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Security Evaluation for Elliptic Curve Pairing-based Cryptography with Conjugate Rational Points by Distributed and Parallelized Experiments

Research Project

Project/Area Number 25280047
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Information security
Research InstitutionOkayama University

Principal Investigator

Nogami Yasuyuki  岡山大学, 自然科学研究科, 准教授 (60314655)

Co-Investigator(Kenkyū-buntansha) Uehara Satoshi  北九州市立大学, 国際環境工学部, 教授 (90213389)
Kusaka Takuya  岡山大学, 大学院自然科学研究科, 講師 (00336918)
Yamai Nariyoshi  東京農工大学, 工学研究院, 教授 (90210319)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥14,170,000 (Direct Cost: ¥10,900,000、Indirect Cost: ¥3,270,000)
Fiscal Year 2015: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Keywordsペアリング暗号 / 乱数検定 / 攻撃・安全性評価 / 並列処理 / データ解析
Outline of Final Research Achievements

In order to evaluate the security of elliptic curve pairing-based cryptography, this research has considered several attacking method, particularly rho method with some improvements and experiments. In detail, this research discussed a random number generator for efficiently carrying out random walks of rational points and then discussed an efficient distributed parallel attacks. Then, this paper also developed some efficient arithmetic operations on elliptic curve and evaluated some other approaches that kept all of generated random rational points for the attack in contrast to rho method. As a result, this research could show that 88 bit pairing-based cryptography could be broken with about three hours computation by 4 PCs. This research still keeps on attacking 114 bit pairing-based cryptography.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • Research Products

    (46 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (3 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 3 results,  Acknowledgement Compliant: 2 results) Presentation (39 results) (of which Int'l Joint Research: 6 results) Remarks (3 results)

  • [Int'l Joint Research] サンノゼ州立大学(米国)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Associative Rational Points for Improving Random Walkswith Collision-based Attack on Elliptic Curve Discrete Logarithm Problem2015

    • Author(s)
      Yasuyuki Nogami, Thomas H. Austin
    • Journal Title

      International Journal of Computer and Information Technology

      Volume: 4 Pages: 728-732

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 整数上のロジスティック写像におけるビット毎の出現頻度に関する考察2015

    • Author(s)
      荒木,宮崎,上原,硴崎
    • Journal Title

      日本応用数理学会論文誌

      Volume: 25 Pages: 191-206

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A geometric sequence binarized with Legendre symbol over odd characteristic field and its properties2014

    • Author(s)
      Y. Nogami, K. Tada, S. Uehara
    • Journal Title

      IEICE, Trans.

      Volume: E97 Pages: 2336-2342

    • NAID

      130004706392

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 楕円曲線暗号解読におけるDynamic DNSを用いた解読成功判定2016

    • Author(s)
      三好俊介,山井成良,野上保之
    • Organizer
      情報処理学会インターネットと運用技術研究会研究報告
    • Place of Presentation
      佐賀
    • Year and Date
      2016-03-03
    • Related Report
      2015 Annual Research Report
  • [Presentation] BN曲線上の楕円離散対数問題の解読におけるモンゴメリ乗算の最適化2016

    • Author(s)
      三好俊介,野上保之,日下卓也,山井成良
    • Organizer
      2016年 暗号と情報セキュリティシンポジウム
    • Place of Presentation
      熊本
    • Year and Date
      2016-01-21
    • Related Report
      2015 Annual Research Report
  • [Presentation] 埋め込み次数2 もしくは3 の合成数位数ペアリングに対する計算効率の検討2016

    • Author(s)
      小野 寛享, 野上 保之, 熊野 晶斗
    • Organizer
      暗号と情報セキュリティシンポジウム2016
    • Place of Presentation
      熊本
    • Year and Date
      2016-01-21
    • Related Report
      2015 Annual Research Report
  • [Presentation] 二種類の方のNTU系列に関するインターリーブ系列2016

    • Author(s)
      土屋,野上,上原
    • Organizer
      2016年暗号と情報セキュリティシンポジウム(SCIS2016)
    • Place of Presentation
      熊本
    • Year and Date
      2016-01-20
    • Related Report
      2015 Annual Research Report
  • [Presentation] 素体上のロジスティック写像の生成系列におけるビット抽出方法と乱数性2016

    • Author(s)
      宮崎,荒木,上原,野上
    • Organizer
      2016年暗号と情報セキュリティシンポジウム(SCIS2016)
    • Place of Presentation
      熊本
    • Year and Date
      2016-01-20
    • Related Report
      2015 Annual Research Report
  • [Presentation] Examining the Linear Complexity of Multi-value Sequence generated by Power Residue Symbol2015

    • Author(s)
      H.Ino, Y.Nogami, N.Begum, S.Uehara, R.Morelos-Zaragoza, K.Tsuchiya
    • Organizer
      ICISS2015
    • Place of Presentation
      Korea(Seoul)
    • Year and Date
      2015-12-15
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An improvement of Tate Pairing with Supersingular Curve2015

    • Author(s)
      A.Kumano, Y.Nogami
    • Organizer
      ICISS2015
    • Place of Presentation
      Korea(Seoul)
    • Year and Date
      2015-12-15
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Consideration on Crosscorrelation of a kind of Trace Sequence over Finite Field2015

    • Author(s)
      H.Ino, Y.Nogami, N.Begum, S.Uehara, R.Morelos-Zaragoza, K.Tsuchiya
    • Organizer
      WICS Poster, CANDAR'15
    • Place of Presentation
      Sapporo
    • Year and Date
      2015-12-09
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 素体上のロジスティック写像による生成系列の連続増加・減少回数について2015

    • Author(s)
      宮崎,荒木,上原,野上
    • Organizer
      第38回情報理論とその応用シンポジウム(SITA2015)
    • Place of Presentation
      倉敷
    • Year and Date
      2015-11-27
    • Related Report
      2015 Annual Research Report
  • [Presentation] 異なるコントロールパラメータにおいて整数上のロジスティック写像が異なる値に写像する入力値の割合2015

    • Author(s)
      荒木,村岡,宮崎,上原,野上
    • Organizer
      第38回情報理論とその応用シンポジウム(SITA2015)
    • Place of Presentation
      倉敷
    • Year and Date
      2015-11-27
    • Related Report
      2015 Annual Research Report
  • [Presentation] 奇標数体上の多値擬似乱数系列の値の分布について2015

    • Author(s)
      小池 将太,野上 保之,土屋 和由,上原 聡
    • Organizer
      第38回情報理論とその応用シンポジウム(SITA2015)
    • Place of Presentation
      倉敷
    • Year and Date
      2015-11-27
    • Related Report
      2015 Annual Research Report
  • [Presentation] 奇標数体上の非原始多項式を用いた擬似乱数系列の生成2015

    • Author(s)
      小川 千晶,野上 保之,土屋 和由,上原 聡
    • Organizer
      第38回情報理論とその応用シンポジウム(SITA2015)
    • Place of Presentation
      倉敷
    • Year and Date
      2015-11-27
    • Related Report
      2015 Annual Research Report
  • [Presentation] トレースやべき乗剰余性を用いて生成される有限体上の擬似乱数系列の性質2015

    • Author(s)
      野上 保之
    • Organizer
      第9回シャノン理論ワークショップ (STW2015)
    • Place of Presentation
      和歌山
    • Year and Date
      2015-09-24
    • Related Report
      2015 Annual Research Report
  • [Presentation] Periods of Sequences Generated by the Logistic Map over Finite Fields with Control Parameter Four2015

    • Author(s)
      K.Tsuchiya, Y.Nogami
    • Organizer
      IWSDA2015
    • Place of Presentation
      India(Bengaluru)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 整数上のロジスティック写像におけるコントロールパラメータの差と入出力の関係2015

    • Author(s)
      荒木,村岡,宮崎,上原,硴崎
    • Organizer
      日本応用数理学会2015年度年会
    • Place of Presentation
      金沢
    • Year and Date
      2015-09-11
    • Related Report
      2015 Annual Research Report
  • [Presentation] A Consideration on Trace Sequence over Finite Field2015

    • Author(s)
      Yasuyuki NOGAMI, Hiroto INO, Kazuyoshi TSUCHIYA, Satoshi UEHARA, ROBERT MORELOS-ZARAGOZA
    • Organizer
      情報理論研究会2015
    • Place of Presentation
      石川
    • Year and Date
      2015-09-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] トレースやべき乗剰余に基づく有限体上の多値系列について2015

    • Author(s)
      野上保之
    • Organizer
      第1回有限体とその擬似乱数系列生成への応用WS
    • Place of Presentation
      群馬
    • Year and Date
      2015-08-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] Solving 94-bit ECDLP with 70 Computers in Parallel2015

    • Author(s)
      S.Miyoshi, Y.Nogami, T.Kusaka, N.Yamai
    • Organizer
      ICPBC2015
    • Place of Presentation
      France(Paris)
    • Year and Date
      2015-08-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Application of Power Residue Symbol for Generating Multi-value Sequence over Odd Characteristic Field2015

    • Author(s)
      H.Ino, Y.Nogami, S.Uehara
    • Organizer
      ITCCSCC2015
    • Place of Presentation
      Korea(Seoul)
    • Year and Date
      2015-06-30
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 素体上のロジスティック写像による生成系列の自己相関と演算精度に近い周期を持つループについて2015

    • Author(s)
      宮崎 武, 荒木 俊輔, 上原 聡, 野上 保之
    • Organizer
      電子情報通信学会 情報セキュリティ研究会
    • Place of Presentation
      北九州市立大学
    • Year and Date
      2015-03-02
    • Related Report
      2014 Annual Research Report
  • [Presentation] 素体上のロジスティック写像による多値系列の相関分布2015

    • Author(s)
      宮崎 武, 荒木 俊輔, 上原 聡, 野上 保之
    • Organizer
      2015年暗号と情報セキュリティ・シンポジウム講演論文集
    • Place of Presentation
      北九州市
    • Year and Date
      2015-01-21 – 2015-01-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] 70台程度の計算機を並列に用いた94bitのECDLPの解読2015

    • Author(s)
      三好 俊介, 野上 保之, 日下 卓也, 山井 成良
    • Organizer
      2015年暗号と情報セキュリティ・シンポジウム講演論文集
    • Place of Presentation
      北九州市
    • Year and Date
      2015-01-21 – 2015-01-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] An application of XTR for the discrete logarithm problem on Barreto-Naehrig curve2014

    • Author(s)
      Y. Kono, Y. Nogami
    • Organizer
      CANDAR/WICS2014
    • Place of Presentation
      静岡
    • Year and Date
      2014-12-10 – 2014-12-12
    • Related Report
      2014 Annual Research Report
  • [Presentation] 奇標数体上の原始多項式とべき乗剰余性に基づいた多値系列の生成2014

    • Author(s)
      手邊 啓介, 野上 保之, 上原 聡
    • Organizer
      第37回情報理論とその応用シンポジウム予稿集
    • Place of Presentation
      宇奈月温泉
    • Year and Date
      2014-12-09 – 2014-12-12
    • Related Report
      2014 Annual Research Report
  • [Presentation] Relations between evaluations of NIST tests and Lyapunov exponents of sequences generated by the Logistic map over integers2014

    • Author(s)
      C. Miyazaki, T. Miyazaki, S. Uehara, S. Araki
    • Organizer
      ISITA204
    • Place of Presentation
      メルボルン
    • Year and Date
      2014-10-26 – 2014-10-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] Some Properties of the Maximum Period on the Logistic Map Over Z_{2^n}2014

    • Author(s)
      K. Yoshida, T. Miyazaki, S. Uehara, S. Araki
    • Organizer
      ISITA2014
    • Place of Presentation
      メルボルン
    • Year and Date
      2014-10-26 – 2014-10-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] A study of an automorphism on the Logistic maps over prime fields2014

    • Author(s)
      T. Miyazaki, S. Araki, S. Uehara, Y. Nogami
    • Organizer
      ISITA2014
    • Place of Presentation
      メルボルン
    • Year and Date
      2014-10-26 – 2014-10-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] An efficient generation of geometric sequences defined with trace and Legendre symbol2014

    • Author(s)
      Y. Nogami, K. Tada, S. Uehara
    • Organizer
      ISITA2014
    • Place of Presentation
      メルボルン
    • Year and Date
      2014-10-26 – 2014-10-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] Experimental Evaluation of the Efficiency of Associative Rational Points for Random Walks on ECDLP2014

    • Author(s)
      Y. Kono, Y. Nogami , T. Kusaka
    • Organizer
      ISCIT2014
    • Place of Presentation
      韓国
    • Year and Date
      2014-09-24 – 2014-09-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] Collision Detection with DNS in Rho Method on BN Curve2014

    • Author(s)
      S. Miyoshi, Y. Nogami
    • Organizer
      ICCE-TW2014
    • Place of Presentation
      台湾
    • Year and Date
      2014-05-26 – 2014-05-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] BN曲線上のECDLPに対するRho法のDNSを用いた衝突検出の性能評価2014

    • Author(s)
      三好 俊介,山井 成良,野上 保之
    • Organizer
      2014年 暗号と情報セキュリティシンポジウム
    • Place of Presentation
      鹿児島
    • Related Report
      2013 Annual Research Report
  • [Presentation] A Binarization of Geometric Sequences with Legendre Symbol and Its Autocorrelation2013

    • Author(s)
      Y. Nogami, K. Tada, S. Uehara
    • Organizer
      IWSDA'13
    • Place of Presentation
      東京
    • Related Report
      2013 Annual Research Report
  • [Presentation] A Study on the Lyapunov Exponents of Sequences Generated by the Logistic Map over Integers2013

    • Author(s)
      T. Miyazaki, C. Miyazaki, S. Uehara, S. Araki
    • Organizer
      IWSDA'13
    • Place of Presentation
      東京
    • Related Report
      2013 Annual Research Report
  • [Presentation] Safe Primeを法とした素体上のロジスティック写像による生成系列に関する一考察2013

    • Author(s)
      宮崎 武, 荒木 俊輔, 上原 聡, 野上 保之
    • Organizer
      日本応用数理学会2013年度年会
    • Place of Presentation
      福岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] 71 ビット程度までの素数のBN曲線におけるG1上のrho法型の衝突攻撃の効率的な実装2013

    • Author(s)
      日下卓也,河野祐輝,野上保之
    • Organizer
      第36回情報理論とその応用シンポジウム
    • Place of Presentation
      伊東
    • Related Report
      2013 Annual Research Report
  • [Presentation] 楕円曲線暗号におけるDNSを用いた衝突判定2013

    • Author(s)
      三好 俊介, 野上 保之, 山井 成良
    • Organizer
      第36回情報理論とその応用シンポジウム
    • Place of Presentation
      伊東
    • Related Report
      2013 Annual Research Report
  • [Presentation] 多値M系列からの変換で得られる2値系列に対する考察2013

    • Author(s)
      多田 和紀,野上 保之,上原 聡
    • Organizer
      第36回情報理論とその応用シンポジウム
    • Place of Presentation
      伊東
    • Related Report
      2013 Annual Research Report
  • [Presentation] 随伴有理点を考慮したランダムウォーク法の提案2013

    • Author(s)
      河野 祐輝, 野上 保之, 日下 卓也
    • Organizer
      第36回情報理論とその応用シンポジウム
    • Place of Presentation
      伊東
    • Related Report
      2013 Annual Research Report
  • [Presentation] ペアリング暗号に対する攻撃2013

    • Author(s)
      野上保之
    • Organizer
      シャノン理論ワークショップ
    • Place of Presentation
      広島
    • Related Report
      2013 Annual Research Report
  • [Remarks] 楕円ペアリング暗号に対する共役有理点ノルムを用いた 分散並列攻撃法の開発と実証実験

    • URL

      http://www.ec.okayama-u.ac.jp/~sws/nogami/Works/Kibanb2013.html

    • Related Report
      2015 Annual Research Report
  • [Remarks] 基盤B概要・成果ページ

    • URL

      http://www.trans.ec.okayama-u.ac.jp/~nogami/Works/Kibanb2013.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] 楕円ペアリング暗号に対する共役有理点ノルムを用いた 分散並列攻撃法の開発と実証実験

    • URL

      http://www.trans.ec.okayama-u.ac.jp/~nogami/Works/Kibanb2013.html

    • Related Report
      2013 Annual Research Report

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Published: 2013-05-21   Modified: 2019-07-29  

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