  Quantum Key Recycling (QKR) is a quantum-cryptographic primitive that allows
one to re-use keys in an unconditionally secure way. By removing the need to
repeatedly generate new keys it improves communication efficiency. Skoric and
de Vries recently proposed a QKR scheme based on 8-state encoding (four bases).
It does not require quantum computers for encryption/decryption but only
single-qubit operations.
  We provide a missing ingredient in the security analysis of this scheme in
the case of noisy channels: accurate bounds on the privacy amplification. We
determine optimal attacks against the message and against the key, for 8-state
encoding as well as 4-state and 6-state conjugate coding. We show that the
Shannon entropy analysis for 8-state encoding reduces to the analysis of
Quantum Key Distribution, whereas 4-state and 6-state suffer from additional
leaks that make them less effective. We also provide results in terms of the
min-entropy. Overall, 8-state encoding yields the highest capacity.
