Constructing a theory of fixed points assciated with one-way functions

2017 Fiscal Year Final Research Report

• Project/Area Number: 26330150
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Information security
• Research Institution: Tohoku University
• Principal Investigator: Shizuya Hiroki 東北大学, 教育情報基盤センター, 教授 (50196383)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 一方向性関数 / 不動点 / 楕円曲線 / 離散対数問題

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.

Free Research Field

暗号理論