| Project/Area Number |
24540180
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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 |
Basic analysis
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| Research Institution | Kumamoto University |
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Principal Investigator |
NAITO Koichiro 熊本大学, 自然科学研究科, 教授 (10164104)
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| Co-Investigator(Kenkyū-buntansha) |
SHIROMOTO Keisuke 熊本大学, 大学院自然科学研究科, 教授 (00343666)
MISAWA Masashi 熊本大学, 大学院自然科学研究科, 教授 (40242672)
WADA Takeshi 島根大学, 大学院総合理工学研究科, 教授 (70294139)
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| Co-Investigator(Renkei-kenkyūsha) |
OGAWA Takayoshi 東北大学, 大学院理学研究科, 教授 (20224107)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | P-進数論 / 格子理論 / 暗号理論 / 力学系 / 非線形偏微分方程式 / 連分数展開 / p-進数論 / 関数解析 |
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| Outline of Final Research Achievements |
Analyzing simultaneous rational approximations of irrational p-adic numbers by using multi-dimensional p-adic approximation lattices, we investigate some recurrent properties of discrete orbits given by quasi-periodic dynamical systems, the frequencies of which are weak Liouville p-adic numbers and we show some unpredictability properties of the orbits. For the symbolic dynamical systems given by the coefficient sequences of expansions of p-adic numbers we give some inequality relations between the recurrent dimensions and the topological entropy of these systems.
For the shortest vector problems of p-adic approximation lattices we compare the theoretical solutions given by the simultaneous approximation problems (SAP) and the numerical solutions estimated by the LLL algorithm. By using these results we propose a new lattice based cryptosystem, the private keys of which are the SAP solutions of p-adic lattices.
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