Two Classes of Crooked Multinomials Inequivalent to Power Functions

Abstract: It is known that crooked functions can be used to construct many interesting combinatorial objects, and a quadratic function is crooked if and only if it is almost perfect nonlinear (APN). In this paper, we introduce two infinite classes of quadratic crooked multinomials on fields of order $2^{2m}$. One class of APN functions constructed in [7] is a particular case of the one we construct in Theorem 1. Moreover, we prove that the two classes of crooked functions constructed in this paper are EA inequivalent to power functions and conjecture that CCZ inequivalence between them also holds.