报告时间：2022年10月14日（周五）14:00-16:00

报告地点：线上腾讯会议，会议ID（484692837）

报告题目：On Boolean functions with several flat spectra（关于具有几个平谱的布尔函数）

Abstract: Boolean functions have many applications in cryptography and coding theory. In this talk, we will give two constructions of Boolean functions which have at least two flat spectra with respect to {H, N}^n. Some known results about bent-negabent functions can be seen as special cases of our results. Furthermore, some lower bounds on the numbers of flat spectra of Boolean functions with respect to {H, N}^n or {I, N}^n are given. In particular, we show that any Maiorana-McFarland bent function of n (n even) variables has at least n/2 +2^(n/2) flat spectra with respect to {H, N}^n. Finally, following the work by Riera, Petrides, and Parker, we develop recursive formulae for the numbers of flat spectra of some structural quadratics, including star function, star-line function, and star-line-star function.

报告简介：布尔函数在密码学和编码理论中有许多应用。在本次报告中，我们将给出在{H, N}^n下至少有两个平谱的布尔函数的两种构造。关于bent-negabent函数的一些已知结果可以看作是我们结果的特例。此外，我们进一步给出了在{H, N}^n或{I, N}^n下布尔函数的平谱数的一些下界。特别是，我们证明了任何n (n为偶数) 变量的 Maiorana-McFarland型Bent函数在{H, N}^n上具有至少n/2 +2^(n/2) 个平谱。最后，根据 Riera、Petrides和Parke的工作，我们推导出诸如星函数、星-线函数和星-线-星函数等结构二次函数的平谱数的递推公式。

报告人介绍：伍高飞，博士，硕士生导师，西安电子科技大学网络与信息安全学院讲师。研究方向为对称密码学和序列设计，在国内外期刊会议上发表论文多篇，主持国家自然科学基金青年基金，陕西省科技计划项目，国家博士后面上项目等课题。