Abstract: Combining the concatenation method, a construction of Bent function of n variables from k Bent function is proposed. After analyzing the cryptographic properties of the Bent function of variables, a new construction method which is different from the original method and the reconstruction method is presented. The necessary and sufficient conditions of Bent function of n variables are derivated and validated. Based on the linear invariance of Bent function of n variables, a new set of Bent function is constructed.

Key words: cryptography, Boolean function, Bent function, nonlinearity

摘要： 结合级联构造方法，通过k元Bent函数级联构造n元Bent函数，分析构造出的n元Bent函数的各种密码学性质，给出一种不同于直接构造和二次构造的新型构造方法。推导并验证n元布尔函数为Bent函数的充要条件，基于n元Bent函数的线性不变性，进一步构造出一个Bent函数集。

关键词: 密码学, 布尔函数, Bent函数, 非线性度

CLC Number: 

• TP309