Abstract
Abstract The paper is concerned with combinatorial description of almost perfect nonlinear functions (APN-functions). A complete characterization of n-place APN-functions in terms of (n − 1)-place subfunctions is obtained. An n-place function is shown to be an APN-function if and only if each of its (n − 1)-place subfunctions is either an APN-function or has the differential uniformity 4 and the admissibility conditions hold. A detailed characterization of 2, 3 or 4-place APN-functions is presented.
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