A new construction for involutions over finite fields  

作　　者：Zhaohui ZHANG Qunying LIAO 

机构地区：[1]College of Mathematical Science,Sichuan Normal University,Chengdu,610066,China

出　　处：《Frontiers of Mathematics in China》2022年第4期553-565,共13页中国高等学校学术文摘·数学（英文）

基　　金：supported by the Notional Natural Science Foundation of China(Grant No.12071321).

摘　　要：In 2020,Niu et al.[Cryptogr.Commun.,2020,12(2):165–185]studied the fixed points of involutions over the finite field with q-elements.This paper further discusses the relationship between the fixed points set and the non-fixed points set 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.

关 键 词：Permutation polynomial INVOLUTION fixed point non-fixed point 

分 类 号：O18[理学—数学]