2017 Fiscal Year Final Research Report
Constructing a theory of fixed points assciated with oneway functions
Project/Area Number 
26330150

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Multiyear 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) 
20140401 – 20180331

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 oneway function is essential for us to keep information and information systems secure. The purpose of this research project is to reinvestigate oneway 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 oneway as far as for the fixed point. We especially attempted to solve an open question concerning the property of fixed points of an ellipticcurve 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 nontrivial fixed points.

Free Research Field 
暗号理論
