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公開鍵暗号に対する格子理論に基づく安全性解析とその暗号設計への応用

Research Project

Project/Area Number 14J08237
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Theory of informatics
Research InstitutionThe University of Tokyo

Principal Investigator

高安 敦  東京大学, 新領域創成科学研究科, 特別研究員(DC1)

Project Period (FY) 2014-04-25 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2016: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2015: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2014: ¥900,000 (Direct Cost: ¥900,000)
Keywords格子 / RSA暗号 / 耐量子暗号 / 最短ベクトル問題 / 格子簡約アルゴリズム / 格子暗号 / 安全性解析 / 法付き方程式
Outline of Annual Research Achievements

今年度は、格子理論に基づいて公開鍵暗号の安全性解析を行うという、本研究課題における非常に先進的な成果をあげ、さらに、ここで得た格子理論の知見を暗号設計にも応用するという理想的な目標においても成果をあげることができ、飛躍的に研究が進んで年度であったと言える。本研究課題の主たる内容である公開鍵暗号の安全性解析の研究は、大きく二つのテーマを行った。一つ目は格子理論に基づくRSA暗号の安全性解析であり、二つ目は格子暗号の安全性解析である。
まず、格子理論に基づくRSA暗号の安全性解析について記す。RSA暗号の理論的な安全性を保証するために、特殊な設定、もしくは、その秘密鍵の部分情報が漏洩した際の安全性の格子理論に基づいた解析は、長く続く暗号理論の代表的な研究テーマの一つである。このテーマにおいて、査読付き国際論文誌・査読付き国際会議予稿集に6件の論文が採録され、国際会議で5件の発表を行った。これらの成果は、国内の暗号・セキュリティ分野において権威のある辻井重男セキュリティ論文特別賞を受賞したものや、国際会議ACISPでBest Student Paper Awardを受賞した成果を含む。
次に、格子暗号の安全性解析における成果を紹介する。上記のRSA暗号を含め、現在実用化されている公開鍵暗号方式は、量子計算機が完成すれば大幅に安全性が低下し、実用上利用できなくなることがわかっている。そのため、量子計算機にも耐性のある格子暗号の研究は、近年の暗号研究の主流なテーマとなっている。今年度は、このテーマに対して、理論的な成果ではあるが、最悪時の理論評価を厳密に行った。この成果は国内学会で発表しており、情報セキュリティ研究奨励賞を受賞している。また、類似な文脈において、格子暗号を攻撃するためのより高速なアルゴリズムを開発した成果を、国際会議で発表している。

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (42 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (13 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 11 results,  Acknowledgement Compliant: 6 results) Presentation (28 results) (of which Int'l Joint Research: 11 results,  Invited: 2 results)

  • [Int'l Joint Research] Chinese Academy of Sciences(中国)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] General Bounds for Small Inverse Problems and Its Applications to Multi-Prime RSA2017

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: Vol. E100-A, No. 1 Pages: 50-61

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Lattice-based Revocable Identity-based Encryption with Bounded Decryption Key Exposure Resistance2017

    • Author(s)
      Atsushi Takayasu and Yohei Watanabe
    • Journal Title

      Information Security and Privacy

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Small CRT-exponent RSA Revisited2017

    • Author(s)
      Atsushi Takayasu, Yao Lu, Liqiang Peng
    • Journal Title

      Advances in Cryptology EUROCRYPT 2017

      Volume: 10211 Pages: 130-159

    • DOI

      10.1007/978-3-319-56614-6_5

    • ISBN
      9783319566139, 9783319566146
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A Tool Kit for Partial Key Exposure Attacks on RSA2017

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Topics in Cryptology CT-RSA 2017

      Volume: 10159 Pages: 58-73

    • DOI

      10.1007/978-3-319-52153-4_4

    • ISBN
      9783319521527, 9783319521534
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Partial Key Exposure Attacks on CRT-RSA: General Improvement for the Exposed Least Significant Bits2016

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Information Security

      Volume: 9866 Pages: 35-47

    • DOI

      10.1007/978-3-319-45871-7_3

    • ISBN
      9783319458700, 9783319458717
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Partial Key Exposure Attacks on RSA with Multiple Exponent Pairs2016

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Information Security and Privacy

      Volume: 9723 Pages: 243-257

    • DOI

      10.1007/978-3-319-40367-0_15

    • ISBN
      9783319403663, 9783319403670
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] General Bounds for Small Inverse Problems and Its Applications to Multi-Prime RSA2015

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Information Security and Cryptology - ICISC 2014 17th International Conference, Seoul, South Korea, December 3-5, 2014, Revised Selected Papers

      Volume: 8949 Pages: 3-17

    • DOI

      10.1007/978-3-319-15943-0_1

    • ISBN
      9783319159423, 9783319159430
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 改善された安全性証明を持つGGHLiteパラメータ2015

    • Author(s)
      高安敦,高島克幸
    • Journal Title

      暗号と情報セキュリティシンポジウム(SCIS2015)予稿集

      Volume: 2D4-2 Pages: 1-8

    • Related Report
      2014 Annual Research Report
  • [Journal Article] Partial Key Exposure Attacks on CRT-RSA: Better Cryptanalysis to Full Size Encryption Exponents2015

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Applied Cryptography and Network Security 13th International Conference, ACNS 2015, New York, USA, June 2-5, 2015. Proceedings

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Better Lattice Constructions for Solving Multivariate Linear Equations Modulo Unknown Divisors2014

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      IEICE TRANSACTIONS

      Volume: Vol. E97-A, No. 6 Pages: 1259-1272

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cryptanalysis of RSA with Multiple Small Secret Exponents2014

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Information Security and Privacy 19th Australasian Conference, ACISP 2014, Wollongong, NSW, Australia, July 7-9, 2014. Proceedings

      Volume: 8544 Pages: 176-191

    • DOI

      10.1007/978-3-319-08344-5_12

    • ISBN
      9783319083438, 9783319083445
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Partial Key Exposure Attacks on RSA: Achieving the Boneh-Durfee Bound2014

    • Author(s)
      Atsushi Takayasu and Noboru Kunihiro
    • Journal Title

      Selected Areas in Cryptography -- SAC 2014 21st International Conference, Montreal, QC, Canada, August 14-15, 2014, Revised Selected Papers

      Volume: 8781 Pages: 345-362

    • DOI

      10.1007/978-3-319-13051-4_21

    • ISBN
      9783319130507, 9783319130514
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 複数の復号指数を持つRSA暗号の安全性解析2014

    • Author(s)
      高安敦,國廣昇
    • Journal Title

      情報セキュリティ研究会予稿集

      Volume: ISEC2014 Pages: 1-4

    • NAID

      110009804650

    • Related Report
      2014 Annual Research Report
  • [Presentation] Lattice-based Revocable Identity-based Encryption with Bounded Decryption Key Exposure Resistance2017

    • Author(s)
      Atsushi Takayasu
    • Organizer
      ACISP 2017
    • Place of Presentation
      ニュージーランド、オークランド
    • Year and Date
      2017-07-03
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Small CRT-exponent RSA Revisited2017

    • Author(s)
      Atsushi Takayasu
    • Organizer
      Eurocrypt 2017
    • Place of Presentation
      フランス、パリ
    • Year and Date
      2017-04-30
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 通常同種写像を用いたDH鍵共有の安全性解析2017

    • Author(s)
      古川悟
    • Organizer
      情報セキュリティ研究会
    • Place of Presentation
      東京、港区、東海大学 高輪キャンパス
    • Year and Date
      2017-03-09
    • Related Report
      2016 Annual Research Report
  • [Presentation] A Tool Kit for Partial Key Exposure Attacks on RSA2017

    • Author(s)
      Atsushi Takayasu
    • Organizer
      RSA Conference
    • Place of Presentation
      アメリカ、カリフォルニア、サンフランシスコ
    • Year and Date
      2017-02-13
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Slide簡約基底に対する最短ベクトル探索の最悪時計算量評価2017

    • Author(s)
      高安敦
    • Organizer
      2017年暗号と情報セキュリティシンポジウム(SCIS 2017)
    • Place of Presentation
      沖縄、那覇市、ロワジールホテル
    • Year and Date
      2017-01-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] Small Secret Exponent Attacks on RSA with Unbalanced Prime Factors2016

    • Author(s)
      Atsushi Takayasu
    • Organizer
      ISITA 2016
    • Place of Presentation
      アメリカ、カリフォルニア、モントレー
    • Year and Date
      2016-10-30
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] CRT-RSAを攻撃する格子の新たな構成法2016

    • Author(s)
      高安敦
    • Organizer
      2016年コンピュータセキュリティシンポジウム(CSS 2016)
    • Place of Presentation
      秋田、秋田市、秋田キャッスルホテル
    • Year and Date
      2016-10-11
    • Related Report
      2016 Annual Research Report
  • [Presentation] Parameter Selections for Approximate GCD Problems2016

    • Author(s)
      Atsushi Takayasu
    • Organizer
      IWSEC 2016
    • Place of Presentation
      東京、千代田区、ソラシティカンファレンスセンター
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Partial Key Exposure Attacks on CRT-RSA: General Improvement for the Exposed Least Significant Bits2016

    • Author(s)
      Atsushi Takayasu
    • Organizer
      ISC 2016
    • Place of Presentation
      アメリカ、ハワイ、ホノルル
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ブロック簡約基底に対する最短ベクトル探索の最悪時計算量評価2016

    • Author(s)
      高安敦
    • Organizer
      情報セキュリティ研究会
    • Place of Presentation
      山口、中市、コミュニティホール
    • Year and Date
      2016-07-14
    • Related Report
      2016 Annual Research Report
  • [Presentation] Partial Key Exposure Attacks on RSA with Multiple Exponent Pairs2016

    • Author(s)
      Atsushi Takayasu
    • Organizer
      ACISP 2016
    • Place of Presentation
      オーストラリア、メルボルン
    • Year and Date
      2016-07-04
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] How to Generalize RSA Cryptanalyses2016

    • Author(s)
      Atsushi Takayasu, Noboru Kunihiro
    • Organizer
      19th International Conference on Practice and Theory in Public-Key Cryptography (PKC 2016)
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      2016-03-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Renyiダイバージェンスの次数を最適化した格子暗号のタイトな帰着2016

    • Author(s)
      高安敦,高島克幸
    • Organizer
      2016年 暗号と情報セキュリティシンポジウム(SCIS 2016)
    • Place of Presentation
      ANAクラウンプラザホテル熊本ニュースカイ (熊本市、熊本県)
    • Year and Date
      2016-01-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] 使用可能領域を有効活用したSieveアルゴリズムの高速化2016

    • Author(s)
      宮崎結香,谷垣友喜,高安敦,國廣昇
    • Organizer
      2016年 暗号と情報セキュリティシンポジウム(SCIS 2016)
    • Place of Presentation
      ANAクラウンプラザホテル熊本ニュースカイ (熊本市、熊本県)
    • Year and Date
      2016-01-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] 最小サンプルでLWE問題を解くためのBKWアルゴリズム2016

    • Author(s)
      上中谷健,國廣昇,高安敦
    • Organizer
      2016年 暗号と情報セキュリティシンポジウム(SCIS 2016)
    • Place of Presentation
      ANAクラウンプラザホテル熊本ニュースカイ (熊本市、熊本県)
    • Year and Date
      2016-01-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] Tighter Security for Efficient Lattice Cryptography via the Renyi Divergence of Optimized Orders2015

    • Author(s)
      Katsuyuki Takashima, Atsushi Takayasu
    • Organizer
      Provable Security - 9th International Conference (ProvSec 2015)
    • Place of Presentation
      Kanazawa Tokyu Hotel (Kanazawa city, Ishikawa)
    • Year and Date
      2015-11-24
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 近似GCD問題のパラメータ解析2015

    • Author(s)
      高安敦,國廣昇
    • Organizer
      2015年 コンピュータセキュリティシンポジウム(CSS 2015)
    • Place of Presentation
      長崎ブリックホール (長崎市、長崎県)
    • Year and Date
      2015-10-21
    • Related Report
      2015 Annual Research Report
  • [Presentation] 低ノイズLPN問題におけるBKWアルゴリズムの解析2015

    • Author(s)
      上中谷健,國廣昇,高安敦
    • Organizer
      2015年 コンピュータセキュリティシンポジウム(CSS 2015)
    • Place of Presentation
      長崎ブリックホール (長崎市、長崎県)
    • Year and Date
      2015-10-21
    • Related Report
      2015 Annual Research Report
  • [Presentation] Faster LLL Reduction to Break the Security of Fully Homomorphic Encryption and Multilinear Map over the Integers2015

    • Author(s)
      Atsushi Takayasu, Noboru Kunihiro
    • Organizer
      10th International Workshop on Security (IWSEC 2015)
    • Place of Presentation
      Todaiji Cultural Center (Nara city, Nara)
    • Year and Date
      2015-08-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Partial Key Exposure Attacks on CRT-RSA: Better Cryptanalysis to Full Size Encryption Exponents2015

    • Author(s)
      Atsushi Takayasu
    • Organizer
      Applied Cryptography and Network Security 13th International Conference, ACNS 2015
    • Place of Presentation
      New York, USA
    • Year and Date
      2015-06-02 – 2015-06-05
    • Related Report
      2014 Annual Research Report
  • [Presentation] Partial Key Exposure Attacks on CRT-RSA: Better Cryptanalysis to Full Size Encryption Exponents2015

    • Author(s)
      Atsushi Takayasu, Noboru Kunihiro
    • Organizer
      13th International Conference on Applied Cryptography and Network Security
    • Place of Presentation
      New York, America
    • Year and Date
      2015-06-02
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 改善された安全性証明を持つGGHLiteパラメータ2015

    • Author(s)
      高安敦
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Place of Presentation
      リーガロイヤルホテル小倉 (北九州市、福岡県)
    • Year and Date
      2015-01-20 – 2015-01-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] General Bounds for Small Inverse Problems and Its Applications to Multi-Prime RSA2014

    • Author(s)
      Atsushi Takayasu
    • Organizer
      Information Security and Cryptology - ICISC 2014 17th International Conference
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2014-12-03 – 2014-12-05
    • Related Report
      2014 Annual Research Report
  • [Presentation] Improved Algorithms for Partial Key Exposure Attacks on RSA2014

    • Author(s)
      Atsushi Takayasu
    • Organizer
      IWSEC 2014, 9th International Workshop on Security
    • Place of Presentation
      Hirosaki University (Hirosaki, Aomori)
    • Year and Date
      2014-08-27 – 2014-08-29
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Partial Key Exposure Attacks on RSA: Achieving Boneh-Durfee's Bound2014

    • Author(s)
      Atsushi Takayasu
    • Organizer
      Selected Areas in Cryptography -- SAC 2014 21st International Conference
    • Place of Presentation
      Montreal, Canada
    • Year and Date
      2014-08-14 – 2014-08-15
    • Related Report
      2014 Annual Research Report
  • [Presentation] Cryptanalysis of RSA with Multiple Small Secret Exponents2014

    • Author(s)
      Atsushi Takayasu
    • Organizer
      Information Security and Privacy 19th Australasian Conference, ACISP 2014
    • Place of Presentation
      Wollongong, Australia
    • Year and Date
      2014-07-07 – 2014-07-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] 複数の復号指数を持つRSA暗号の安全性解析2014

    • Author(s)
      高安敦
    • Organizer
      情報セキュリティ研究会
    • Place of Presentation
      サン・リフレ函館 (函館市、北海道)
    • Year and Date
      2014-07-03 – 2014-07-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] Partial Key Exposure Attacks on RSA When Most Significant Bits of d Known2014

    • Author(s)
      Atsushi Takayasu
    • Organizer
      9th ACM Symposium on Information, Computer and Communications Security, ASIA CCS 2014
    • Place of Presentation
      Kyoto Garden Palace (Kyoto, Kamigyo-ku)
    • Year and Date
      2014-06-04 – 2014-06-06
    • Related Report
      2014 Annual Research Report

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Published: 2015-01-22   Modified: 2024-03-26  

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