Research on Security Analysis of Public Key Cryptosystems

• Project/Area Number: 22700006
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: KUNIHIRO Noboru 東京大学, 大学院・新領域創成科学研究科, 准教授 (60345436)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 公開鍵暗号 / 安全性評価 / 格子理論 / RSA暗号 / 暗号の安全性解析

Research Abstract

Our research goal is to establish theories on security analysis of public key cryptosystems. We employ the lattice theory for its analysis. We succeeded in obtaining more accurate conditions for solving some problems related to public key cryptosystems such as RSA scheme and knapsack scheme. Then, we succeeded in providing more accurate security analysis for such schemes. These results enable us to use cryptographic technologies more securely and adequately.

Research Products

• [Journal Article] Better Lattice Constructions for Solving Multivariate Linear Equations Modulo Unknown Divisors (2013)
  • Author(s): A. Takayasu and N. Kunihiro
  • Journal Title: Proc. Of ACISP2013 Volume: (掲載決定)
  • NAID: 130004770855
  • Peer Reviewed
• [Journal Article] Recovering RSA Secret Keys from Noisy Key Bits with Erasures and Errors (2013)
  • Author(s): N. Kunihiro, N. Shinohara and T. Izu
  • Journal Title: Proc. Of PKC2013 Volume: 7778 Pages: 180-197
  • NAID: 130004770856
  • Peer Reviewed
• [Journal Article] Recovering RSA Secret Keys from Noisy Key Bits with Erasures and Errors (2013)
  • Author(s): Noboru Kunihiro, Naoyuki Shinohara and Tetsuya Izu
  • Journal Title: In Proc. of PKC2013 Volume: 7778 Pages: 180-197
  • DOI: 10.1007/978-3-642-36362-7_12
  • NAID: 130004770856
  • ISBN: 9783642363610, 9783642363627
  • Peer Reviewed
• [Journal Article] Random Sampling Reduction with Precomputation (2013)
  • Author(s): Masayuki Yoshino and Noboru Kunihiro
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E96.A Issue: 1 Pages: 150-157
  • DOI: 10.1587/transfun.E96.A.150
  • NAID: 10031167097
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] On Optimal Bounds of Small Inverse Problems and Approximate GCD Problems with Higher Degree (2012)
  • Author(s): N. Kunihiro
  • Journal Title: Proc. Of ISC2012 Volume: 7483 Pages: 55-69
  • Peer Reviewed
• [Journal Article] Optimal Bounds for Multi-Prime Phi-Hiding Assumption (2012)
  • Author(s): K. Tosu and N. Kunihiro
  • Journal Title: Proc. Of ACISP2012 Volume: LNCS7372 Pages: 1-14
  • Peer Reviewed
• [Journal Article] FasterAlgorithm for Solving Hard knapsacks forModerate Message Length (2012)
  • Author(s): Y. Nagashima and N. Kunihiro
  • Journal Title: Proc. Of ACISP2012 Volume: LNCS7372 Pages: 43-56
  • Peer Reviewed
• [Journal Article] On the Hardness of Subset Sum Problem from Different Intervals (2012)
  • Author(s): J. Kogure, N. Kunihiro and H. YAMAMOTO
  • Journal Title: IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences Volume: Vol. E95-A, No.5 Pages: 903-908
  • NAID: 10030938213
  • Peer Reviewed
• [Journal Article] Optimal Bounds for Multi-Prime Φ-Hiding Assumption (2012)
  • Author(s): Kaori Tosu, Noboru Kunihiro
  • Journal Title: In Proc. of ACISP2012 Volume: 7372 Pages: 1-14
  • DOI: 10.1007/978-3-642-31448-3_1
  • ISBN: 9783642314476, 9783642314483
  • Peer Reviewed
• [Journal Article] Faster Algorithm for Solving Hard Knapsacks for Moderate Message Length (2012)
  • Author(s): Yuji Nagashima, Noboru Kunihiro
  • Journal Title: In Proc. of ACISP2012 Volume: 7372 Pages: 43-56
  • DOI: 10.1007/978-3-642-31448-3_4
  • ISBN: 9783642314476, 9783642314483
  • Peer Reviewed
• [Journal Article] On Optimal Bounds of Small Inverse Problems and Approximate GCD Problems with Higher Degree (2012)
  • Author(s): Noboru Kunihiro
  • Journal Title: In Proc. of ISC2012 Volume: 7483 Pages: 55-69
  • DOI: 10.1007/978-3-642-33383-5_4
  • ISBN: 9783642333828, 9783642333835
  • Peer Reviewed
• [Journal Article] On the Hardness of Subset Sum Problem from Different Intervals (2012)
  • Author(s): Jun Kogure, Noboru Kunihiro, Hirosuke Yamamoto
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E95.A Issue: 5 Pages: 903-908
  • DOI: 10.1587/transfun.E95.A.903
  • NAID: 130002133677
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] A Unified Framework for Small Secret Exponent Attack on RSA (2011)
  • Author(s): N. Kunihiro, N. Shinohara and T. Izu
  • Journal Title: Proc. Of SAC2011 Volume: LNCS7118 Pages: 260-277
  • NAID: 130004770857
  • Peer Reviewed
• [Journal Article] 格子理論を用いた暗号解読の最近の研究動向 (2011)
  • Author(s): 國廣昇
  • Journal Title: 電子情報通信学会 基礎・境界ソサイエティ Fundamentals Review Volume: Vol. 5, No. 1 Pages: 42-55
  • NAID: 130004554673
• [Journal Article] Solving Generalized Small Inverse Problems IEICE Transactions on Fundamentals of Electronics (2011)
  • Author(s): N. Kunihiro
  • Journal Title: Communications and Computer Sciences Volume: Vol. E94-A, No.6 Pages: 1274-1284
  • Peer Reviewed
• [Journal Article] Small Secret CRT-Exponent Attacks on Takagi's RSA,"IEICE Transactions on Fundamentals of Electronics (2011)
  • Author(s): N. Shinohara, T. Izu and N. Kunihiro
  • Journal Title: Communications and Computer Sciences Volume: Vol. E94-A, No.1 Pages: 19-27
  • Peer Reviewed
• [Journal Article] Solving Generalized Small Inverse Problems (2011)
  • Author(s): Noboru Kunihiro
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E94-A Issue: 6 Pages: 1274-1284
  • DOI: 10.1587/transfun.E94.A.1274
  • NAID: 10029802265
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] Recent Results on Lattice-Based Cryptanalysis (2011)
  • Author(s): 國廣昇
  • Journal Title: IEICE ESS Fundamentals Review Volume: 5 Issue: 1 Pages: 42-55
  • DOI: 10.1587/essfr.5.42
  • NAID: 130004554673
  • ISSN: 1882-0875
• [Journal Article] Small Secret CRT-Exponent Attacks on Takagi's RSA (2011)
  • Author(s): N.Shinohara, T.Izu, N.Kunihiro
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: Vol.E94-A,No.1 Pages: 19-27
  • NAID: 10027986308
  • Peer Reviewed
• [Journal Article] New Conditions for Secure Knapsack Schemes against Lattice Attack (2010)
  • Author(s): N. Kunihiro
  • Journal Title: IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences Volume: Vol. E93-A, No.6 Pages: 1058-1065
  • NAID: 10026864617
  • Peer Reviewed
• [Journal Article] Public Key Encryption Schemes from the (B)CDH Assumption with Better Efficiency (2010)
  • Author(s): S.Yamada, Y.Kawai, G.Hanaoka, N.Kunihiro
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: Vol.E93-A,No.11 Pages: 1984-1993
  • NAID: 10027984559
  • Peer Reviewed
• [Journal Article] New Conditions for Secure Knapsack Schemes against Lattice Attack (2010)
  • Author(s): N.Kunihiro
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: Vol.E93-A,No.6 Pages: 1058-1065
  • NAID: 10026864617
  • Peer Reviewed
• [Presentation] 多変数法付き線形方程式アルゴリズムの改良 (2013)
  • Author(s): 高安敦， 國廣昇
  • Organizer: SCIS2013
  • Place of Presentation: 京都市ウェスティン都ホテル京都
• [Presentation] 密度の高いナップサック暗号の安全性評価 -問題の分割による計算量の削減 (2013)
  • Author(s): 長嶋祐志， 國廣昇
  • Organizer: SCIS2013
  • Place of Presentation: 京都市ウェスティン都ホテル京都
• [Presentation] Optimal Bounds for Multi-Prime Phi-Hiding Assumption (2012)
  • Author(s): Kaori Tosu, Noboru Kunihiro
  • Organizer: ACISP2012
  • Place of Presentation: オーストラリア・ウロンゴン(発表確定)
  • Year and Date: 2012-07-09
• [Presentation] Faster Algorithm for Solving Hard knapsacks for Moderate Message Length (2012)
  • Author(s): Yuji Nagashima, Noboru Kunihiro
  • Organizer: ACISP2012
  • Place of Presentation: オーストラリア・ウロンゴン(発表確定)
  • Year and Date: 2012-07-09
• [Presentation] チュートリアル:格子簡約を用いたRSA暗号への攻撃 (2012)
  • Author(s): 國廣昇
  • Organizer: Lattice Crypto Day 2012 Japan (LCD2012J)
  • Place of Presentation: Japan
  • Year and Date: 2012-03-15
• [Presentation] 格子簡約を用いたRSA暗号への攻撃 (2012)
  • Author(s): 國廣昇
  • Organizer: Lattice Crypto Day 2012 Japan (LCD2012J)
  • Place of Presentation: IIJ・中会議室(招待講演)
  • Year and Date: 2012-03-15
• [Presentation] 近似GCD問題に対する改良アルゴリズム (2012)
  • Author(s): 高安敦，國廣昇
  • Organizer: 情報セキュリティ研究会
  • Place of Presentation: 札幌市北海道工業大学
• [Presentation] 格子簡約アルゴリズムを用いた暗号の安全性解析 (2011)
  • Author(s): 國廣昇
  • Organizer: 第3回暗号及び情報セキュリティと数学の相関ワークショップ
  • Place of Presentation: 中央大学
  • Year and Date: 2011-12-21
• [Presentation] 格子簡約アルゴリズムを用いた暗号の安全性解析 (2011)
  • Author(s): 國廣昇
  • Organizer: 第3回暗号及び情報セキュリティと数学の相関ワークショップ
  • Place of Presentation: 中央大・後楽園キャンパス(招待講演)
  • Year and Date: 2011-12-21
• [Presentation] Generalized Security Analysis of the Random Key Bits Leakage Attack (2011)
  • Author(s): Jun Kogure, Noboru Kunihiro, Hirosuke Yamamoto
  • Organizer: WISA2011
  • Place of Presentation: 韓国・済州島
  • Year and Date: 2011-08-22
• [Presentation] A Unified Framework for Small Secret Exponent Attack on RSA (2011)
  • Author(s): Noboru Kunihiro, Naoyuki Shinohara, Totsuya Izu
  • Organizer: Selected Areas in Cryptography (SAC) 2011
  • Place of Presentation: カナダ・トロント
  • Year and Date: 2011-08-12
• [Presentation] Solving Generalized Small Inverse Problems (2010)
  • Author(s): N.Kunihiro
  • Organizer: ACISP2010
  • Place of Presentation: オーストラリア・シドニー
  • Year and Date: 2010-07-07