The easiest solution, under Unix at least, is to call 'stty' to change the terminal's "echo" attribute. I know of no way to do this under Windows or any non-Unix platform, and there may be a more standardized way of doing this (such as via curses or some Term-based module):

print "login: "
my $login = <>;
print "Password: "
system('/usr/bin/stty', '-echo');  # Disable echoing
my $password = <>;
system('/usr/bin/stty', 'echo');   # Turn it back on
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