  Differential uniformity is a significant concept in cryptography as it
quantifies the degree of security of S-boxes respect to differential attacks.
Power functions of the form $F(x)=x^d$ with low differential uniformity have
been extensively studied in the past decades due to their strong resistance to
differential attacks and low implementation cost in hardware. In this paper, we
give an affirmative answer to a recent conjecture proposed by Budaghyan,
Calderini, Carlet, Davidova and Kaleyski about the differential uniformity of
$F(x)=x^d$ over $\mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and
$d=2^{3n}+2^{2n}+2^{n}-1$, and we completely determine its differential
spectrum.
