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

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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.