We analysis the Lagarias--Odlyzko low-density attack precisely,
and 
show that this low-density attack can be applied to the Chor--Rivest
and the Okamoto--Tanaka--Uchiyama cryptosystemes,
which are considered to be secure against the low-density attack.
According to our analysis, 
these schemes turn out to be no longer secure against
the low-density attack.