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**2015/1244**

**Title:**

On values of vectorial Boolean functions and related problems in APN functions

**Authors:**
George Shushuev

**Abstract:**

In this paper we prove that there are only differential 4-uniform functions which are on distance 1 from an APN function. Also we prove that there are no APN functions of distance 1 from another APN functions up to dimension 5. We determine some properties of the set of values of an arbitrary vectorial Boolean function from F_n^2 to F_n^2 in connection to the set of values of its derivatives. These results are connected to several open question concerning metric properties of APN functions.

**ePrint:**
https://eprint.iacr.org/2015/1244

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