On those multiplicative subgroups of $${\mathbb F}_{2^n}^*$$ which are Sidon sets and/or sum-free sets

Abstract

We study those multiplicative subgroups of $${\mathbb F}_{2^n}^*$$ which are Sidon sets and/or sum-free sets in the group $$({\mathbb F}_{2^n},+)$$ . These Sidon and sum-free sets play an important role relative to the exponents of APN power functions, as shown by a paper co-authored by the first author.