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Theoretical security analysis for multivariate cryptography

Research Project

Project/Area Number 20K19802
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 60070:Information security-related
Research InstitutionIbaraki University (2023)
Nihon University (2020-2022)

Principal Investigator

Nakamura Shuhei  茨城大学, 理工学研究科(工学野), 助教 (00824038)

Project Period (FY) 2020-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2020: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords多変数多項式暗号 / 耐量子計算機暗号 / 連立代数方程式問題 / Bi-graded 多項式系 / Multi-graded 多項式系 / MinRank問題 / Kipnis-Shamir手法 / 鍵復元攻撃 / Rainbow / 直接攻撃 / RBS攻撃 / Tomae-Wolf algorithm / BIPC問題 / Rainbow 暗号 / MinRank 問題 / グレブナー基底計算 / 耐量子暗号
Outline of Research at the Start

身近なところで広く利用される暗号は, 第三者が秘匿な情報を得ようとした際に困難な数学問題を解くよう設計することで, 情報の取得が困難である状態を作り出すことを目的としている. しかしながら, 現在暗号で利用される数学問題は量子計算機を用いた場合に十分解くことが可能であるため, 量子計算機の実現による将来的な攻撃に耐性のある数学問題を基にした暗号を開発することは重要な課題である. 本研究ではこのような暗号の候補として期待される多変数多項式暗号の安全性を理論的に評価することを目指す.

Outline of Final Research Achievements

This research project targets multivariate cryptography, and aims to analyze its security. As a result of this research, we were able to obtain new results in the analysis of two attacks against Rainbow, a multivariate signature scheme that was being actively researched at the time the research began. In addition, in analyzing the security of multivariate cryptography, it is necessary to estimate the complexity required to solve a system of polynomial equations, and we were able to propose a new method for this estimation.

Academic Significance and Societal Importance of the Research Achievements

公開鍵暗号はインターネット等で秘匿な情報を安全に通信するための技術で広く身近に利用されている. しかしながら, 現在利用されている公開鍵暗号は, 大規模な量子計算機が実現した場合に容易に解かれることが予想されている. このため, 量子計算機を用いても解読困難な耐量子計算機暗号を設計することは重要な課題となっている. 現在耐量子計算機暗号の標準化を目的としたの世界的なプロジェクトが米国標準技術研究所により進められており, Rainbow方式をはじめとした多変数多項式暗号が活発に研究されている. 本研究課題はこの多変数多項式暗号の安全性解析を目的としている.

Report

(5 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (13 results)

All 2023 2022 2021 2020

All Journal Article (10 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 7 results,  Open Access: 1 results) Presentation (3 results) (of which Invited: 1 results)

  • [Journal Article] A New Analysis of the Kipnis-Shamir Method Solving the MinRank Problem2023

    • Author(s)
      S. Nakamura, Y. Whang, Y. Ikematsu
    • Journal Title

      IEICE Transactions

      Volume: E106-A(3) Pages: 203-211

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Three-Pass Identification Scheme Based on MinRank Problem with Half Cheating Probability2023

    • Author(s)
      B. Santoso , Y. Ikematsu , S. Nakamura, T. Yasuda
    • Journal Title

      ISITA 2022

      Volume: -

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Recent Progress in the Security Evaluation of Multivariate Public-Key Cryptography2023

    • Author(s)
      Y. Ikematsu, S. Nakamura, T. Takagi
    • Journal Title

      IET Information Security

      Volume: -

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] New complexity estimation on the Rainbow-Band-Separation attack2021

    • Author(s)
      Shuhei Nakamura, Yasuhiko Ikematsu, Yacheng Wang, Jintai Ding, Tsuyoshi Takagi
    • Journal Title

      Theoretical Computer Science

      Volume: 896 Pages: 1-18

    • DOI

      10.1016/j.tcs.2021.09.043

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Security Analysis via Algebraic Attack Against "A New Encryption Scheme for Multivariate Quadratic System"2021

    • Author(s)
      Yasuhiko Ikematsu and Shuhei Nakamura
    • Journal Title

      Proceedings of the Seventh International Conference on Mathematics and Computing

      Volume: 1412 Pages: 9-21

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Security Analysis on an ElGamal-Like Multivariate Encryption Scheme Based on Isomorphism of Polynomials2021

    • Author(s)
      Yasuhiko Ikematsu, Shuhei Nakamura, Bagus Santoso, Takanori Yasuda
    • Journal Title

      Information Security and Cryptology. Inscrypt 2021. Lecture Notes in Computer Science. Springer,

      Volume: 13007 Pages: 235-250

    • DOI

      10.1007/978-3-030-88323-2_12

    • ISBN
      9783030883225, 9783030883232
    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Improving Thomae-Wolf Algorithm for Solving Underdetermined Multivariate Quadratic Polynomial Problem2021

    • Author(s)
      Hiroki Furue, Shuhei Nakamura and Tsuyoshi Takagi
    • Journal Title

      PQCrypto 2021, Lecture Notes in Computer Science

      Volume: 12841 Pages: 65-78

    • DOI

      10.1007/978-3-030-81293-5_4

    • ISBN
      9783030812928, 9783030812935
    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] New Complexity Estimation on the Rainbow-Band-Separation Attack2020

    • Author(s)
      Nakamura, S., Ikematsu, Y., Wang, Y., Ding, J. and Takagi, T.
    • Journal Title

      IACR Cryptology ePrint Archive

      Volume: 703 Pages: 1-19

    • Related Report
      2020 Research-status Report
  • [Journal Article] Analysis on the MinRank Attack using Kipnis-Shamir Method Against Rainbow2020

    • Author(s)
      Nakamura, S., Wang, Y. and Ikematsu, Y.
    • Journal Title

      IACR Cryptology ePrint Archive

      Volume: 908 Pages: 1-17

    • Related Report
      2020 Research-status Report
  • [Journal Article] Formal Power Series on Algebraic Cryptanalysis2020

    • Author(s)
      Shuhei Nakamura
    • Journal Title

      arXiv.org e-Print archive

      Volume: 2007.14729 Pages: 1-18

    • Related Report
      2020 Research-status Report
  • [Presentation] 暗号における連立代数方程式問題を評価する新しい不変量の検討2022

    • Author(s)
      中村周平, 横溝恭平
    • Organizer
      第41回数理科学講演会
    • Related Report
      2022 Research-status Report
  • [Presentation] 多変数多項式暗号における連立代数方程式の求解計算量評価2021

    • Author(s)
      中村周平
    • Organizer
      総務省プロジェクト「5G等のための耐量子計算機暗号の機能付加技術等(耐量子 コンピュータセキュリティ技術)」招待講演
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] New Complexity Estimation on the Rainbow-Band-Separation attack2020

    • Author(s)
      Shuhei Nakamura
    • Organizer
      コンピュータセキュリティシンポジウム2020
    • Related Report
      2020 Research-status Report

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Published: 2020-04-28   Modified: 2025-01-30  

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