2017 Fiscal Year Final Research Report
New principle of cryptosystem via translation of Diophantine equations
| Project/Area Number |
26520208
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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 | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Nihon University |
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Principal Investigator |
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| Research Collaborator |
AKIYAMA Koichiro
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| Project Period (FY) |
2014-07-18 – 2018-03-31
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| Keywords | 公開鍵暗号 / 多項式写像 / 鍵共有方式 / 暗号方式 / 安全証明 / 可逆写像 / ディオファントス方程式 / ディオファントス近似 |
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| Outline of Final Research Achievements |
We propose a new key exchange protocol using polynomial maps, whose security relies on the hardness in finding the solutions to certain polynomial equations. In particular, it concerns polynomial Diophantine equations combined with several translations. Under the assumption that protocol is established honestly, we prove with K. Akiyama, S. Nakamura and M. Ito that our protocol is secure in the sense of the hardness of recovering the common key from the observed data.
Form the viewpoint of Diophantine problem in number theory, by means of the method above, we also obtain new results related to the irrationality of polylogarithms and values of special functions of form of Dirichlet series with periodic coefficients.
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| Free Research Field |
数論・ディオファントス問題・暗号原理
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