Security Analysis of Public-Key Cryptography by Large-Scale Experiments

• Project/Area Number: 22650014
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Computer system/Network
• Research Institution: Kyushu University
• Principal Investigator: TAKAGI Tsuyoshi 九州大学, マス・フォア・インダストリ研究所, 教授 (60404802)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,260,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,700,000 (Direct Cost: ¥1,700,000)
• Keywords: 暗号・認証 / 公開鍵暗号 / ペアリング暗号 / 離散対数問題 / 大規模実験 / 大規模計算

Research Abstract

The security of pairing-based cryptography, which is one of next-generation public-key cryptography, is based on the difficulty of solving the discrete logarithm problem over finite fields. In this researchwe analyzed the discrete logarithm problem over finite field GF(36n) used for efficient implementation of pairing-based cryptography by large-scale experiments. In 2012 we successfully achieved the top-record of solving the discrete logarithms over finite field GF(3582) of 923 bits using a PC cluster of 252 CPUs in about 153 days, and it enables us to precisely estimate the upper bound of computational ability of expected attackers

Research Products

• [Journal Article] GF(p^12)上の離散対数問題に対する数体篩法の計算機実験 (2013)
  • Author(s): 早坂健一郎, 青木和麻呂, 小林鉄太郎, 高木剛
  • Journal Title: 2013年暗号と情報セキュリティシンポジウム Volume: SCIS2013 Pages: 122-122
• [Journal Article] Breaking Pairing-Based Cryptosystems using ηT Pairing over GF(397), 18th International Conference on the Theory and Application of Cryptology and Information Security (2012)
  • Author(s): Takuya Hayashi, Takeshi Shimoyama, Naoyuki Shinohara, Tsuyoshi Takagi
  • Journal Title: Asiacrypt 2012 Volume: LNCS 7658 Pages: 43-60
  • DOI: 10.1007/978-3-642-34961-4_5
  • ISBN: 9783642349607, 9783642349614
  • Peer Reviewed
• [Journal Article] GF(3n)上の ηT ペアリングを用いたペアリング暗号の安全性評価 (2012)
  • Author(s): 林卓也, 下山武司, 篠原直行, 高木剛
  • Journal Title: 電子情報通信学会研究報告, 信学技報 Volume: Vol.112, No.39 Pages: 1-5
• [Journal Article] Key Length Estimation of Pairing-Based Cryptosystems using ηTPairing, 8th International Conference (2012)
  • Author(s): Naoyuki Shinohara, Takeshi Shimoyama, Takuya Hayashi, Tsuyoshi Takagi
  • Journal Title: ISPEC 2012 Volume: LNCS 7232 Pages: 228-244
  • DOI: 10.1007/978-3-642-29101-2_16
  • ISBN: 9783642291005, 9783642291012
  • Peer Reviewed
• [Journal Article] 数体篩法における Joux-Lercier の多項式選択法について (2012)
  • Author(s): 坂本恭一, 林卓也, 高木剛
  • Journal Title: 2012 年暗号と情報セキュリティシンポジウム, SCIS2012 Volume: 2B1-2 Pages: 27-27
  • Peer Reviewed
• [Journal Article] Solving a 676-bit Discrete Logarithm Problem in GF(36n), IEICE Transaction, Fundamentals of Electronics (2012)
  • Author(s): Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shin'ichiro Matsuo, Masaaki Shirase, Tsuyoshi Takagi
  • Journal Title: Communi- cations and Computer Sciences:A Volume: Vol.E95-A, No.1 Pages: 204-212
  • Peer Reviewed
• [Journal Article] GF(3＾n)上のηTペアリングを用いたペアリング暗号の安全性評価 (2012)
  • Author(s): 林卓也, 下山武司, 篠原直行, 高木剛
  • Journal Title: 信学技報 (IEICE Technical Report) Volume: Vol.112, No.211 Pages: 1-5
• [Journal Article] Solving a 676-bit Discrete Logarithm Problem in GF(3^<6n>) (2012)
  • Author(s): Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shin'ichiro Matsuo, Masaaki Shirase, Tsuyoshi Takagi
  • Journal Title: IEICE Transaction Volume: Vol.E95-A, No.1 Pages: 204-212
  • NAID: 10030534822
  • Peer Reviewed
• [Journal Article] 数体節法におけるJoux-Lercierの多項式選択法について (2012)
  • Author(s): 坂本恭一, 林卓也, 高木剛
  • Journal Title: 2012年暗号と情報セキュリティシンポジウム Volume: SCIS 2012 Pages: 27-27
• [Journal Article] 離散対数問題に対する 解読世界記録の推移 (2011)
  • Author(s): 林卓也, 高木剛
  • Journal Title: 電子情報通信学会誌 Volume: 94巻 11号 Pages: 977-981
  • NAID: 110008762196
  • URL: http://ci.nii.ac.jp/naid/110008762196
• [Journal Article] An Experiment of Number Field Sieve over GF(p) of Low Hamming Weight Characteristic (2011)
  • Author(s): Kenichiro Hayasaka, Tsuyoshi Takagi
  • Journal Title: International Work- shop on Coding and Cryptology, IWCC 2011 Volume: LNCS 6639 Pages: 191-200
  • DOI: 10.1007/978-3-642-20901-7_11
  • NAID: 10027596429
  • ISBN: 9783642209000, 9783642209017
  • Peer Reviewed
• [Journal Article] 離散対数問題に対する解読世界記録の推移 (2011)
  • Author(s): 林卓也, 高木剛
  • Journal Title: 電子情報通信学会誌 Volume: 94巻11号 Pages: 977-981
  • NAID: 110008762196
• [Journal Article] An Experiment of Number Field Sieve over GF(p) of Low Hamming Weight Characteristic (2011)
  • Author(s): Kenichiro Hayasaka, Tsuyoshi Takagi
  • Journal Title: International Workshop on Coding and Cryptology, IWCC 2011 Volume: LNCS 6639 Pages: 191-200
  • NAID: 10027596429
  • Peer Reviewed
• [Journal Article] 離散対数問題解読世界記録更新への道-676 ビットの解読- (2010)
  • Author(s): 林卓也, 高木剛
  • Journal Title: 情報処理 Volume: Vol.51, No.9 Pages: 1181-1188
  • NAID: 110007700785
  • URL: http://ci.nii.ac.jp/naid/110007700785
• [Journal Article] Solving a 676-bit Discrete Logarithm Problem in GF(36n) (2010)
  • Author(s): Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shin'ichiro Matsuo, Masaaki Shirase, Tsuyoshi Takagi
  • Journal Title: 13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010 Volume: LNCS 6056 Pages: 351-367
  • DOI: 10.1007/978-3-642-13013-7_21
  • NAID: 10030534822
  • ISBN: 9783642130120, 9783642130137
  • Peer Reviewed
• [Journal Article] 素体 GF(p)上の離散対数問題に対する数体篩法の比較実験 (2010)
  • Author(s): 早坂健一郎, 高木剛
  • Journal Title: 情報処理学会コンピュータセキュリティシンポジウム, CSS2010 Volume: 2B1-1 Pages: 489-494
  • Peer Reviewed
• [Journal Article] Solving a 676-bit Discrete Logarithm Problem in GF(3^{6n}) (2010)
  • Author(s): Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shin'ichiro Matsuo, Masaaki Shirase, Tsuyoshi Takagi
  • Journal Title: 13th International Conference on Practice and Theory in Public Key Cryptography Volume: LNCS 6056 Pages: 351-367
  • NAID: 10030534822
  • Peer Reviewed
• [Journal Article] 離散対数問題解読世界記録更新への道-676ビットの解読- (2010)
  • Author(s): 林卓也, 高木剛
  • Journal Title: 情報処理 Volume: Vol.51 No.9 Pages: 1181-1188
  • NAID: 110007700785
• [Journal Article] 素体GF(p)上の離散対数問題に対する数体篩法の比較実験 (2010)
  • Author(s): 早坂健一郎, 高木剛
  • Journal Title: 情報処理学会 コンピュータセキュリティシンポジウム Volume: 2B1-1 Pages: 489-494
• [Presentation] 次世代公開鍵暗号に関する研究の最前線 (2013)
  • Author(s): 高木剛
  • Organizer: NICT 情報通信セキュリティシンポジウム 2013
  • Place of Presentation: 品川フロントビル
  • Year and Date: 2013-02-14
• [Presentation] 次世代公開鍵暗号に関する研究の最前線 (2013)
  • Author(s): 高木 剛
  • Organizer: NICT情報通信セキュリティシンポジウム2013
  • Place of Presentation: 品川フロントビル(東京)
  • Invited
• [Presentation] 有限体上の離散対数問題の困難性 (2012)
  • Author(s): 高木剛
  • Organizer: 2012 年電子情報通信学会総合大会
  • Place of Presentation: 岡山大学
  • Year and Date: 2012-03-22
• [Presentation] 有限体上の離散対数問題の困難性 (2012)
  • Author(s): 高木剛
  • Organizer: 2012年電子情報通信学会総合大会
  • Place of Presentation: 岡山大学(招待講演)
  • Year and Date: 2012-03-22
• [Presentation] An Experiment of Number Field Sieve over GF(p) of Low Hamming Weight Characteristic (2011)
  • Author(s): Tsuyoshi Takagi
  • Organizer: Inter- national Workshop on Coding and Cryptology, IWCC 2011
  • Place of Presentation: Qingdao Garden Hotel, 青島,中国.
  • Year and Date: 2011-06-02
• [Presentation] An Experiment of Number Field Sieve over GF(p) of Low Hamming Weight Characteristic (2011)
  • Author(s): Tsuyoshi Takagi
  • Organizer: International Workshop on Coding and Cryptology, IWCC 2011
  • Place of Presentation: Qingdao Garden Hotel, Qingdao, China(招待講演)
  • Year and Date: 2011-06-02
• [Presentation] 次世代公開鍵暗号‐ペアリング暗号‐ (2010)
  • Author(s): 高木剛
  • Organizer: 統計科学研究会, 第15回情報・統計科学シンポジウム(BIC シンポジウム)
  • Place of Presentation: 九州大学伊都キャンパス
  • Year and Date: 2010-12-03
• [Presentation] 次世代公開鍵暗号-ペアリング暗号- (2010)
  • Author(s): 高木剛
  • Organizer: 統計科学研究会 第15回情報・統計科学シンポジウム(BICシンポジウム)
  • Place of Presentation: 九州大学伊都キャンパス
  • Year and Date: 2010-12-03
• [Remarks]
  • URL: http://imi.kyushu-u.ac.jp/~takagi/
• [Remarks] http://imi.kyushu-u.ac.jp/~takagi/
• [Remarks]
  • URL: http://imi.math.kyushu-u.ac.jp/~takagi/
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/~takagi/