Crooked maps in \(\mathbb F_{2^n}\) (Q2370651)

Almost perfect nonlinear (APN) maps provide the best resistance against the differential cryptanalysis. A special class of APN maps are called \(crooked\). Crooked maps can be used to construct many interesting combinatorial objects -- codes, graphs, schemes, etc. The only known crooked maps are polynomials with exponents of binary weight 2. In this paper, the authors study the question whether other crooked maps exist. Using combinatorics in the cyclic group of order \(n\), the authors show that in a class of maps including power maps only the ones with exponents of binary weight 2 can be crooked.