Parameter Dependency and Sufficient lterations for Limit Figures in Authentication Algorithm

In this paper, we deal with the parameter dependency for the limit figures and the sufficient number of iterations in drawing the limit figures of quadratic transformations. The structure of the limit figures depends on the coefficients of the transformation, and has turned out to be complicated. Using the property that the limit figures are one-way functions, Da-te (2001) proposed an authentication algorithm. For the purpose of verification of the securities in the authentication algorithm, we show the experimental results for some properties of the limit figures.