Low c-differentially uniform functions via an extension of Dillon's switching method
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In this paper we generalize Dillon's switching method to characterize the exact c-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known c-differential uniformity in a controllable number of coordinates to render more such functions. We present several applications of the method in constructing PcN and APcN functions with respect to all c≠ 1. As a byproduct, we generalize some result of [Y. Wu, N. Li, X. Zeng, New PcN and APcN functions over finite fields, Designs Codes Crypt. 89 (2021), 2637–2651]. Computational results rendering functions with low differential uniformity, as well as, other good cryptographic properties are sprinkled throughout the paper.
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