有限域上对合的一类新构造

A New Construction for Involutions over Finite Fields

2020年牛泰霖等人在[Cryptogr.Commun.,2020,12(2):165-185]中研究了q元有限域F_(q)上对合的不动点.基于此,本文讨论了F_(q)上两个对合f_(1)(x),f_(2)(x)的不动点集合与非不动点集合之间的关系,由此得到复合函数f_(1)οf_(2)(x)为F_(q)上对合的充要条件.特别地,由此完全确定了两个特殊有限域上的一类对合.

In 2020,Niu et al.in[Cryptogr.Commun.,2020,12(2):165-185]studied the fixed points of involutions over finite fields with q-elements.This paper further discusses the relationship between the fixed points and the non-fixed points of two involutions f_(1)(x)and f_(2)(x)over the finite field F_(q),and then obtains a necessary and sufficient condition for that the composite function f_(1)■f_(2)(x)is also an involution over F_(q).In particular,a special class of involutions over some finite fields is determined completely.