  It is repeatedly and persistently claimed in the literature that a specific
trace criterion $d$ would guarantee universal composition security in quantum
cryptography. Currently that is the sole basis of unconditional security claim
in quantum key distribution. In this paper, it is shown that just security
against known-plaintext attacks when the generated key is used in direct
encryption is not provided by $d$. The problem is directly connected with
several general problems in the existing unconditional security proofs in
quantum key distribution. A number of issues will be clarified concerning the
nature of true security, privacy amplification, key generation rate and the
mathematical approach needed for their determination in concrete protocols.
