A class of permutations on \({\mathbb {Z}}_{p}\) with differential uniformity at most 3

In this paper, we give a class of permutations on \({\mathbb {Z}}_{p}\) ${\mathbb{Z}}_p$ having differential uniformity at most 3, where prime p satisfies \(p \equiv 1 \pmod {4}\) $p\equiv 1(mod4)$ . Further, we present a sufficient condition for differential uniformity exactly 3 and identify a subclass achieving this value.