半Bent函数和多输出布尔函数的构造

半bent函数是一类非线性度几乎最优且平衡的布尔函数,它弥补了bent函数的一些不足,如变元个数可以是奇数,具有平衡性.半bent函数可用于对称密码系统的设计和CDMA系统中的正交可变扩频码的构造.本文利用不相交线性码构造了一类新的半bent函数,设输入维度为n,当n=2k+1时,将F2^n划分为2^k+1个[n,k]线性码和1个[n,k+1]线性码,通过从该码集中选取合适线性码作支撑集来构造新的半bent函数.另一方面,多输出布尔函数(向量值函数)在应用中的效率更高,因此其使用场景更为广泛.本文同时利用不相交线性码构造了(n,n-k)平衡的多输出布尔函数,其中n/3

Constructions of Semi-bent Functions and Multi-output Boolean Functions

Semi-bent functions are balanced Boolean functions with high nonlinearity,which complements some shortcomings of bent functions.For example,semi-bent functions are balanced and the number of input variables can be odd.Apart from the applications in cryptography,semi-bent functions are also widely used in certain combinatorial designs such as construction of orthogonal variable spreading factor codes used in CDMA systems and for the sequence design.In this paper,a new construction method of semi-bent functions by using disjoint linear codes is proposed.For example,when n=2k+1,F2^n can be divided into 2^k+1 of[n,k]linear codes and one[n,k+1]linear code,these disjoint linear codes can be used to construct new semi-bent functions.In addition,multi-output Boolean functions are very efficient in many applications,so they are widely used.This paper constructs a class of(n,n-k)balanced multi-output Boolean functions by using disjoint linear codes,where n/3