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Construction of post quantum cryptography systems by p-adic analysis

Research Project

Project/Area Number 15K04978
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKumamoto University

Principal Investigator

Naito Koichiro  熊本大学, 大学院先端科学研究部(工), 名誉教授 (10164104)

Co-Investigator(Kenkyū-buntansha) 城本 啓介  熊本大学, 大学院先端科学研究部(工), 教授 (00343666)
Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsp-進数論 / 格子暗号理論 / 耐量子計算機暗号 / 記号力学系理論 / expander グラフ / Ramanujanグラフ / 擬似乱数生成器 / 符号理論 / 耐量子暗号理論 / ディオファンタス近似
Outline of Final Research Achievements

Using the theory of symbol dynamics and p-adic analysis, we construct pseudorandom generators and we theoretically and numerically estimate their randomness.
Constructing the knapsack type matrices which contain these pseudorandom sequences and using the p-adic approximation lattices given by these pseudorandom matrices, we propose some lattice cryptosystems and, furthermore, we propose an construction method of non-regular Ramanujan graphs, the adjacency matrices of which are these pseudorandom matrices. Our total research achievements are 18 papers and 20 lecture papers.

Academic Significance and Societal Importance of the Research Achievements

量子計算機の実現が予想される事例が頻繁に報告されている現在、特にランダム性を取り入れ安全性をより高めた暗号研究が早急に必要であるため、本研究で解析されたp-進擬似乱数生成器とそれを利用した格子型暗号系の提案は今後の耐量子計算機暗号研究における重要な基礎研究成果である。さらにまた、極めて高性能な情報拡散伝達性をもつ Ramanujan expanderグラフは情報関連分野における最重要研究課題の一つであるため, 本研究で解析されたより一般的な非正則Ramanujanに関わる研究結果も重要な基礎研究成果である。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report

Research Products

(51 results)

All 2020 2019 2018 2017 2016 2015

All Journal Article Presentation

  • [Journal Article] Pseudorandom number generator by p-adic chaos and Ramanujan expander graphs2020

    • Author(s)
      Koichiro Naito
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: -

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Randomness of p-adic discrete dynamical systems and its applications to cryptosystems2019

    • Author(s)
      Koichiro Naito
    • Journal Title

      Proc. 10th International Conference on Nonlinear Anal. Convex Anal. 2017

      Volume: -

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simultaneous approximation problems and knapsack cryptosystems with commitment schemes in p-adic numberlands2018

    • Author(s)
      Shoichi Kamada, Koichiro Naito
    • Journal Title

      Journal of Nonlinear and Convex Analysis: Proceedings of the fifth Asian Conference on Nonlinear Analysis and Optimization

      Volume: 19 Pages: 15871597-15871597

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shortest vector problems of p-adic random lattices and their application to a p-adic knapsack type cryptosystem2018

    • Author(s)
      Shoichi Kamada, Koichiro Naito
    • Journal Title

      Journal of Nonlinear and Convex Analysis: Proceedings of the fifth Asian Conference on Nonlinear Analysis and Optimization

      Volume: 19 Pages: 15991608-15991608

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On critical exponents of Dowling matroids2018

    • Author(s)
      Y. Koga, T. Maruta, K. Shiromoto
    • Journal Title

      Designs, Codes and Cryptography

      Volume: 86 Pages: 1947-1962

    • DOI

      10.1007/s10623-017-0431-8

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Unpredictability of quasi-periodic dynamical systems with multiple frequencies of a p-adic extremal number and its square2018

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Journal Title

      Journal of Nonlinear and Convex Analysis

      Volume: 18 Pages: 1349-1359

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Randomness of p-adic discrete dynamical systems and its applications to cryptosystems2018

    • Author(s)
      Koichiro Naito
    • Journal Title

      Proc. the 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis

      Volume: ー

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] The shortest vector problems in p-adic lattices and simultaneous approximation problems of p-adic numbers2017

    • Author(s)
      Hirohito Inoue and Koichiro Naito
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 3 Pages: 213-224

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simultaneous approximations of p-adic numbers and their applications to cryptography2017

    • Author(s)
      Hirohito Inoue, Shoichi Kamada and Koichiro Naito
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 3 Pages: 225-238

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Transference principle on simultaneous approximation problems of p-adic numbers and multidimensional p-adic approximation lattices2017

    • Author(s)
      Hirohito Inoue, Shoichi Kamada and Koichiro Naito
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 3 Pages: 239-249

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Unpredictability of quasi-periodic dynamical systems with multiple frequencies of a p-adic extremal number2017

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Journal Title

      J. Nonlinear and Convex Analysis

      Volume: -

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Shortest vector problems of p-adic random lattices2017

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Journal Title

      Proceedings of NAO-Asia2016

      Volume: -

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simultaneous approximation problems and knapsack cryptosystems with commitment schemes in p-adic numberlands2017

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Journal Title

      Proceedings of NAO-Asia2016

      Volume: -

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simultaneous Approximation Problems of p-Adic Numbers and p-Adic Knapsack Cryptosystems - Alice in p-Adic Numberland -2016

    • Author(s)
      Hirohito Inoue, Shoichi Kamada and Koichiro Naito
    • Journal Title

      P-Adic Numbers, Ultrametric Analysis, and Applications

      Volume: 8 Pages: 312-324

    • DOI

      10.1134/s207004661604004x

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Transference principle on simultaneous approximation problems of p-adic numbers and construction of lattice based cryptosystems2016

    • Author(s)
      Hirohito Inoue, Shoichi Kamada and Koichiro Naito
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2011 Pages: 57-63

    • Related Report
      2016 Research-status Report
    • Open Access
  • [Journal Article] On the Covering Dimension of a Linear Code2016

    • Author(s)
      Thomas Britz and Keisuke Shiromoto
    • Journal Title

      IEEE Trans. Information Theory

      Volume: 62 Pages: 2694-2701

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A generalization of Kung's theorem2016

    • Author(s)
      Trygve Johnsen, Keisuke Shiromoto, Hugues Verdure
    • Journal Title

      Des. Codes Cryptography

      Volume: - Pages: 169-178

    • DOI

      10.1007/s10623-015-0139-6

    • Related Report
      2016 Research-status Report 2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The shortest vector problems in p-adic lattices and simultaneous approximation problems of p-adic numbers2016

    • Author(s)
      Hirohito Inoue, Koichiro Naito
    • Journal Title

      Proc. of ICM Satellite Conf. 2014: the 4th Asian Conf. on Nonlinear Anal. and Optim.

      Volume: 4

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simultaneous approximations of p-adic numbers and their applications to cryptography2016

    • Author(s)
      Hirohito Inoue, Shoichi Kamada, Koichiro Naito
    • Journal Title

      Proc. of ICM Satellite Conf. 2014: the 4th Asian Conf. on Nonlinear Anal. and Optim.

      Volume: 4

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Transference principle on simultaneous approximation problems of p-adic numbers and multidimensional p-adic approximation lattices2016

    • Author(s)
      Hirohito Inoue, Shoichi Kamada, Koichiro Naito
    • Journal Title

      Proc. of ICM Satellite Conf. 2014: the 4th Asian Conf. on Nonlinear Anal. and Optim.

      Volume: 4

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Entropy and recurrent dimensions of discrete dynamical systems given by p-adic expansions2015

    • Author(s)
      Hirohito Inoue, Koichiro Naito
    • Journal Title

      P-Adic Numbers, Ultrametric Analysis, and Applications

      Volume: 7 Pages: 157-167

    • DOI

      10.1134/s2070046615020077

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simultaneous rational approximations of a p-adic number and its powers by p-adic approximation lattices2015

    • Author(s)
      Hirohito Inoue, Koichiro Naito
    • Journal Title

      Proc. of the 8th International Conf. on Nonlinear Anal. and Convex Anal.

      Volume: 8 Pages: 155-166

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lattice reduction algorithms and their cryptographic applications2015

    • Author(s)
      Hirohito Inoue, Koichiro Naito, Yuma Yamada
    • Journal Title

      Proc. of the 8th International Conf. on Nonlinear Anal. and Convex Anal.

      Volume: 8 Pages: 167-176

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] The shortest vector problems in p-adic approximation lattices and their applications to cryptography2015

    • Author(s)
      Hirohito Inoue, Koichiro Naito
    • Journal Title

      京都大学数理解析研究所講究録 1963 「非線形解析学と凸解析学の研究」

      Volume: 1963 Pages: 16-23

    • Related Report
      2015 Research-status Report
  • [Presentation] Critical Problem for Binary Matroids2019

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 17th Japan-Korea Workshop on Algebra and Combinatorics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Critical Problem for Binary Matroids2019

    • Author(s)
      城本 啓介
    • Organizer
      研究集会「組合せ論的符号理論」
    • Related Report
      2018 Annual Research Report
  • [Presentation] Pseudorandom number generator by p-adic chaos and Ramanujan expander graphs2018

    • Author(s)
      Koichiro Naito
    • Organizer
      The 6th Asian Conference on Nonlinear Analysis and Optimization
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Critical Problem for Binary Matroids2018

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      Monash Univ. Discrete Maths Research Group Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Codes with Rank Metric and Matroids2018

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The Japanese Conference on Combinatorics and its Applications (JCCA 2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Critical Problem for matroids and Code2018

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      Discrete Structures and Algorithms Seminar in University of Melbourne
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Unpredictability and randomness of p-adic symbolic dynamical systems2017

    • Author(s)
      Koichiro Naito
    • Organizer
      The 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Randomness of p-adic discrete dynamical systems and its applications to cryptosystem2017

    • Author(s)
      Koichiro Naito
    • Organizer
      The 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Matroids and Codes with Rank Metric2017

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      5th International Combinatorics Conference (5ICC) 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Codes with Rank-Metric and Matroids2017

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      Japanese Conference on Combinatorics and its Applications (JCCA2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 符号とマトロイドの極値問題について2017

    • Author(s)
      城本啓介
    • Organizer
      愛媛大学数学科談話会(第45回代数セミナー 2017)
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Compact knapsack problems and p-adic lattices2017

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Organizer
      Workshop「数論とエルゴード理論2017」
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Related Report
      2016 Research-status Report
  • [Presentation] Critical problem for matroids and codes2017

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      Discrete Mathematics Research Group meeting
    • Place of Presentation
      Monash University, Melbourne, Australia
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 符号理論的マトロイド理論へのいざない2017

    • Author(s)
      城本 啓介
    • Organizer
      筑波大学組合せ論・情報理論セミナー
    • Place of Presentation
      筑波大学、茨城
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Critical problem in coding theory2016

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 4th Japan-Taiwan Conference on Combinatorics and its Applications
    • Place of Presentation
      北九州国際会議場
    • Year and Date
      2016-03-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Simultaneous approximation problems of p-adic numbers and their application to lattice based cryptosystems2016

    • Author(s)
      Shoichi Kamada, Hirohito Inoue, Koichiro Naito
    • Organizer
      日本数学会九州支部会
    • Place of Presentation
      九州大学
    • Year and Date
      2016-02-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Complexity and recurrency of p-adic dynamical systems and its application2016

    • Author(s)
      Hirohito Inoue, Koichiro Naito
    • Organizer
      日本数学会九州支部会
    • Place of Presentation
      九州大学
    • Year and Date
      2016-02-13
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Multi-dimensional p-adic approximation lattices and their applications to knapsack cryptosystems2016

    • Author(s)
      Shoichi Kamada, Hirohito Inoue, Koichiro Naito
    • Organizer
      Workshop「数論とエルゴード理論2016」
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Year and Date
      2016-02-06
    • Related Report
      2015 Research-status Report
  • [Presentation] Construction of lattice based cryptosystems by simultaneous approximation problems in p-adic numberlands2016

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Organizer
      International Workshop on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Shortest vector problems on the random p-adic lattices given by powers of a p-adic number and their applications to p-adic knapsack type cryptosystem2016

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Organizer
      The 6th Asian Conf. on Nonlinear Analysis and Optimization 2016
    • Place of Presentation
      Toki Messe, Niigata
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Simultaneous approximation problems and knapsack cryptosystems with commitment schemes in p-adic numberlands2016

    • Author(s)
      Shoichi Kamada and Koichiro Naito
    • Organizer
      The 6th Asian Conf. on Nonlinear Analysis and Optimization 2016
    • Place of Presentation
      Toki Messe, Niigata
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Simultaneous approximation problems and knapsack cryptosystems in p-adic numberlands2016

    • Author(s)
      Hirohito Inoue, Shoichi Kamada, Koichiro Naito and Keisuke Shiromoto
    • Organizer
      Numeration 2016
    • Place of Presentation
      Czech Technical University, Prague
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the covering number of matroids2016

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 40th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (40ACCMCC)
    • Place of Presentation
      University of Newcastle, Newcastle, Australia
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Codes from complete bipartite graphs and 3-regular graphs2015

    • Author(s)
      Keisuke Shiromoto, Shunpei Yamaguchi
    • Organizer
      39th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of Queensland, Australia
    • Year and Date
      2015-12-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Critical exponents of Dowling matroids2015

    • Author(s)
      Yoshitaka Koga, Keisuke Shiromoto
    • Organizer
      39th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of Queensland, Australia
    • Year and Date
      2015-12-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Transference principle on simultaneous approximation problems of p-adic numbers and construction of lattice based cryptosystems2015

    • Author(s)
      Shoichi Kamada, Hirohito Inoue, Koichiro Naito
    • Organizer
      International Workshop on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On covering dimension of linear codes and matroids2015

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      25th British Combinatorial Conference
    • Place of Presentation
      University of Warwick, UK
    • Year and Date
      2015-07-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

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Published: 2015-04-16   Modified: 2020-03-30  

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