  Randomness extraction is of fundamental importance for information-theoretic
cryptography. It allows to transform a raw key about which an attacker has some
limited knowledge into a fully secure random key, on which the attacker has
essentially no information. Up to date, only very few randomness-extraction
techniques are known to work against an attacker holding quantum information on
the raw key. This is very much in contrast to the classical (non-quantum)
setting, which is much better understood and for which a vast amount of
different techniques are known and proven to work.
  We prove a new randomness-extraction technique, which is known to work in the
classical setting, to be secure against a quantum attacker as well. Randomness
extraction is done by XOR'ing a so-called delta-biased mask to the raw key. Our
result allows to extend the classical applications of this extractor to the
quantum setting. We discuss the following two applications. We show how to
encrypt a long message with a short key, information-theoretically secure
against a quantum attacker, provided that the attacker has enough quantum
uncertainty on the message. This generalizes the concept of entropically-secure
encryption to the case of a quantum attacker. As second application, we show
how to do error-correction without leaking partial information to a quantum
attacker. Such a technique is useful in settings where the raw key may contain
errors, since standard error-correction techniques may provide the attacker
with information on, say, a secret key that was used to obtain the raw key.
