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Title:
On the minimal value set size of APN functions
Authors: Ingo Czerwinski
Abstract:We give a lower bound for the size of the value set of almost perfect nonlinear (APN) functions (F\colon \mathbb{F}_2^n \to \mathbb{F}_2^n) in explicit form and proof it with methods of linear programming. It coincides with the bound given in [CHP17]. For (n) even it is (\frac{ 2^n + 2 }{3}) and sharp as the simple example (F(x) = x^3) shows. The sharp lower bound for (n) odd has to lie between (\frac{ 2^n + 1 }{3}) and (2^{n-1}). Sharp bounds for the cases (n = 3) and (n = 5) are explicitly given.
ePrint: https://eprint.iacr.org/2020/705
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