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Security Evaluation of High Functional Encryption toward Post-Quantum Era

Research Project

Project/Area Number 16H02780
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Theory of informatics
Research InstitutionUniversity of Tsukuba (2018-2019)
The University of Tokyo (2016-2017)

Principal Investigator

Kunihiro Noboru  筑波大学, システム情報系, 教授 (60345436)

Co-Investigator(Kenkyū-buntansha) NGUYEN PHONG  東京大学, 大学院情報理工学系研究科, 客員教授 (80771419)
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Fiscal Year 2018: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2016: ¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Keywords暗号理論 / 安全性評価 / ポスト量子暗号 / 安全評価
Outline of Final Research Achievements

Lattice-based cryptography is expected as a post-quantum cryptosystem.Its security relies on the difficulty of lattice-related problems.We have succeeded in giving a precise analysis of its difficulty.In particular, we have obtained results on algorithms for solving the Shortest Vector Problem.We have evaluated how the realization of quantum computers affects conventional cryptographic techniques such as RSA cryptography.Specifically, we have given a comprehensive understanding of several physical experiments and discussed their effects on the real world.Furthermore, we have studied the security evaluation of conventional cryptography and have obtained results on its security.Through these results, we have succeeded in giving a security evaluation for cryptography in the post-quantum era, and have given a basis to use cryptography securely.

Academic Significance and Societal Importance of the Research Achievements

本課題では,ポスト量子時代を見据えた暗号技術に関して研究を行った.それにより,ポスト量子暗号方式の安全性の根拠となる問題の困難さを与えるとともに,量子計算機の現代暗号に対する影響に関して成果を得た.様々な条件下でのRSA暗号を代表とする現代暗号の安全性評価も与えている.以上の成果を通して,ポスト量子時代を見据えた暗号技術の安全性評価を与えることに成功しており,安心して暗号技術を利用する基礎を与えた.

Report

(4 results)
  • 2019 Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (65 results)

All 2020 2019 2018 2017 2016

All Journal Article (25 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 25 results,  Acknowledgement Compliant: 8 results) Presentation (39 results) (of which Int'l Joint Research: 5 results,  Invited: 3 results) Book (1 results)

  • [Journal Article] Worst case short lattice vector enumeration on block reduced bases of arbitrary blocksizes2020

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

      Discrete Applied Mathematics

      Volume: 277 Pages: 198-220

    • DOI

      10.1016/j.dam.2019.09.017

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Improved CRT-RSA Secret Key Recovery Method from Sliding Window Leakage2020

    • Author(s)
      Oonishi Kento, Huang Xiaoxuan, Kunihiro Noboru
    • Journal Title

      Proc. of ICISC2019

      Volume: LNCS 11975 Pages: 278-296

    • DOI

      10.1007/978-3-030-40921-0_17

    • ISBN
      9783030409203, 9783030409210
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Partial key exposure attacks on RSA: Achieving the Boneh-Durfee bound2019

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

      Theoretical Computer Science

      Volume: 761 Pages: 51-77

    • DOI

      10.1016/j.tcs.2018.08.021

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Attacking Noisy Secret CRT-RSA Exponents in Binary Method2019

    • Author(s)
      Oonishi Kento, Kunihiro Noboru
    • Journal Title

      Proc. of ICISC2018

      Volume: LNCS11396 Pages: 37-54

    • DOI

      10.1007/978-3-030-12146-4_3

    • ISBN
      9783030121457, 9783030121464
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Certifying Variant of RSA with Generalized Moduli2018

    • Author(s)
      Lu Yao, Kunihiro Noboru, Zhang Rui, Peng Liqiang, Ma Hui
    • Journal Title

      Proc. of ICICS2018

      Volume: LNCS11149 Pages: 598-608

    • DOI

      10.1007/978-3-030-01950-1_35

    • ISBN
      9783030019495, 9783030019501
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multi-party Key Exchange Protocols from Supersingular Isogenies2018

    • Author(s)
      Furukawa Satoshi, Kunihiro Noboru, Takashima Katsuyuki
    • Journal Title

      Proc. of ISITA2018

      Volume: - Pages: 208-212

    • DOI

      10.23919/isita.2018.8664316

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decentralized Netting Protocol over Consortium Blockchain2018

    • Author(s)
      Naganuma Ken, Yoshino Masayuki, Sato Hisayoshi, Yamada Nishio, Suzuki Takayuki, Kunihiro Noboru
    • Journal Title

      Proc. of ISITA2018

      Volume: - Pages: 174-177

    • DOI

      10.23919/isita.2018.8664259

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inference Attacks on Encrypted Databases Based on Order Preserving Assignment Problem2018

    • Author(s)
      Onozawa Sota, Kunihiro Noboru, Yoshino Masayuki, Naganuma Ken
    • Journal Title

      Proc. of IWSEC2018

      Volume: LNCS11049 Pages: 35-47

    • DOI

      10.1007/978-3-319-97916-8_3

    • ISBN
      9783319979151, 9783319979168
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Deterministic Algorithm for Computing Divisors in an Interval2018

    • Author(s)
      Peng Liqiang, Lu Yao, Kunihiro Noboru, Zhang Rui, Hu Lei
    • Journal Title

      Proc. of ACISP2018

      Volume: LNCS10946 Pages: 3-12

    • DOI

      10.1007/978-3-319-93638-3_1

    • ISBN
      9783319936376, 9783319936383
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Cryptanalysis of RSA Variants with Modified Euler Quotient2018

    • Author(s)
      Zheng Mengce, Kunihiro Noboru, Hu Honggang
    • Journal Title

      Proc. of Africacrypt2018

      Volume: LNCS10831 Pages: 266-281

    • DOI

      10.1007/978-3-319-89339-6_15

    • ISBN
      9783319893389, 9783319893396
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Mathematical Approach for Recovering Secret Key from Its Noisy Version2017

    • Author(s)
      Kunihiro Noboru
    • Journal Title

      Mathematical Modelling for Next-Generation Cryptography

      Volume: 29 Pages: 199-217

    • DOI

      10.1007/978-981-10-5065-7_11

    • ISBN
      9789811050640, 9789811050657
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recent Progress on Coppersmith’s Lattice-Based Method: A Survey2017

    • Author(s)
      Lu Yao, Peng Liqiang and Kunihiro Noboru
    • Journal Title

      Mathematical Modelling for Next-Generation Cryptography

      Volume: 29 Pages: 297-312

    • DOI

      10.1007/978-981-10-5065-7_16

    • ISBN
      9789811050640, 9789811050657
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Improved Factoring Attacks on Multi-prime RSA with Small Prime Difference2017

    • Author(s)
      Zheng Mengce, Kunihiro Noboru and Hu Honggang
    • Journal Title

      Proc. of ACISP 2017

      Volume: 10342 Pages: 324-342

    • DOI

      10.1007/978-3-319-60055-0_17

    • ISBN
      9783319600543, 9783319600550
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Solving the DLP with Low Hamming Weight Product Exponents and Improved Attacks on the GPS Identification Scheme2017

    • Author(s)
      Ying Jason H. M. and Kunihiro Noboru
    • Journal Title

      Proc. of ACISP 2017

      Volume: 10343 Pages: 460-467

    • DOI

      10.1007/978-3-319-59870-3_31

    • ISBN
      9783319598697, 9783319598703
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Bounds in Various Generalized Settings of the Discrete Logarithm Problem2017

    • Author(s)
      Ying Jason H. M. and Kunihiro Noboru
    • Journal Title

      Proc. of ACNS 2017

      Volume: 10355 Pages: 498-517

    • DOI

      10.1007/978-3-319-61204-1_25

    • ISBN
      9783319612034, 9783319612041
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Random Sampling Revisited: Lattice Enumeration with Discrete Pruning2017

    • Author(s)
      Aono Yoshinori, Nguyen Phong Q.
    • Journal Title

      Advances in Cryptology, EUROCRYPT 2017, Lecture Notes in Computer Science, Springer

      Volume: 10211 Pages: 65-102

    • DOI

      10.1007/978-3-319-56614-6_3

    • ISBN
      9783319566139, 9783319566146
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [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: E100.A Issue: 1 Pages: 50-61

    • DOI

      10.1587/transfun.E100.A.50

    • NAID

      130005180864

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / 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] Improved Key Recovery Algorithms from Noisy RSA Secret Keys with Analog Noise2017

    • Author(s)
      Noboru Kunihiro and Yuki Takahashi
    • Journal Title

      Proc. of CT-RSA2017

      Volume: LNCS10159 Pages: 328-343

    • DOI

      10.1007/978-3-319-52153-4_19

    • ISBN
      9783319521527, 9783319521534
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Improved Differential Fault Analysis on Camellia-1282016

    • Author(s)
      Toru Akishita and Noboru Kunihiro
    • Journal Title

      Proc. of COSADE2016

      Volume: LNCS 9689 Pages: 130-143

    • DOI

      10.1007/978-3-319-43283-0_8

    • ISBN
      9783319432823, 9783319432830
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / 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] 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] Small Secret Exponent Attacks on RSA with Unbalanced Prime Factors2016

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

      Proc. of ISITA2016

      Volume: - Pages: 236-240

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cold Boot Attack Methods for the Discrete Logarithm Problem2016

    • Author(s)
      Jason Ying and Noboru Kunihiro
    • Journal Title

      Proc. of CANDAR2016

      Volume: - Pages: 154-160

    • DOI

      10.1109/candar.2016.0037

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Decryption of Frequent Password Hashes in Rainbow Tables2016

    • Author(s)
      Jason Ying and Noboru Kunihiro
    • Journal Title

      Proc. of CANDAR2016

      Volume: - Pages: 655-661

    • DOI

      10.1109/candar.2016.0117

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Arduino Uno上に実装されたEd25519に対するマルチショット単純電力解析攻撃2020

    • Author(s)
      大西健斗,梨本翔永,鈴木大輔,國廣昇
    • Organizer
      SCIS2020
    • Related Report
      2018 Annual Research Report
  • [Presentation] 複数人鍵共有プロトコルSIBDの実装2020

    • Author(s)
      カク海萍,國廣昇
    • Organizer
      情報処理学会全国大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] アニーリング計算による素因数分解について (その2)2020

    • Author(s)
      伊豆哲也,清水俊也,篠原直行,盛合 志帆,國廣 昇
    • Organizer
      SCIS2020
    • Related Report
      2018 Annual Research Report
  • [Presentation] New Quantum Algorithms for Modular Inverse and Its Application on the Elliptic Curve Discrete Logarithm Problem2019

    • Author(s)
      Ryo Kurama and Noboru Kunihiro
    • Organizer
      AQIS2019 (Poster Presentation)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Quantum Factoring Algorithm: Resource Estimation and Survey of Experiments2019

    • Author(s)
      Noboru Kunihiro
    • Organizer
      MOQC2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Sliding Window法の誤りつき演算情報を用いたCRT-RSA秘密鍵復元手法2019

    • Author(s)
      大西健斗,國廣 昇
    • Organizer
      CSS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] Cayley hash function-map based on LPS-type Ramanujan graphs2019

    • Author(s)
      Hyungrok Jo, Noboru Kunihiro, Yoshinori Yamasaki
    • Organizer
      CSS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] 剰余逆元計算の新しい量子アルゴリズムと楕円曲線離散対数問題への応用2019

    • Author(s)
      鞍馬遼,國廣昇
    • Organizer
      ISEC研究会2019年7月
    • Related Report
      2018 Annual Research Report
  • [Presentation] Attacking Noisy Secret CRT-RSA Exponents in Binary Method (from ICISC 2018)2019

    • Author(s)
      大西健斗,國廣昇
    • Organizer
      ISEC研究会2019年5月
    • Related Report
      2018 Annual Research Report
  • [Presentation] 効率的な量子剰余加算回路の提案とその実装2019

    • Author(s)
      大西健斗,田中智樹,宇野隼平,山本直樹,國廣昇
    • Organizer
      第41回量子情報技術研究会 (QIT41)
    • Related Report
      2018 Annual Research Report
  • [Presentation] Sliding Window法の演算情報に基づくビット復元率の厳密な解析2019

    • Author(s)
      大西健斗,黄暁萱,國廣昇
    • Organizer
      SCIS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] Sliding Window法からの漏洩情報を用いた秘密鍵復元アルゴリズムの改良2019

    • Author(s)
      黄暁萱,大西健斗,國廣昇
    • Organizer
      SCIS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] 大きい復号鍵をもつRSA暗号に対する部分鍵導出攻撃の改良2019

    • Author(s)
      鈴木海地,高安敦,國廣昇
    • Organizer
      SCIS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] アニーリング計算による素因数分解について2019

    • Author(s)
      清水俊也,伊豆哲也,篠原直行,盛合志帆,國廣昇
    • Organizer
      SCIS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] 乗算可能な線形秘密分散法の整数計画法による構成2019

    • Author(s)
      江利口礼央,國廣昇
    • Organizer
      SCIS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] 準同型署名の弱安全性から強安全性への効率的な変換2019

    • Author(s)
      伊藤宗一郎,勝又秀一,國廣昇
    • Organizer
      SCIS2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] 数論変換におけるサイドチャネル情報を用いたRing-LWE暗号方式の秘密鍵復元攻撃2019

    • Author(s)
      大西健斗,國廣昇
    • Organizer
      ISEC研究会2019年3月
    • Related Report
      2018 Annual Research Report
  • [Presentation] Sliding window法からの漏洩情報を用いた秘密鍵復元攻撃の改良2018

    • Author(s)
      黄 暁萱,大西 健斗,國廣 昇
    • Organizer
      CSS2018
    • Related Report
      2018 Annual Research Report
  • [Presentation] RSA暗号の部分鍵導出攻撃の拡張2018

    • Author(s)
      鈴木海地,高安 敦,國廣 昇
    • Organizer
      ISEC研究会2018年7月
    • Related Report
      2018 Annual Research Report
  • [Presentation] 安全性を高めた共通鍵暗号の量子アルゴリズムに対する詳細な安全性評価2018

    • Author(s)
      安井 捷,國廣 昇
    • Organizer
      ISEC研究会2018年7月
    • Related Report
      2018 Annual Research Report
  • [Presentation] いくつかの理想的な秘密分散法を用いた最適な複数割り当て法2018

    • Author(s)
      江利口礼央,國廣昇,岩本 貢
    • Organizer
      SITA2018
    • Related Report
      2018 Annual Research Report
  • [Presentation] Shorのアルゴリズムに基づく素因数分解実験の調査2018

    • Author(s)
      國廣昇
    • Organizer
      QIT39
    • Related Report
      2018 Annual Research Report
  • [Presentation] Sliding Window法の誤りつき演算情報を用いたCRT-RSA秘密鍵復元アルゴリズム2018

    • Author(s)
      大西健斗,國廣昇
    • Organizer
      SCIS2018
    • Related Report
      2017 Annual Research Report
  • [Presentation] 素因数分解の現状2018

    • Author(s)
      伊豆 哲也,國廣 昇
    • Organizer
      SCIS2018
    • Related Report
      2017 Annual Research Report
  • [Presentation] Edwards型楕円曲線におけるHidden Number Problem2018

    • Author(s)
      小野澤 綜大,高安敦,國廣昇
    • Organizer
      SCIS2018
    • Related Report
      2017 Annual Research Report
  • [Presentation] 楕円曲線Hidden Number Problem のEdwards 曲線への拡張2018

    • Author(s)
      小野澤 綜大,高安 敦,國廣 昇
    • Organizer
      応用数理学会第14回研究部会連合発表会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Recovering RSA Secret Keys from Noisy Keys2017

    • Author(s)
      Noboru Kunihiro
    • Organizer
      WICS
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 2^m-ary法に基づく誤りつき演算情報を用いたCRT-RSA秘密鍵復元アルゴリズム2017

    • Author(s)
      大西健斗,國廣昇
    • Organizer
      ISEC研究会7月
    • Related Report
      2017 Annual Research Report
  • [Presentation] 楕円曲線ディフィー・ヘルマン鍵共有に対する格子簡約攻撃2017

    • Author(s)
      小野澤綜大,高安 敦,國廣 昇
    • Organizer
      ISEC研究会11月
    • Related Report
      2017 Annual Research Report
  • [Presentation] Recovering CRT-RSA Secret Keys from Noisy Secret Exponents2017

    • Author(s)
      Kento Oonishi and Noboru Kunihiro
    • Organizer
      IWSEC2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Recovering RSA Secret Keys from Noisy Keys2017

    • Author(s)
      Noboru Kunihiro
    • Organizer
      UTokyo - IIT Madras Workshop on Theoretical Computer Science
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [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,高安敦,國廣昇
    • Organizer
      電子情報通信学会情報セキュリティ研究会
    • Related Report
      2016 Annual Research Report
  • [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,國廣昇
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Related Report
      2016 Annual Research Report
  • [Presentation] On the Computational Complexity of the DLP with Low Hamming Weight Product Exponents2017

    • Author(s)
      Jason Ying. Noboru Kunihiro
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Related Report
      2016 Annual Research Report
  • [Presentation] Improved Factoring Attacks on Multi-Prime RSA with Small Prime Difference2017

    • Author(s)
      Mengce Zheng, Noboru Kunihiro, Honggang Hu
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Related Report
      2016 Annual Research Report
  • [Presentation] 超特異楕円曲線の同種写像を用いた擬似ランダム関数の構成2017

    • Author(s)
      古川悟,國廣昇,高島克幸
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Related Report
      2016 Annual Research Report
  • [Presentation] サイドチャネル攻撃によるCRT-RSA秘密鍵の復元2017

    • Author(s)
      大西健斗,國廣昇
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Related Report
      2016 Annual Research Report
  • [Presentation] アナログ情報からのRSA鍵復元アルゴリズムの理論解析2017

    • Author(s)
      國廣昇
    • Organizer
      暗号と情報セキュリティシンポジウム
    • Related Report
      2016 Annual Research Report
  • [Presentation] ブロック簡約格子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,國廣昇
    • Organizer
      電子情報通信学会情報セキュリティ研究会
    • Related Report
      2016 Annual Research Report
  • [Book] Mathematical modelling for next-generation cryptography : Crest Crypto-math Project2018

    • Author(s)
      Tsuyoshi Takagi, Masato Wakayama, Keisuke Tanaka, Noboru Kunihiro, Kazufumi Kimoto, and Dung Hoang Duong
    • Total Pages
      368
    • Publisher
      Springer
    • ISBN
      9789811050640
    • Related Report
      2017 Annual Research Report

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Published: 2016-04-21   Modified: 2021-02-19  

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