Linear cryptanalysis, introduced in 1994 by Matsui, will most certainly open-up the way to new attack methods which may be made more efficient when compared or combined with differential cryptanalysis. This paper exhibits new relations between linear and differential cryptanalysis and presents new classes of functions which are optimally resistant to these attacks. In particular, we prove that linear-resistant functions, which generally present Bent properties, are differential-resistant as well and thus, present perfect nonlinear properties