On the exponents of APN power functions and Sidon sets, SUM-free sets, and Dickson Polynomials

We derive necessary conditions related to the notions, in additive combinatorics, of Sidon sets and sum-free sets, on those exponents d ∈ Z/(2ⁿ − 1)Z, which are such that F (x) = x^d is an APN function over F₂n (which is an important cryptographic property). We study to what extent these new conditions may...