Constructions of Semi-Bent Functions by Modifying the Supports of Quadratic Boolean Functions

抄録

Semi-bent functions have almost maximal nonlinearity. In this paper, two classes of semi-bent functions are constructed by modifying the supports of two quadratic Boolean functions $f_1(x_1,x_2,\cdots,x_n)=\bigoplus\limits^{k}_{i=1}x_{2i-1}x_{2i}$ with $n=2k+1\geq3$ and $f_2(x_1,x_2,\cdots,x_n)=\bigoplus\limits^{k}_{i=1}x_{2i-1}x_{2i}$ with $n=2k+2\geq4$. Meanwhile, the algebraic normal forms of the newly constructed semi-bent functions are determined.