Partially APN functions with APN-like polynomial representations

Abstract

In this paper we investigate several families of monomial functions with APN-like exponents that are not APN, but are partially 0-APN for infinitely many extensions of the binary field F2. We also investigate the differential uniformity of some binomial partial APN functions. Furthermore, the partial APN-ness for some classes of multinomial functions is investigated. We show also that the size of the pAPN spectrum is preserved under CCZ-equivalence.