一类有限域上的置换多项式

摘要

有限域上的置换多项式在科学工程中的多个领域有着广泛的应用,尤其应用于现代通讯、密码学等领域中基于Zha等人在文献[23]中提出,当t为偶数时,有限域Fpn上形如(xpk一x+δ)t+γx十βTr(x)的多项式是置换的,通过进一步研究,运用证明置换多项式的一般方法,将其改进为无论t为奇数或偶数,(xpk+1一xk+δ)t+ γx十βTr(x)形式的多项式在Fpn上均是置换的.%Permutation polynomials over finite fields have been applied in wild areas of science and engineering,especially in the modern communication technology,cryptography and so on.Based on paper [23],it has been proved that when t is any even integer,the form (xpk-x+δ)t +γx+βTr(x) is a class of permutation polynomials over Fpn.Our work proved that whenever t is any even or odd integer,the form (xpk+1-xp +δ)t+ γx+βTr(x)is permutation polynomials over Fpn.