GAPN多项式函数的构造

Constructions of GAPN Polynomial Functions

提出了一类GAPN单项式和一类GAPN二项式,推广了以前的两类构造;还提出了一种由已知GAPN函数构造大量GAPN多项式函数的方法.文章的构造能生成扩展仿射不等价于所有已知GAPN函数的GAPN函数,此外还对GAPN函数的差分性质进行了初步探讨.

In this paper,we propose a class of GAPN monomials and a class of GAPN binomials,generalizing two previous constructions.A new method is proposed to construct a large number of GAPN polynomials from known GAPN functions.The constructions proposed in this paper can generate new GAPN functions extended affine inequivalent to all known GAPN functions.In addition,the differential properties of GAPN functions are also discussed.