On a Family of Planar Mappings
Kyureghyan Gohar, Tan Yin · NATO science for peace and security series. D, Information and communication security · 2009
A mapping f : GF(q) → GF(q) is called planar if for every nonzero a ∈ GF(q) the difference mapping Df,a: xf(x + a) - f(x) - f(a) is a permutation of GF(q). In this note we show that for certain choices of β,γ the mapping f(x) = Tr(βxq+1) + γx2is planar on GF(q3).