Regular Section
The Explicit Dual of Leander's Monomial Bent Function
2021 Volume E104.A Issue 9 Pages 1357-1360
Details
2021 Volume E104.A Issue 9 Pages 1357-1360
Permutation polynomials and their compositional inverses are crucial for construction of Maiorana-McFarland bent functions and their dual functions, which have the optimal nonlinearity for resisting against the linear attack on block ciphers and on stream ciphers. In this letter, we give the explicit compositional inverse of the permutation binomial $f(z)=z^{2^{r}+2}+\alpha z\in\mathbb{F}_{2^{2r}}[z]$. Based on that, we obtain the dual of monomial bent function $f(x)={\rm Tr}_1^{4r}(x^{2^{2r}+2^{r+1}+1})$. Our result suggests that the dual of f is not a monomial any more, and it is not always EA-equivalent to f.