  Functions with low c-differential uniformity have optimal resistance to some
types of differential cryptanalysis. In this paper, we investigate the
c-differential uniformity of power functions over finite fields. Based on some
known almost perfect nonlinear functions, we present several classes of power
functions $f(x)=x^d$ with $_{c}\Delta_f\leq3$. Especially, two new classes of
perfect c-nonlinear power functions are proposed.
