Generalized isotopic shift construction for APN functions

In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299–5309, 2020), when the initial function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for $$n=8$$ n = 8 and produces fifteen new APN functions for $$n=9$$ n = 9 .

Differentially low uniform permutations from known 4-uniform functions

Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential uniformity. In particular, we give two constructions of differentially 6-uniform functions, modifying the Gold function and the Bracken–Leander function on a subfield.