You'll probably want to use the tr/abc/xyz/ function. (Which will refer you to perldoc perlop, specifically the Quote and Quote-like operators.) The scheme you have will likely cause you a bit of grief:

$ cat cryppled.pl
#!/usr/bin/perl
use strict;
use warnings;
my %map = (
    a=>'b', b=>'d', c=>'g', d=>'c', e=>'f', f=>'a'
);
my $orig = 'abcdefgh';
print "orig: '$orig'\n";

my $new1 = $orig;
for my $k (keys %map) {
    $new1 =~ s/$map{$k}/$k/g;
}
print "new1: '$new1'\n";

my $new2 = $orig;
for my $k (reverse keys %map) {
    $new2 =~ s/$map{$k}/$k/g;
}
print "new2: '$new2'\n";

my $new3 = $orig;
$new3 =~ tr/abcdef/bdgcfa/;
print "new3: '$new3'\n";

$ perl crypplyd.pl
orig: 'abcdefgh'
new1: 'ffdbeedh'
new2: 'eaaaeech'
new3: 'bdgcfagh'
[download]

...roboticus

Update: The original documentation link was a bit brief, so I added the second one.

When your only tool is a hammer, all problems look like your thumb.