  The $c$-differential uniformity is recently proposed to reflect resistance
against some variants of differential attack. Finding functions with low
$c$-differential uniformity is attracting attention from many researchers. For
even characteristic, it is known that permutations of low Carlitz rank have
good cryptographic parameters, for example, low differential uniformity, high
nonlinearity, etc. In this paper we show that permutations with low Carlitz
rank have low $c$-differential uniformity. We also investigate $c$-differential
uniformity of permutations with Carlitz rank 3 in detail.
