Let q be a power of a prime p, and let Sqbe the set of permutations of {0, 1,…, q – 1). As Sq is isomorphic to the group of permutations of Fq, the field of q elements, each element of 5, can be regarded as a polynomial over Fq. Various authors (e.g. [1], [2], [3]) have considered functions f(x) such that
f(x) ∈ Sq, and (f(x) + λ×) ∈ Sq
for some λ ∈ Fq when λ = 1, f(x) is a complete mapping polynomial ([3]).