| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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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