Biprojective Almost Perfect Nonlinear Functions

In this paper, we introduce the concept of biprojectivity in studying the cryptographically important almost perfect nonlinear (APN) functions. Although several known families of biprojective APN functions exist in the literature, the concept itself has not been explicitly observed and studied in detail. We give a survey of known APN families and functions that fall into the biprojective setting, then provide a method for finding such families and functions. We finally give two new infinite families of biprojective APN functions
${\mathsf {CCZ}}$
-inequivalent to any known APN function and study their properties.