Paper 2018/769

Constructing APN functions through isotopic shifts

Lilya Budaghyan and Marco Calderini and Claude Carlet and Robert S. Coulter and Irene Villa

Abstract

Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, information theory as well as mathematics. Building new APN families is a challenge which has not been successfully addressed for more than seven years now. The most general known equivalence relation preserving APN property in characteristic 2 is CCZ-equivalence. Extended to general characteristic, it also preserves planarity. In the case of quadratic planar functions, it is a particular case of isotopic equivalence. We apply the idea of isotopic equivalence to transform APN functions in characteristic 2 into other functions, some of which can be APN. We deduce new quadratic APN functions and a new quadratic APN family.