Construction of permutations with low c-differential and boomerang uniformities

Vectorial boolean functions with low c-differential and boomerang uniformities, especially the almost perfect c-nonlinear functions, are widely used in cryptography. This paper constructed a new class of non-monomial functions over finite fields by using trace functions. By calculating Weil sums we obtained the c-difference distribution table of this class of functions, and we concluded that they are almost perfect c-nonlinear functions over finite fields. Furthermore, it is proved that the constructed functions have low boomerang uniformity.