  It has been pointed out by Yuen that the security theory of quantum key
distribution(QKD) guided by Shor-Preskill theory has serious defects, in
particular their key rate theory is not correct. Theory groups of QKD tried to
improve several defects. Especially, Renner employed trace distance and quantum
leftover Hash Lemma. However, the present theory encountered a problem of a
quantitative evaluation of security. To cope with it, he uses a wrong
interpretation on the trace distance and its level epsilon_{sec}, and justifies
the unconditional security of own system when epsilon_{sec} is 10^{-6 } ~
10^{-20}. In this paper, we discuss the following problems. What is the origin
of the misconception of the present theory? How does the present theory lead to
the misconception?. To show their process toward the misconception,
Koashi-Preskill's theory which has a typical misconception is examined. A main
point of our comment is that QKD theory ignores the security requirement
against attacker which is necessary to compare whole encryption schemes from
classical to quantum. To clarify it, we emphasize that the trace distance
itself cannot have any operational meaning such as failure probability, and it
is only mathematical tool as a measure of closeness. As a result, it is given
that the security with above values derived from their formulation means
nothing in the general cryptological sense. In addition, I point out that a
comment by Bennett and Riedel on unconditional security of QKD is not correct.
Also, I point out that the experimental systems of groups of Los Alamos,
Toshiba-UK, NICT, and others cannot have security guarantee even in future.
