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Study on Security Analysis of Elliptic and Hyperelliptic Cryptosystems against Weil Descent Attack

Research Project

Project/Area Number 20560370
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Communication/Network engineering
Research InstitutionChuo University

Principal Investigator

CHAO Jinhui  Chuo University, 理工学部, 教授 (60227345)

Co-Investigator(Renkei-kenkyūsha) FUMIYUKI Momose  中央大学, 大学院・理工学研究科, 教授 (80182187)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords暗号理論 / 楕円暗号 / 超楕円暗号 / 安全性解析 / Weil decent攻撃 / 情報セキュリティ / Weil descent攻撃 / GHS攻撃 / Weil restriction
Research Abstract

This research is to analyze security of elliptic and hyperelliptic cryptosystems, which are supposed to be the safest cryptosystems, against the recently developed Weil descent GHS attack. In particular, we will show a complete classification of all elliptic and hyperelliptic curved used in the cryptosystems which are weak against the Weil descent GHS attack, find the number and classes of these weak curves and algorithms to test if a random curve is safe or not. These results then provide a full understanding on risk and damage of the cryptosystems again the GHS attack.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (43 results)

All 2011 2010 2009 2008

All Journal Article (28 results) (of which Peer Reviewed: 8 results) Presentation (13 results) Book (2 results)

  • [Journal Article] Elliptic curves with weak coverings over cubic extensions of finite fields with even characteristic II Proceedings of SCIS20112011

    • Author(s)
      M.Shimura, F.Momose, J.Chao
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] Security Analysis of Elliptic/hyperelliptic Curves against GHS Attack without Isogeny Condition Proceedings of SCIS20112011

    • Author(s)
      H.Yoshimori, T.Iijima, J.Chao
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] Elliptic curves with weak coverings over cubic extensions of finite fields with even characteristic II2011

    • Author(s)
      M.Shimura, F.Momose, J.Chao
    • Journal Title

      Proceedings of SCIS2011,「暗号と情報セキュリティシンポジウム」電子情報通信学会

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Security Analysis of Elliptic/hyperelliptic Curves against GHS Attack without Isogeny Condition2011

    • Author(s)
      H.Yoshimori, T.Iijima, J.Chao
    • Journal Title

      Proceedings of SCIS2011,「暗号と情報セキュリティシンポジウム」電子情報通信学会

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 画像正規化と特徴点抽出を利用した電子透かし方式2011

    • Author(s)
      施剛, 趙晋輝
    • Journal Title

      Proceeings of SCIS2011,「暗号と情報セキュリティシンポジウム」電子情報通信学会

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Elliptic and hyerelliptic curves with weak covering without isogeny condition Proceedings of SCIS20102010

    • Author(s)
      T.Iijima, F.Momose, J.Chao
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] Elliptic curves with weak covering on cubic extension of finite fields with even characteristic Proceedings of SCIS20092010

    • Author(s)
      M.Shimura, F.Momose, J.Chao
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] Iwasawa Decomposition and Computational Riemannian Geometry2010

    • Author(s)
      R.Lenz, R.Mochizuki, J.Chao
    • Journal Title

      Proceedings of ICPR2010, 2010 International Conference on Pattern Recognition

      Pages: 4472-4475

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On curvature of color spaces and its implication2010

    • Author(s)
      K.Toko, J.Chao, R.Lenz
    • Journal Title

      Proceedings of CGIV2010, 5th European Conference on Colours in Graphics, Imaging, and Vision.

      Pages: 393-398

    • NAID

      110007581203

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ハッシュ関数MD4に対するChosen Prefix attackの考察2010

    • Author(s)
      宮崎祐輔、趙晋輝
    • Journal Title

      Proceedings of SCIS2010,「暗号と情報セキュリティシンポジウム」電子情報通信学会

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Elliptic and hyerelliptic curves with weak covering without isogeny condition2010

    • Author(s)
      T.Iijima, F.Momose, J.Chao
    • Journal Title

      Proceedings of SCIS2010,「暗号と情報セキュリティシンポジウム」電子情報通信学会

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Elliptic curves with weak covering on cubic extension of finite fields with even characteristic2010

    • Author(s)
      M.Shimura, F.Momose, J.Chao
    • Journal Title

      Proceedings of SCIS2009,「暗号と情報セキュリティシンポジウム」電子情報通信学会

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Elliptic curves with weak covering over cubic extensions of finite fields with even characteristic2010

    • Author(s)
      M.Shimura, F.Momose, J.Chao
    • Journal Title

      Proceedings of SCIS2010 (CD ROM)

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Classification of Elliptic/hyperelliptic Curves with Weak Coverings against GHS Attack without Isogeny Condition2010

    • Author(s)
      T.Iijima, F.Momose, J.Chao
    • Journal Title

      Proceed.Of SCIS2010, IACR eprint : http://eprint.iacr.org/2009/613 (CD ROM)

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 書評"R.Avanzi, C.Doche, T.Lange, K.Nguyen, F.Vercauteren : Handbook of hyperelliptic curve cryptography"2009

    • Author(s)
      趙晋輝、松尾和人、百瀬文之
    • Journal Title

      数学(日本数学会) 第61巻4号

      Pages: 433-436

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics2009

    • Author(s)
      F.Momose, J.Chao
    • Journal Title

      IACR E-print Archive

      Pages: 1-56

    • URL

      http://eprint.iacr.org/2009/236

    • Related Report
      2010 Final Research Report
  • [Journal Article] Classification of elliptic/hyperelliptic curves with weak coverings against GHS attack without isogeny condition2009

    • Author(s)
      T.Iijima, F.Momose, J.Chao
    • Journal Title

      IACR E-print Archive

      Pages: 1-32

    • URL

      http://eprint.iacr.org/2009/613

    • Related Report
      2010 Final Research Report
  • [Journal Article] Classification of Weil Restrictions Obtained by (2,…,2) Coverings of P^1 without Isogeny Condition in Small Genus Cases Proceedings of SCIS20092009

    • Author(s)
      T.Iijima, F.Momose, J.Chao
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] Color-reproduction using Riemann normal coordinates2009

    • Author(s)
      S.Ohshima, R.Mochizuki, J.Chao, R.Lenz
    • Journal Title

      Computational Color Imaging, Springer-Verlag 5646

      Pages: 140-149

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics2009

    • Author(s)
      F.Momose, J.Chao
    • Journal Title

      IACR eprint archive http://eprint.iacr.org/2009/236 (CD ROM)

    • Related Report
      2009 Annual Research Report
  • [Journal Article] An Invariant Metric on the Manifold of Second Order Moments2009

    • Author(s)
      R.Lenz, S.Oshima, R.Mochizuki, J.Chao
    • Journal Title

      Proceedings ICCV2009, CRICV, IEEE

      Pages: 1923-1930

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] R.Avanzi, C.Doche, T.Lange, K.Nguyen and F.Vercauteren : Handbook of hyperelliptic curve cryptography 書評2009

    • Author(s)
      趙晋輝, 松尾和人, 百瀬文之
    • Journal Title

      数学 61

      Pages: 433-436

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of Weil Restrictions Obtained by (2, . . ., 2) Coverings of P^1 without Isogeny Condition in Small Genus Cases2009

    • Author(s)
      T. Iijima, F. Momose, J. Chao
    • Journal Title

      Proceedings of SCIS 2009 (CD-ROM)

    • Related Report
      2008 Annual Research Report
  • [Journal Article] On Implementation of GHS Attack against Elliptic Curve Cryptosystems over Cubic Extension Fields of Odd Characteristics2008

    • Author(s)
      N.Hashizume, F.Momose, J.Chao
    • Journal Title

      IACR E-print Archive

      Pages: 1-34

    • URL

      http://eprint.iacr.org/2008/215

    • Related Report
      2010 Final Research Report
  • [Journal Article] On Certain Classes of Elliptic/Hyper-elliptic Curves with Weak Coverings against GHS Attack Proceedings of SCIS20082008

    • Author(s)
      T.Iijima, F.Momose, J.Chao
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] 「奇標数3次拡大体上の楕円曲線暗号に対するGHS攻撃の実装」Proceedins of SCIS20082008

    • Author(s)
      橋詰直紀、百瀬文之、趙晋輝
    • Journal Title

      暗号と情報セキュリティシンポジウム(電子情報通信学会)

    • Related Report
      2010 Final Research Report
  • [Journal Article] Color-weak correction by discrimination threshold matching2008

    • Author(s)
      R. Mochizuki, T. Nakamura, J. Chao, R. Lenz
    • Journal Title

      Proceedings of 4th European Conference on Color in graphics image and vision CGIV2008

      Pages: 208-213

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Riemann geometry for color characterization and mapping2008

    • Author(s)
      J. Chao, R. Lenz, D. Matsumoto, T. Nakamura
    • Journal Title

      Proceedings of 4th European Conference on Color in graphics image and vision CGIV2008

      Pages: 277-282

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 類似度の高いファイル構造に基づくマルウェア情報提供システムの提案2011

    • Author(s)
      上井恭輔、寺田真敏、趙晋輝
    • Organizer
      情報処理学会コンピュータセキュリティ研究会
    • Place of Presentation
      関西大学
    • Year and Date
      2011-03-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] 拡大体上の楕円曲線のnon-hyperelliptic被覆の構成法に関する考察2011

    • Author(s)
      原弘幸,飯島努,志村真帆呂,趙晋輝
    • Organizer
      電子情報通信学会暗号と情報セキュリティ研究会
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-03-05
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 奇標数3次拡大体上の楕円曲線に対するB.Smith変換を用いた攻撃2011

    • Author(s)
      2大川一樹,飯島努,趙晋輝
    • Organizer
      電子情報通信学会暗号と情報セキュリティ研究会
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-03-03
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 不正者追跡と失効可能な属性ベース暗号に関する研究2011

    • Author(s)
      佐藤祐一, 森山大輔, 土井洋, 趙晋輝
    • Organizer
      電子情報通信学会暗号と情報セキュリティ研究会
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-03-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] Elliptic and hyperelliptic curves with weak covering under isogeny condition2011

    • Author(s)
      飯島努、趙晋輝
    • Organizer
      International workshop on ECDLP (Elliptic curve discrete logarithm problems)
    • Place of Presentation
      Ecole Polytechnique Fdrale de Lausanne Switzerland(招待講演)
    • Related Report
      2010 Final Research Report
  • [Presentation] 色空間の曲率に関する考察とその応用2010

    • Author(s)
      藤稿航平, 趙晋輝
    • Organizer
      電子情報通信学会、ヒューマンインフォメーション研究会(ITE-HI)
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-02-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] ハッシュ関数MD4に対する Chosen Prefix Attack の考察2010

    • Author(s)
      宮崎祐輔, 趙晋輝
    • Organizer
      2010年暗号と情報セキュリティシンポジウム
    • Place of Presentation
      高松市
    • Year and Date
      2010-01-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] リーマン正規座標系を用いた色空間における色差保存写像の構築と色弱補正方式への応用2009

    • Author(s)
      大島哲, 望月理香, 趙晋輝
    • Organizer
      電子情報通信学会HCGシンポジウム
    • Place of Presentation
      札幌
    • Year and Date
      2009-12-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] 弱定常確率場の線形モデルによる3D形状表現とその不変特徴量2009

    • Author(s)
      高橋祥, 趙晋輝
    • Organizer
      電子情報通信学会パターン認識・メディア理解(PRMU)研究会
    • Place of Presentation
      広島大学
    • Year and Date
      2009-10-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] 「楕円曲線上の公開鍵暗号」シンポジウム「数学的土壌の上に花開く暗号技術-楕円曲線と暗号理論」2009

    • Author(s)
      趙晋輝
    • Place of Presentation
      中央大学駿河台記念館(招待講演)
    • Year and Date
      2009-09-29
    • Related Report
      2010 Final Research Report
  • [Presentation] 最大マージンクラスタリングにおける cutting-plane アルゴリズムへのカーネル法の適用2009

    • Author(s)
      高橋宏子, 塚原裕史, 趙
    • Organizer
      日本神経回路学会第19回全国大会
    • Place of Presentation
      東北大学
    • Year and Date
      2009-09-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] 色空間の局所等長変換を用いたプリンタの色再現方式に関する考察2009

    • Author(s)
      武田智史, 望月理香, 趙晋輝
    • Organizer
      日本色彩学会視覚基礎研究会2009年度第2回研究発表会
    • Place of Presentation
      工学院大学
    • Year and Date
      2009-08-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] 静止画像の特徴点を利用した電子透かし2009

    • Author(s)
      千葉晃宏, 趙晋輝, 合志清一
    • Organizer
      Proceedings of SCIS2009
    • Place of Presentation
      大津プリンスホテル
    • Year and Date
      2009-01-23
    • Related Report
      2008 Annual Research Report
  • [Book] 暗号理論と楕円曲線2008

    • Author(s)
      辻井重男、笠原正雄、趙晋輝
    • Publisher
      森北出版
    • Related Report
      2010 Final Research Report
  • [Book] 暗号理論と楕円曲線2008

    • Author(s)
      辻井, 笠原(編)趙(主著者)
    • Total Pages
      252
    • Publisher
      森北出版
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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