几类基于0-线性转换的置换多项式

有限域上的置换多项式在密码学,编码理论和序列设计等领域中有着广泛的应用.至今,对于置换多项式的研究已取得一系列的进展,研究者提出利用AGW准则、分段函数等来构造和证明置换,而对于置换多项式的分类仅有少数几种被提出,因此构造不同类型的置换多项式是一个值得研究的问题.本文利用迹函数和线性化多项式构造了一类有限域上具有特殊形式的无限类置换多项式.首先,我们对一类线性化多项式和一类二次齐次多项式进行讨论,当其存在线性转换时,给出其需要满足的条件.进一步地,当这两类多项式存在0-线性转换时,我们利用这两类函数构造出了有限域上具有特殊形式的两类置换多项式.

Several Classes of Permutation Polynomials from 0-Linear Translators

Permutation polynomials over finite fields are widely used in cryptography, coding theory and sequence design. The study of permutation polynomials has made a great progress. Some construction methods such as AGW criterion and piecewise function method have been proposed.However, only a few types of permutation polynomials are known. Thus, it is desirable to construct new classes of permutation polynomials. This paper constructs a class of infinite permutation polynomials with special form over finite fields by using trace function and linearized polynomials. First of all, a class of linearized polynomials and a class of quadratic homogeneous polynomials are discussed,and the conditions for the existence of linear transformation are derived. Then, two classes of permutation polynomial are obtained by employing the 0-linear translator of the investigated two classes of polynomials respectively.