Fourier Spectra of Binomial APN Functions

On the Fourier Spectra of the Infinite Families of Quadratic APN Functions

It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the new quadranomial family of APN functions. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.

奇特征下回旋镖均匀度与扩展差分之间的联系及其应用

A connection between the boomerang uniformity and the extended differential in odd characteristic and applications

本文首次建立经典差分/回旋镖均匀度与 c-差分均匀度的联系，证明奇 APN 函数的回旋镖均匀度等于其 (-1)-差分均匀度，并据此构造低差分均匀度函数、完成 p=3 情形的置换多项式刻画，推广奇特征下的差分均匀度上界。

多因素函数的统计学与其傅里叶变换

Statistics of a multi-factor function from its Fourier transform

通过傅里叶变换推导多因素函数的总体统计量，提出m系数/索引湮灭定理，揭示傅里叶域中项的索引和为零的特性，用于分析设计工具及搜索算法约束。