摘要
由于非线性组合函数的密码性质通常可以由函数的Walsh谱和自相关函数来刻划 ,因而对函数的密码性质的分析通常要计算大量的Walsh循环谱值和自相关函数值来验证 .该文利用一类k阶拟Bent函数的特殊性质 ,把对这类函数的密码性质的研究转化为对矩阵性质的研究 ,如平衡性、相关免疫性、扩散性、最高代数次数等 .这种转化避开了大量的计算 ,同时为构造密码性质好的k阶拟Bent函数提供了一种更为简洁且易于实现的方法 .
In this paper, the cryptographic properties of a special kind of k -order quasi-Bent functions are studied by a new kind of method, which is denoted by the matrix method. The cryptographic properties of the k -order quasi-Bent functions, such as balancedness, correlation immunity, propagation criterion and the highest algebraic degree can all be easily decided only by the distributions of 0 and 1 in the character matrix, which is different from the spectrum method and the auto-correlation method. The method proposed here can also be used to construct the k -order quasi-Bent functions with good cryptographic properties, which is more effective and much simpler than the spectrum method and can be carried out easily.
出处
《计算机学报》
EI
CSCD
北大核心
2004年第4期543-547,共5页
Chinese Journal of Computers
关键词
部分BENT函数
k阶拟Bent函数
特征矩阵
相关免疫性
代数次数
partially-Bent function
k -order quasi-Bent functions
characteristic matrix
correlation immunity
algebraic degree
