  Privacy amplification (PA) is an essential post-processing step in quantum
key distribution (QKD) for removing any information an eavesdropper may have on
the final secret key. In this paper, we consider delaying PA of the final key
after its use in one-time pad encryption and prove its security. We prove that
the security and the key generation rate are not affected by delaying PA.
Delaying PA has two applications: it serves as a tool for significantly
simplifying the security proof of QKD with a two-way quantum channel, and also
it is useful in QKD networks with trusted relays. To illustrate the power of
the delayed PA idea, we use it to prove the security of a qubit-based two-way
deterministic QKD protocol which uses four states and four encoding operations.
