Constructing APN functions through isotopic shifts [article]

Lilya Budaghyan, Marco Calderini, Claude Carlet, Robert S. Coulter, Irene Villa
2018 IACR Cryptology ePrint Archive  
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
more » ... ic 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.
dblp:journals/iacr/BudaghyanCCCV18 fatcat:bafviyi52fa53iirzj4dnmjgme