The Leftover Hash Lemma states that the output of a two-universal hash
function applied to an input with sufficiently high entropy is almost
uniformly random. In its standard formu- lation, the lemma refers to a
notion of randomness that is (usu- ally implicitly) defined with
respect to classical side information.  Here, a strictly more general
version of the Leftover Hash Lemma that is valid even if side
information is represented by the state of a quantum system is
shown. Our result applies to almost two-uni- versal families of hash
functions. The generalized Leftover Hash Lemma has applications in
cryptography, e.g., for key agreement in the presence of an adversary
who is not restricted to classical information processing.