Construction of post quantum cryptography systems by p-adic analysis
| Project/Area Number |
15K04978
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kumamoto University |
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Principal Investigator |
Naito Koichiro 熊本大学, 大学院先端科学研究部(工), 名誉教授 (10164104)
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| 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)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| 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)
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| Keywords | p-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 |
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| 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.
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| 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。
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Report
(5 results)
Research Products
(51 results)
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[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
Int'l Joint Research
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[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
Int'l Joint Research
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