  Privacy amplification is a necessary step in all quantum key distribution
protocols, and error correction is needed in each except when signals of many
photons are used in the key communication in quantum noise approach. No
security analysis of error correcting code information leak to the attacker has
ever been provided, while an ad hoc formula is currently employed to account
for such leak in the key generation rate. It is also commonly believed that
privacy amplification allows the users to at least establish a short key of
arbitrarily close to perfect security. In this paper we show how the lack of
rigorous error correction analysis makes the otherwise valid privacy
amplification results invalid, and that there exists a limit on how close to
perfect a generated key can be obtained from privacy amplification. In
addition, there is a necessary tradeoff between key rate and security, and the
best theoretical values from current theories would not generate enough
near-uniform key bits to cover the message authentication key cost in
disturbance-information tradeoff protocols of the BB84 variety.
