Differential cryptanalysis famously uses statistical biases in the
propagation of differences in a block cipher to attack the cipher. In this
paper, we investigate the existence of more general statistical biases in the
differences. To this end, we discuss the $c$-differential uniformity of
S-boxes, which is a concept that was recently introduced in Ellingsen et. al.
to measure certain statistical biases that could potentially be used in attacks
similar to differential attacks. Firstly, we prove that a large class of
potential candidates for S-boxes necessarily has large $c$-differential
uniformity for all but at most $B$ choices of $c$, where $B$ is a constant
independent of the size of the finite field $q$. This result implies that for a
large class of functions, certain statistical differential biases are
inevitable.

In a second part, we discuss the practical possibility of designing a
differential attack based on weaknesses of S-boxes related to their
$c$-differential uniformity.

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