New PcN and APcN functions over finite fields

Functions with low c-differential uniformity were proposed in 2020 and attracted lots of attention, especially the PcN and APcN functions, due to their applications in cryptography. The objective of this paper is to study PcN and APcN functions. As a consequence, we propose a class of PcN functions and four classes of APcN functions by using the cyclotomic technique and the switch method. In addition, four classes of PcN or APcN functions are presented by virtue of (generalized) AGW criterion.

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