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ペアリング暗号の効率化とその実装

Research Project

Project/Area Number 19J21086
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Review Section Basic Section 60070:Information security-related
Research InstitutionOkayama University

Principal Investigator

南條 由紀  岡山大学, 自然科学研究科, 特別研究員(DC1)

Project Period (FY) 2019-04-25 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2021: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2020: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2019: ¥900,000 (Direct Cost: ¥900,000)
Keywords公開鍵暗号 / ペアリング暗号 / 楕円曲線 / 高速化
Outline of Research at the Start

公開鍵暗号方式であるIDベース暗号や検索可能暗号方式などの高機能な暗号プロトコルの実用化が進んでいるが,これらの暗号プロトコルに用いられるペアリング暗号にかかる計算コストが問題となっており,その効率化が求められている.そこで本研究では,ペアリングに対する計算効率の良い新たな拡大体構成法や,実用的なペアリングのパラメータを提案し,ペアリング暗号の高速化を図る.また,処理能力の低いIoTデバイスに対して,十分なソフトウェア効率化を行ったペアリング暗号の実装を行う.

Outline of Annual Research Achievements

楕円曲線上で定義されるペアリングと呼ばれる写像を利用することで、様々な機能をもつ暗号が実現できる。しかしながら、ペアリングの計算にかかる計算量が大きいことが課題となっている。このため、本研究では計算量を減らすことを目的としている。本年度は主に下記の研究を行なった。
ペアリング暗号の安全性と効率性を両立させるためには楕円曲線の選択が重要である。これまでは埋込み次数と呼ばれるパラメータkがk=12,16の楕円曲線が主に活用されてきたが、近年では新たにk=10,11,13,14などの楕円曲線が推奨されている。しかしながら、新たに推奨された楕円曲線については、最終べきと呼ばれる、ペアリングの一部の計算ステップの効率的な計算アルゴリズムが提案されていない。このため、本研究ではこれらの曲線に適用可能な一つの効率的な最終べきの計算アルゴリズムを導出した。既存の計算アルゴリズムと比較すると、k=10の楕円曲線についてはおよそ16%、k=11,13,14の楕円曲線についてはおよそ83%計算コストが削減できることが分かった。
また、新たに推奨された楕円曲線だけでなく、kが素数の楕円曲線の重要度も上がっている。本研究では、まず小さな素数kをもつ曲線について最終べきの計算アルゴリズムを導出した。その結果に基づき、k=1 mod 6を満たす任意の素数kに対して適用可能な最終べきの計算アルゴリズムを導出した。既存の計算アルゴリズムの計算量オーダーはO(k^2)であるが、提案アルゴリズムの場合はO(k)である。このため、提案アルゴリズムを用いることにより明らかに計算量を削減できる。
上記の成果はいずれも国際会議 The 9-th International Symposium on Computing and Networking (CANDAR’21)にて発表した。

Research Progress Status

令和3年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和3年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • Research Products

    (24 results)

All 2022 2021 2020 2019

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Open Access: 4 results) Presentation (20 results) (of which Int'l Joint Research: 11 results)

  • [Journal Article] Improvement of Final Exponentiation for Pairings on BLS Curves with Embedding Degree 152021

    • Author(s)
      NANJO Yuki、SHIRASE Masaaki、KUSAKA Takuya、NOGAMI Yasuyuki
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E104.A Issue: 1 Pages: 315-318

    • DOI

      10.1587/transfun.2020EAL2046

    • NAID

      130007964848

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2021-01-01
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Restrictions of Integer Parameters for Generating Attractive BLS Subfamilies of Pairing-Friendly Elliptic Curves with Specific Embedding Degrees2021

    • Author(s)
      Nanjo Yuki、Shirase Masaaki、Kusaka Takuya、Nogami Yasuyuki
    • Journal Title

      International Journal of Networking and Computing

      Volume: 11 Issue: 2 Pages: 383-411

    • DOI

      10.15803/ijnc.11.2_383

    • NAID

      130008063316

    • ISSN
      2185-2839, 2185-2847
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Construction Method of an Isomorphic Map between Quadratic Extension Fields Applicable for SIDH2020

    • Author(s)
      NANJO Yuki、SHIRASE Masaaki、KUSAKA Takuya、NOGAMI Yasuyuki
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E103.A Issue: 12 Pages: 1403-1406

    • DOI

      10.1587/transfun.2020TAL0002

    • NAID

      130007948374

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2020-12-01
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Performance Analysis and Evaluation of SIDH Applied Several Implementation-Friendly Quadratic Extension Fields2020

    • Author(s)
      Nanjo Yuki、Shirase Masaaki、Kusaka Takuya、Nogami Yasuyuki
    • Journal Title

      International Journal of Networking and Computing

      Volume: 10 Issue: 2 Pages: 227-241

    • DOI

      10.15803/ijnc.10.2_227

    • NAID

      130007878726

    • ISSN
      2185-2839, 2185-2847
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] FK12曲線上のペアリングにおける最終べきアルゴリズムの改良2022

    • Author(s)
      池坂和真、南條由紀、小寺雄太、日下卓也、野上保之
    • Organizer
      2022年暗号と情報セキュリティシンポジウム(SCIS2022)
    • Related Report
      2021 Annual Research Report
  • [Presentation] BLS12曲線上のペアリングにおけるG2上の有理点生成の高速化2022

    • Author(s)
      飯田智宏、服部大地、松村陸矢、南條由紀、小寺雄太、日下卓也、野上保之
    • Organizer
      2022年暗号と情報セキュリティシンポジウム(SCIS2022)
    • Related Report
      2021 Annual Research Report
  • [Presentation] Calculation Costs Estimations of Final Exponentiation for Pairing-Friendly Elliptic Curves Resistant to Special TNFS2021

    • Author(s)
      Yuki Nanjo、Masaaki Shirase、Yuta Kodera、Takuya Kusaka、Yasuyuki Nogami
    • Organizer
      The 36th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC2021)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Optimal Curve Parameters for BLS12 Elliptic Curve Pairing and Its Efficiency Evaluation2021

    • Author(s)
      Daichi Hattori、Yuto Takahashi、Tomoya Tatara、Yuki Nanjo、Takuya Kusaka、Yasuyuki Nogami
    • Organizer
      2021 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW2021)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Efficient Final Exponentiation for Pairings on Several Curves Resistant to Special TNFS2021

    • Author(s)
      Yuki Nanjo、Masaaki Shirase、Yuta Kodera、Takuya Kusaka、Yasuyuki Nogami
    • Organizer
      The Ninth International Symposium on Computing and Networking (CANDAR2021/Track5)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Construction Method of Final Exponentiation for a Specific Cyclotomic Family of Pairing-Friendly Elliptic Curves with Prime Embedding Degrees2021

    • Author(s)
      Yuki Nanjo、Masaaki Shirase、Yuta Kodera、Takuya Kusaka、Yasuyuki Nogami
    • Organizer
      The Ninth International Symposium on Computing and Networking (CANDAR2021/Track5)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Technique for Fast Miller’s Algorithm of Ate Pairings on Elliptic Curves with Embedding Degrees of Multiple of Three2020

    • Author(s)
      Yuki Nanjo, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      The 35-th International Technical Conference on Circuits/Systems, Computers and Communications
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Explicit Formula of Cyclotomic Cubing Available for Pairings on Elliptic Curves with Embedding Degrees of Multiple of Three2020

    • Author(s)
      Yuki Nanjo, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      The 35-th International Technical Conference on Circuits/Systems, Computers and Communications
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Implementation and Evaluation of a Pairing on Elliptic Curves with Embedding Degree 142020

    • Author(s)
      Zihao Song, Rikuya Matsumura, Yuto Takahashi, Yuki Nanjo, Takuya Kusaka, Yasuyuki Nogami, Tsutomu Matsumoto
    • Organizer
      The 35-th International Technical Conference on Circuits/Systems, Computers and Communications
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Implementation and Evaluation of Ate Pairings on Elliptic Curves with Embedding Degree 10 Applied Type-II All-One Polynomial Extension Field of Degree 52020

    • Author(s)
      Rikuya Matsumura, Yuto Takahashi, Yuki Nanjo, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      The 35-th International Technical Conference on Circuits/Systems, Computers and Communications
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Specific Congruence Classes of Integer Parameters for Generating BLS Curves for Fast Pairings2020

    • Author(s)
      Yuki Nanjo, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      The 8-th International Symposium on Computing and Networking Workshop
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 任意のBLS曲線の最終べきのhard partについて2020

    • Author(s)
      白勢政明, 南條由紀
    • Organizer
      情報セキュリティ研究会(ISEC)
    • Related Report
      2020 Annual Research Report
  • [Presentation] BLS12曲線におけるペアリング計算のための最適曲線パラメータの提案とその実装評価2020

    • Author(s)
      服部大地, 高橋裕人, 多田羅友也, 南條由紀, 小寺雄太, 日下卓也, 野上保之
    • Organizer
      情報セキュリティ研究会(ISEC)
    • Related Report
      2020 Annual Research Report
  • [Presentation] Evaluation of Pairing on Elliptic Curves with Embedding Degree 15 with Type-II All-one Polynomial Extension Field of Degree 52020

    • Author(s)
      Yuki Nanjo, Yuta Kodera, Rikuya Matsumura, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      2020年暗号と情報セキュリティシンポジウム(SCIS2020)
    • Related Report
      2019 Annual Research Report
  • [Presentation] A Performance Analysis of Supersingular Isogeny Diffie-Hellman with Several Classes of the Quadratic Extension Fields2019

    • Author(s)
      Yuki Nanjo, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      情報セキュリティ研究会(ISEC)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Improvement of Miller's Algorithm of Pairing on Elliptic Curves with Embedding Degree 15 by Using Sparse Multiplication in Affine Coordinates2019

    • Author(s)
      Yuki Nanjo, Yuto Takahashi, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      コンピュータセキュリティシンポジウム2019(CSS2019)
    • Related Report
      2019 Annual Research Report
  • [Presentation] 埋め込み次数14のTate及びAteペアリングの実装2019

    • Author(s)
      宋子 豪, 松村 陸矢, 南條 由紀, 野上 保之, 日下 卓也
    • Organizer
      ハードウェアセキュリティ研究会(HWS)
    • Related Report
      2019 Annual Research Report
  • [Presentation] 埋め込み次数10のペアリング曲線の実装とその評価2019

    • Author(s)
      松村 陸矢, 高橋 裕人, 多田羅 友也, 南條 由紀, 日下 卓也, 野上 保之
    • Organizer
      第42回情報理論とその応用シンポジウム(SITA2019)
    • Related Report
      2019 Annual Research Report
  • [Presentation] A Performance Analysis and Evaluation of SIDH with Several Classes of the Quadratic Extension Fields2019

    • Author(s)
      Yuki Nanjo, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami
    • Organizer
      The Seventh International Symposium on Computing and Networking (CANDAR2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Implementation and Evaluation of Pairing Library ELiPS for BLS Curve with Several Techniques2019

    • Author(s)
      Yuto Takahashi, Yuki Nanjo, Takuya Kusaka, Yasuyuki Nogami, Tadaki Kanenari, Tomoya Tatara
    • Organizer
      The 34th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research

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Published: 2019-05-29   Modified: 2024-03-26  

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