| Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2015: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
It is clear today that the notion of one-way function is essential for us to keep information and information systems secure. The purpose of this research project is to re-investigate one-way functions from a viewpoint of fixed points. Intuitively a fixed point x of a function f is defined as f(x)=x. Since the output is the same as the input, the function looks not to be one-way as far as for the fixed point.
We especially attempted to solve an open question concerning the property of fixed points of an elliptic-curve version of a cryptographic function, and in fact have given a partial solution to the question: among all the elliptic curves, more than a half curves lead to a function that has a trivial fixed point. We have also shown quantitative estimation for non-trivial fixed points.
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