  In our previous work, it was demonstrated that the attacker could not
pin-down the correct keys to start the Y00 protocol with a probability of one
under the assistance of unlimitedly long known-plaintext attacks and optimal
quantum measurements on the attacker's quantum memory. However, there were
several assumptions that the Y00 system utilized linear-feedback shift
registers as pseudo-random-number generators, and a fast correlation attack was
disabled by irregular mapping on the Y00 systems. This study generalizes such
an attack to remove the assumptions of the previous work. The framework of the
security analyses of this study reiterates two well-known results from the
past: (1) Y00 systems would be cryptanalyzed when the system is not designed
well; (2) the system is possibly information-theoretically secure when the
system is designed well, although the attacker's confidence in the correct key
increases over time but the success probability of key recovery does not reach
unity in finite time; (3) the breach time of the shared keys is increasingly
threatened with time. Hence, a key-refreshment procedure for the Y00 protocol
is provided herein. Such security analyses are important not only in key
refreshment but also in initial key agreement situations.
