格子攻撃

      中邑聡史, 安田雅哉

      2022年暗号と情報セキュリティシンポジウム（SCIS2022）   1 2022

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    • 適切な素数選択によるKLPTアルゴリズムを利用した同種写像構成計算

      高橋康, 神戸祐太, 安田雅哉, 横山和弘

      2022年暗号と情報セキュリティシンポジウム（SCIS2022）   1 2022

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    • SIKEに対するvOW法の内部関数の新計算手法

      神戸祐太, 高橋康, 相川勇輔, 工藤桃成, 安田雅哉, 高島克幸, 横山和弘

      2022年暗号と情報セキュリティシンポジウム（SCIS2022）   1 2022

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      Authorship：Corresponding author   Publishing type：Meeting report  

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    • Selection of primes in the KLPT algorithm for construction of fast isogeny (poster)

      Yasushi Takahashi, Yuta Kambe, Masaya Yasuda, Kazuhiro Yokoyama

      poster session in IWSEC 2021   9 2021

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      Language：English   Publishing type：Research paper, summary (international conference)  

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    • 探索Ring-LWE問題に対するKannan の埋め込み法の拡張

      中邑聡史, 安田雅哉

      日本応用数理学会2021年度年会「数論アルゴリズムとその応用」（JANT）セッション（オンライン開催）   9 2021

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      Language：Japanese  

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    • Kohel-Lauter-Petit-Tignolアルゴリズムの構成的Deuring対応への適用

      神戸祐太, 相川勇輔, 工藤桃成, 安田雅哉, 高島克幸, 横山和弘

      2021年暗号と情報セキュリティシンポジウム（SCIS2021）   1 2021

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    • 代数構造を持つ格子上の最短ベクトル探索アルゴリズムの開発

      中邑聡史, 安田雅哉

      2021年暗号と情報セキュリティシンポジウム（SCIS2021）   1 2021

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      Language：Japanese   Publishing type：Research paper, summary (national, other academic conference)  

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    • Introduction to algebraic approaches for solving isogeny path-finding problems Invited

      Masaya YASUDA, Kazuhiro YOKOYAMA

      RIMS Conference on Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties   10 2020

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      Authorship：Lead author  

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    • Kohel-Lauter-Petit-Tignolアルゴリズムのsageにおける実装報告

      神戸祐太, 安田雅哉, 横山和弘

      日本応用数理学会2020年度年会（オンライン開催）   8 9 2020

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    • 指数計算法による素体上のECDLP解読の高速化 (第26回日本数式処理学会大会報告)

      横田 祐貴, 工藤 桃成, 安田 雅哉

      数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation24 ( 2 ) 35 - 38   5 2018

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      Language：Japanese   Publisher：日本数式処理学会  

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    • Relation between torsion points and reduction of elliptic curves over number fields (計算代数システムによる新しい数学の開拓と進展)

      Yasuda Masaya

      数理解析研究所講究録 ( 2012 ) 41 - 65   12 2016

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      Language：English   Publisher：京都大学数理解析研究所  

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    • Applications of Fully Homomorphic Encryption

        99 ( 12 ) 1167 - 1175   12 2016

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    • On the Possibility of Recovering Short Generators over Ideal Lattices for Cyclotomic Fields

        116 ( 35 ) 25 - 32   19 5 2016

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    • Comparison of Babai's nearest plane and rounding algorithms in Laine-Lauter's key recovery attack for LWE

      Momonari Kudo, Yang Guo, Masaya Yasuda

      Proceedings of 2016 Symposium on Cryptography and Information Security (SCIS2016)2D4-1   1 2016

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    • Searchable Encryption : A Technology That Enables Searches on Encrypted Data

      KOGURE Jun, SHIMOYAMA Takeshi, YASUDA Masaya

      The Journal of the Institute of Electronics, Information, and Communication Engineers98 ( 3 ) 202 - 206   3 2015

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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    • AI-1-2 Applications of (fully) homomorphic encryption

      Yasuda Masaya

      Proceedings of the IEICE General Conference2015   "SS - 71"   24 2 2015

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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    • Countermeasure to Attack against a Privacy-preserving Biometric Authentication by using Homomorphic Encryption

      SAKEMI Yumi, TAKENAKA Masahiko, TORII Naoya, YASUDA Masaya

      IEICE technical report. Social Implications of Technology and Information Ethics114 ( 116 ) 293 - 300   3 7 2014

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      Biometric authentication attracts much attention because of the reuse problem of IDs and passwords. Recently, privacy-preserving biometric authentication schemes in which authentication process is exectuted on encrypted biometric information by homomorphic-encryption have been proposed. In our previous work, we have shown a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption proposed by Hattori et al. when a binary coding is used. In addition, we have also proposed a countermeasure to our attack. Furthermore, a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption by Yasuda et al. have been proposed. In this paper, we consider about applicability of the proposed countermeasure which verifies whether a feature vector is a binary code or not to our attack against Hattori et al. scheme to Yasuda et al. scheme. As a result, it is difficult to apply the countermeasure to Yasuda et al. scheme. Then, we consider about new countermeasure that uses Xor masking, multiplicative masking and additive masking, respectively.

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    • Vulnerability in a Privacy-preserving Biometric Authentication by using Homomorphic Encryption

      SAKEMI Yumi, TAKENAKA Masahiko, TORII Naoya, YASUDA Masaya

      IEICE technical report. Social Implications of Technology and Information Ethics114 ( 116 ) 287 - 292   3 7 2014

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      Biometric authentication attracts much attention because of the reuse problem of IDs and passwords. Recently, privacy-preserving biometric authentication in which authentication is executed on encrypted biometric information by homomorphic-encryption have been proposed. In our previous work, we have shown a spoofing attack to arbitrary user against a cancelable biometric authentication scheme by using homomorphic encryption proposed by Hattori et al. when binary coding is used. In addition, a recovery attack for encrypted template have been proposed by using our spoofing attack. These attack use a problem in process that calculates a squared euclidean distance between template and biometric information to compare. Therefore, our attack is not applicable to scheme that does not use a squared euclidean distance. This paper shows that an adversary can spoof to an arbitrary users with high probability against a privacy-preserving biometric authentication scheme by Yasuda et al. that uses hamming distance. Furthermore, by extending our proposed spoofing attack, we show that an adversary is able to recover the original biometric information by using the decryption server as a authentication oracle. These proposed attack are applicable if the feature vector is represented by a binary coding.

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    • Countermeasure to Attack against a Privacy-preserving Biometric Authentication by using Homomorphic Encryption

      Yumi Sakemi, Masahiko Takenaka, Naoya Torii, Masaya Yasuda

      IPSJ SIG Notes2014 ( 45 ) 1 - 8   26 6 2014

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      Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

      Biometric authentication attracts much attention because of the reuse problem of IDs and passwords. Recently, privacy-preserving biometric authentication schemes in which authentication process is exectuted on encrypted biometric information by homomorphic-encryption have been proposed. In our previous work, we have shown a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption proposed by Hattori et al. when a binary coding is used. In addition, we have also proposed a countermeasure to our attack. Furthermore, a spoofing attack to arbitrary user and a recovery attack for template against a cancelable biometric authentication scheme based on homomorphic encryption by Yasuda et al. have been proposed. In this paper, we consider about applicability of the proposed countermeasure which verifies whether a feature vector is a binary code or not to our attack against Hattori et al. scheme to Yasuda et al. scheme. As a result, it is difficult to apply the countermeasure to Yasuda et al. scheme. Then, we consider about new countermeasure that uses Xor masking, multiplicative masking and additive masking, respectively.

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    • Vulnerability in a Privacy-preserving Biometric Authentication by using Homomorphic Encryption

      Yumi Sakemi, Masahiko Takenaka, Naoya Torii, Masaya Yasuda

      IPSJ SIG Notes2014 ( 44 ) 1 - 6   26 6 2014

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      Vulnerability in a Privacy-preserving Biometric Authentication by using Homomorphic Encryption

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    • Secret computation of purchase history data using somewhat homomorphic encryption

      Pacific journal of mathematics for industry : PJMI6   37 - 45   2014

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      Language：English   Publisher：Institute of Mathematics for Industry, Kyushu University ; c2014-  

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    • RL-003 A customer information analysis between enterprises using homomorphic encryption

      Yasuda Masaya, Shimoyama Takeshi, Yokoyama Kazuhiro, Kogure Jun

        12 ( 4 ) 15 - 22   20 8 2013

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      Language：Japanese   Publisher：Forum on Information Technology  

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    • A proposal of key binding technology using lattice masking

      SUGIMURA Yuka, YASUDA Masaya, YAMADA Shigefumi, ABE Narishige, SHINZAKI Takashi

        113 ( 138 ) 297 - 304   18 7 2013

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      Recently, the biometric template protection technology has been actively researched in biometrics.In this technology, the enrollment biometric data called a template are protected by some conversion.Among many approaches for the template protection technology, we here focus on the key binding approach. In the key binding approach, helper data is generated from joint data of a user's specific key with user's biometric data, and the user's specific key can be extracted only when the enrolled biometric data and a query data are sufficiently similar.By handling digital signature or document information as a user's specific key, the key binding approach can be applied to the digital signature, and document encryption/decryption.Hence the key binding approach is expected to be applied not only to authentication but also to various application scenarios. While conventional schemes like fuzzy commitment and fuzzy vault schemes use the error correcting code technique to achieve the key binding approach, we present a new scheme using so called the lattice masking.The notion of the lattice masking is derived from a combination of the random masking technique and the lattice theory. In this paper, we describe the feature of our scheme and also introduce a concrete application example.

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    • A proposal of key binding technology using lattice masking

        2013 ( 44 ) 1 - 8   11 7 2013

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    • A proposal of key binding technology using lattice masking

        2013 ( 44 ) 1 - 8   11 7 2013

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    • 楕円曲線暗号の攻撃とその安全性 (Computer Algebra : Design of Algorithms, Implementations and Applications)

      安田 雅哉

      数理解析研究所講究録1814   74 - 84   10 2012

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      Language：Japanese   Publisher：京都大学  

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    • A report on SHARCS 2012

      YASUDA Masaya, IZU Tetsuya, SHIMOYAMA Takeshi, KOGURE Jun

      Technical report of IEICE. ISEC112 ( 39 ) 33 - 38   11 5 2012

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    • On the attack against Gentry's somewhat homomorphic encryption using LLL algorithm (II)

      YAJIMA Jun, YASUDA Masaya, SHIMOYAMA Takeshi, KOGURE Jun

      Technical report of IEICE. ISEC111 ( 285 ) 13 - 17   7 11 2011

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      After Gentry proposed a concrete method for constructing a fully homomorphic encryption scheme, it becomes popular to research on applications with homomorphic encryption schemes. Gentry's construction starts from a somewhat homomorphic encryption (SHE) scheme, which supports limited evaluation over encrypted data. To analyze the relation between its evaluations and security, we attacked the lattice problem ensuring the security of Gentry's SHE scheme. In this paper, we mainly report our experimental results of attacking the lattice problem of 512 dimension using the LLL algorithm.

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    • On the attack against Gentry's somewhat homomorphic encryption using LLL algorithm (II)

      YAJIMA Jun, YASUDA Masaya, SHIMOYAMA Takeshi, KOGURE Jun

      IEICE technical report. Life intelligence and office information systems111 ( 286 ) 13 - 17   7 11 2011

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      After Gentry proposed a concrete method for constructing a fully homomorphic encryption scheme, it becomes popular to research on applications with homomorphic encryption schemes. Gentry's construction starts from a somewhat homomorphic encryption (SHE) scheme, which supports limited evaluation over encrypted data. To analyze the relation between its evaluations and security, we attacked the lattice problem ensuring the security of Gentry's SHE scheme. In this paper, we mainly report our experimental results of attacking the lattice problem of 512 dimension using the LLL algorithm.

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    • On the attack against Gentry's somewhat homomorphic encryption using LLL algorithm

        2011 ( 3 ) 576 - 581   12 10 2011

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    • Experimental Analysis of Cheon's Algorithm against Pairing-friendly Curves

      Tetsuya Izu, Masahiko Takenaka, Masaya Yasuda

        52 ( 9 ) 2652 - 2661   15 9 2011

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    • On the security of the fully-homomorphic encryption scheme based on ideal lattices

      YASUDA Masaya, YAJIMA Jun, SHIMOYAMA Takeshi, KOGURE Jun

      IEICE technical report111 ( 204 ) 43 - 50   2 9 2011

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      A fully-homomorphic encryption is a public-key encryption that allows one to fully interact with encypted data without being able to decrypt, and it is expected to be applied for the area of cloud computing. In this paper, we consider the security of the fully-homomorphic encryption scheme based on ideal lattices. The security of this scheme relies on the infeasibility of the SSSP and the BDDP, which are computational mathematical problems. We here study on the relation between the parameters of this scheme and the infeasibility of the BDDP.

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    • Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library (Part II)

        2011 ( 24 ) 1 - 8   5 7 2011

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    • Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library (Part II)

        2011 ( 24 ) 1 - 8   5 7 2011

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    • Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library (Part II)

      SAKEMI Yumi, IZU Tetsuya, TAKENAKA Masahiko, YASUDA Masaya

      IEICE technical report111 ( 125 ) 151 - 158   5 7 2011

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      Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a positive integer α from elements G, αG, α^dG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r-1. In 2010, Sakemi et al. implemented Cheon's algorithm for solving DLPwAI, and solved a DLPwAI in a group with 128-bit order r in about 131 hours with a single core on an elliptic curve defined over a prime finite field which is used in the TinyTate library for embedded cryptographic devices. However, since their implementation was based on Shanks' Baby-step Giant-step (BSGS) algorithm as a sub-algorithm, it required a large amount of memory (246 GByte) so that it was concluded that applying other DLPwAIs with larger parameter is infeasible. In this article, we implemented Cheon's algorithm based on Pollard's ρ-algorithm in order to reduce the required memory. As a result, we have succeeded solving the same DLPwAI in about 136 hours by a single core with less memory (0.5 MByte).

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    • On random walks of Pollard's rho method for the ECDLP on Koblitz curves

      JMI : journal of math-for-industry3 ( 0 ) 107 - 112   2011

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      Language：English   Publisher：Faculty of Mathematics, Kyushu University  

      Pollard's rho method is the asymptotically fastest known attack for the elliptic curve discrete logarithm problem (ECDLP) except special cases. It works by giving a pseudo-random sequence defined by an iteration function and then detecting a collision in the sequence. We note that the number of iterations before obtaining a collision is significant for the running time of the rho method and depends on the choice of an iteration function. For many iteration functions suitable for the ECDLP on elliptic curves except Koblitz curves, the number of iterations before obtaining a collision had been investigated. In this paper, we propose a new iteration function on Koblitz curves which is an extension of the iteration function proposed by Gallant et al. and analyze the performance on our iteration function experimentally.

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      Other Link： http://hdl.handle.net/2324/20144

    • On the examination on speeding Cheon's algorithm

        2010 ( 2 ) 8p   8 2010

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    • On the proportion of the curves constructed by Brezing-Weng in the pairing-friendly curves

        2010 ( 2 ) 7p   8 2010

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    • DLP with Auxiliary Input and the Security of Cryptographic Protocols

      IZU Tetsuya, TAKENAKA Masahiko, HANAOKA Goichiro, YASUDA Masaya

      IEICE technical report110 ( 114 ) 189 - 194   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The security of publick-key cryptographic protocols are reduced to the infeasibility of underlying mathematical problems. More cryptographic protocols have been designed, more new mathematical problems have been introduced. Especially in paring-based protocols, a various problems related to the Diffie-Hellman problem (Diffie-Hellman related problems) have been used. Compared to the fundamental mathematical problems such as the integer factoring problem or the discrete logarithm problem, the infeasibility of these newly introduced problems are not fully evaluated yet. In 2006, Cheon proposed an algorithm to solve the discrete logarithm problem with auxiliary input (DLPwAI), however, since the problem is tightly related to the Diffie-Hellman related problems, Cheon's algorithm also solves Diffie-Hellman related problems. This manuscript discusses the relation between the security of cryptographic protocols based on Diffie-Hellman related problems and Cheon's algorithm.

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    • On the examination on speeding Cheon's algorithm

      YASUDA Masaya, IZU Tetsuya, TAKENAKA Masahiko

      IEICE technical report110 ( 114 ) 173 - 180   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The security of many cryptographic systems is based on the hardness of the discrete logarithm problem (DLP). In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input, whcich works better than conventional algorithms. In recent years, we reported experimental results on Cheon's algorithm for DLP on an elliptic curve used for pairing-based cryptography. In this paper, we explain some methods of speeding Cheon's algorithm, which were not used in our past experiment. We also describe the effect of speeding Cheon's algorithm.

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    • DLP with Auxiliary Input and the Security of Cryptographic Protocols

      IZU Tetsuya, TAKENAKA Masahiko, HANAOKA Goichiro, YASUDA Masaya

      IEICE technical report110 ( 113 ) 189 - 194   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The security of publick-key cryptographic protocols are reduced to the infeasibility of underlying mathematical problems. More cryptographic protocols have been designed, more new mathematical problems have been introduced. Especially in paring-based protocols, a various problems related to the Diffie-Hellman problem (Diffie-Hellman related problems) have been used. Compared to the fundamental mathematical problems such as the integer factoring problem or the discrete logarithm problem, the infeasibility of these newly introduced problems are not fully evaluated yet. In 2006, Cheon proposed an algorithm to solve the discrete logarithm problem with auxiliary input (DLPwAI), however, since the problem is tightly related to the Diffie-Hellman related problems, Cheon's algorithm also solves Diffie-Hellman related problems. This manuscript discusses the relation between the security of cryptographic protocols based on Diffie-Hellman related problems and Cheon's algorithm.

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    • On the examination on speeding Cheon's algorithm

      YASUDA Masaya, IZU Tetsuya, TAKENAKA Masahiko

      IEICE technical report110 ( 113 ) 173 - 180   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The security of many cryptographic systems is based on the hardness of the discrete logarithm problem (DLP). In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input, whcich works better than conventional algorithms. In recent years, we reported experimental results on Cheon's algorithm for DLP on an elliptic curve used for pairing-based cryptography. In this paper, we explain some methods of speeding Cheon's algorithm, which were not used in our past experiment. We also describe the effect of speeding Cheon's algorithm.

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    • On the proportion of the curves constructed by Brezing-Weng in the pairing-friendly curves

      YASUDA Takanori, YASUDA Masaya, SHIMOYAMA Takeshi, KOGURE Jun

      IEICE technical report110 ( 113 ) 181 - 187   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The Brezing-Weng curves are a kind of pairing-friendly curves. In this paper, we investigate the proportion of the Brezing-Weng curves with a maximal cyclic subgroup of at most 160 bit prime order in the all pairing-friendly curves with the same condition. The number of the all pairing-friendly curves is given by the experiment and theoretical expectation.

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    • On the proportion of the curves constructed by Brezing-Weng in the pairing-friendly curves

      YASUDA Takanori, YASUDA Masaya, SHIMOYAMA Takeshi, KOGURE Jun

      IEICE technical report110 ( 114 ) 181 - 187   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The Brezing-Weng curves are a kind of pairing-friendly curves. In this paper, we investigate the proportion of the Brezing-Weng curves with a maximal cyclic subgroup of at most 160 bit prime order in the all pairing-friendly curves with the same condition. The number of the all pairing-friendly curves is given by the experiment and theoretical expectation.

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    • On the proportion of the curves constructed by Brezing-Weng in the pairing-friendly curves

      YASUDA Takanori, YASUDA Masaya, SHIMOYAMA Takeshi, KOGURE Jun

      IEICE technical report110 ( 115 ) 181 - 187   24 6 2010

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      Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

      The Brezing-Weng curves are a kind of pairing-friendly curves. In this paper, we investigate the proportion of the Brezing-Weng curves with a maximal cyclic subgroup of at most 160 bit prime order in the all pairing-friendly curves with the same condition. The number of the all pairing-friendly curves is given by the experiment and theoretical expectation.

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    • 楕円曲線暗号の攻撃評価

      安田 雅哉, 伊豆 哲也, 下山 武司, 小暮 淳

      全国大会講演論文集72   569 - 570   8 3 2010

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    Books and Other Publications

    • 代数曲線の計算理論と暗号への応用

      相川勇輔, 神戸祐太, 工藤桃成, 高島克幸, 安田雅哉（ Role： Joint author ,  第1章と第2章）

      日本数学会・数学メモアール第10巻  10 2024 

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    • Theory and Practice of Cryptography: Understanding Security in the Quantum Era

      （ Role： Joint author）

      5 2024 

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    • NIST標準化の格子暗号方式の紹介

      安田雅哉（ Role： Sole author ,  会誌11月号（特集「耐量子計算機暗号の最新動向」における記事））

      電子情報通信学会  11 2023 

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    • 格子暗号解読のための数学的基礎：格子基底簡約アルゴリズム入門

      青野良範, 安田雅哉（ Role： Joint author）

      近代科学社  9 2019 

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    Presentations

    • 格子アルゴリズムと暗号解読への応用 Invited

      安田雅哉

      京都大学MACSセミナー「暗号理論の数理と社会実装」  21 11 2024 

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      Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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    • 超特異楕円曲線の自己準同型環計算と同種写像問題の求解 Invited

      安田雅哉

      名城大学理工学部数学科・談話会  24 5 2024 

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      Language：Japanese   Presentation type：Oral presentation (general)  

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    • 格子ベース準同型暗号の応用と格子基底簡約

      安田雅哉

      研究集会「暗号と量子計算」(東京工業大学)  21 12 2023 

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      Event date： 21 12 2023 - 21 12 2023

      Language：Japanese   Presentation type：Oral presentation (general)  

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    • 格子問題の求解アルゴリズムとその応用

      安田雅哉

      2023年度東大数理・情報数学セミナー  11 2023 

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      Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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    • 数理暗号の紹介：格子暗号と同種写像暗号 Invited

      安田雅哉

      日本数学会・秋季総合分科会・代数学（特別講演）  20 9 2023 

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      Language：Japanese   Presentation type：Oral presentation (invited, special)  

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    • Lattice Basis Reduction and Its Application to Cryptanalysis

      Masaya Yasuda

      Mathematics for Industry in the Asia Pacific Area at SIAM Conference on Computational Science and Engineering (CSE23))  2 3 2023 

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      Language：English   Presentation type：Symposium, workshop panel (nominated)  

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    • 格子基底簡約とLWE/NTRU問題に対する格子攻撃 Invited

      安田雅哉

      九大IMI共同利用「耐量子計算機暗号と量子情報の数理」  3 8 2022 

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      Event date： 1 8 2022 - 4 8 2022

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    • 最短ベクトル問題を解くための格子基底簡約とその大規模並列化 Invited

      安田雅哉

      研究集会「量子暗号理論と耐量子暗号」（早稲田大学・Zoomによるオンライン開催）  18 3 2022 

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      Event date： 18 3 2022 - 18 3 2022

      Language：Japanese   Presentation type：Oral presentation (invited, special)  

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    • 現代の暗号技術を支える数学

      安田 雅哉

      KISTEC教育講座「情報セキュリティ理解のための先端暗号技術入門」  25 11 2021 

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      Event date： 25 11 2021 - 30 11 2021

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    • Introduction to lattice basis reduction and its massive parallelization Invited

      Masaya Yasuda

      Design and Evaluation for New-generation Cryptography  16 11 2021 

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      Event date： 16 11 2021 - 17 11 2021

      Language：Japanese   Presentation type：Oral presentation (invited, special)  

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    • Introduction to lattice basis reduction for solving the shortest vector problem

      Masaya Yasuda

      Mathematics of quasiperiodic order and related topics  8 11 2021 

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      Event date： 8 11 2021 - 10 11 2021

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    Research Projects

    • Developments of theory of hyperplane arrangements and application to black box of AI

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

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      4 2025 - 3 2030

      Grant number：25H00399

      Grant amount：\201630000 （ Direct Cost: \155100000 、 Indirect Cost：\46530000 ）

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    • Investigation and exploration of mathematical solutions for isogeny problems with auxiliary information

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

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      6 2023 - 3 2026

      Grant number：23K18469

      Grant amount：\6500000 （ Direct Cost: \5000000 、 Indirect Cost：\1500000 ）

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    • 格子暗号の大規模解読実験と解読計算量評価

      日本学術振興会  科学研究費助成事業 基盤研究(B) 

      安田 雅哉, 鍛冶 静雄, 藤澤 克樹, 青野 良範

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      4 2020 - 3 2024

      Grant number：20H04142

      Grant amount：\17550000 （ Direct Cost: \13500000 、 Indirect Cost：\4050000 ）

      量子計算機による暗号解読にも耐性のある耐量子計算機暗号（Post-Quantum Cryptography）の有力候補である格子暗号の安全性は、格子上の最短ベクトル問題（SVP, Shortest Vector Problem）や最近ベクトル問題（CVP, Closest Vector Problem）などの格子問題の計算困難性に基づく。本年度（2021年度）は、格子問題に対する解読アルゴリズムの大規模並列化フレームワークの設計・開発・求解実験に成功した。具体的には、昨年度開発した並列化システムをベースに、格子問題に対する効率的な求解法である格子基底簡約・列挙法・篩法の異なる3つの格子アルゴリズムを大規模計算機システム上で同時に動作可能とする並列化フレームワークCMAP-LAP（Configurable Massively Parallel Solver for Lattice Problems）の開発に成功した。また、今回開発したCMAP-LAPフレームワークにおける格子基底簡約としてDeepBKZアルゴリズムを採用し、最大100,032並列プロセスを持つ大規模計算機上で、130次元程度のSVPを約100時間以内で求解可能であることを実験的に示した。本研究成果は、高性能計算分野のトップ国際会議の1つであるHigh Performance Computing（HiPC2021）に採択された。また、格子暗号方式の安全性に直接関係するLWEやNTRU問題に対して、新しい攻撃手法を提案すると共に、求解実験によりその有効性を示した。LWEやNTRU問題に対する解析結果は、暗号分野における多数の査読付き国際会議・国際雑誌に採択された。

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    • 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

      日本学術振興会  科学研究費助成事業 挑戦的研究(萌芽) 

      安田 雅哉

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      6 2019 - 3 2022

      Grant number：19K22847

      Grant amount：\6500000 （ Direct Cost: \5000000 、 Indirect Cost：\1500000 ）

      近年、超特異楕円曲線間の同種写像の列を利用した同種写像暗号は、量子計算機による暗号解読でも耐性のある耐量子計算機暗号技術（Post-Quantum Cryptography）の1つとして期待されている。具体的には、米国標準技術研究所NISTが2016年以降進めている耐量子計算機暗号の標準化プロセスにおいて、超特異楕円曲線上の鍵交換アルゴリズムSIKE（Supersingular Isogeny Key Encapsulation）は2020年7月にThird Roundに進むことが許可された15方式の内の1つに選出された。同種写像暗号の安全性は、2つの同種な楕円曲線を結ぶ同種写像の列を具体的に計算する同種写像問題の計算量困難性に依存する。一方、楕円曲線論において、有限体上の超特異楕円曲線全体と四元数環におけるmaximal order全体が1対1に対応するDeuring対応が知られている。本年度（2021年度）は、超特異楕円曲線のDeuring対応下における四元数環上の同種写像問題を効率的に解くKohel-Lauter-Petit-Tignol（KLPT）アルゴリズムの高速実装に成功した。また、実装開発したKLPTアルゴリズムに加えて、超特異楕円曲線のねじれ点の高速探索法を提案し、与えられたイデアルにDeuring対応する超特異楕円曲線を求める構成的Deuring対応問題を実用的な処理時間で求解可能であることを示した。（近年、構成的Deuring対応計算は超特異楕円曲線の同種写像列を利用した署名方式などで非常に注目されている。）これらの研究成果は、多数の国内会議で発表すると共に、査読付きの国際会議・国際雑誌にも採択された。

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    • Security Analysis of Post-Quantum Cryptography

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) 

      Tsuyoshi Takagi

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      4 2017 - 3 2020

      Grant number：17K00185

      Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）

      In this research project, we conducted research on the derivation of secure cryptographic parameters for the standardization of post-quantum cryptography (PQC). In particular, we evaluated the difficulty of the Learning with Errors (LWE) problem, which is the basis of the security of lattice-based cryptography, and we achieved a world record for solving the 70-dimensional LWE problem in 32.7 CPU hours in the LWE challenge hosted by Darmstadt University of Technology. We also constructed an efficient key exchange scheme based on the difficulty of the ring-LWE problem and proposed cryptographic parameters to achieve the security level of the NIST PQC standardization project. Furthermore, the security of various attack methods against lattice-based cryptography (modulus switching attack, key reuse attack, etc.) was evaluated.

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    • Evaluation of the complexity of solving LWE problems and establishment of setting method of secure parameters for lattice-based homomorphic encryption

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      Yasuda Masaya

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      4 2016 - 3 2020

      Grant number：16H02830

      Grant amount：\14040000 （ Direct Cost: \10800000 、 Indirect Cost：\3240000 ）

      Lattice-based cryptography is a next-generation cryptography that is resistant to quantum computers and is also applicable to construction of high-functional cryptography such as homomorphic encryption. In particular, LWE-based schemes have excellent processing performance. The security of lattice-based cryptography is based on the computational hardness of lattice problems such as the shortest vector problem, but these problems are NP-hard and only known as asymptotic complexity. In this research, we had developed new algorithms to efficiently solve lattice problems such as the shortest vector and the LWE problems, and also evaluated their performance by experiments. Furthermore, we had implemented LWE-based homomorphic encryption schemes and demonstrated the performance in concrete applications such as secure matrix multiplications and secure statistical processing.

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