  Quantum key distribution allows two parties, traditionally known as Alice and
Bob, to establish a secure random cryptographic key if, firstly, they have
access to a quantum communication channel, and secondly, they can exchange
classical public messages which can be monitored but not altered by an
eavesdropper, Eve. Quantum key distribution provides perfect security because,
unlike its classical counterpart, it relies on the laws of physics rather than
on ensuring that successful eavesdropping would require excessive computational
effort. However, security proofs of quantum key distribution are not trivial
and are usually restricted in their applicability to specific protocols. In
contrast, we present a general and conceptually simple proof which can be
applied to a number of different protocols. It relies on the fact that a
cryptographic procedure called privacy amplification is equally secure when an
adversary's memory for data storage is quantum rather than classical.
