Create a reverse hash: 

        %by_value = reverse %by_key;
        $key = $by_value{$value};

    That's not particularly efficient. It would be more
    space-efficient to use: 

        while (($key, $value) = each %by_key) {
            $by_value{$value} = $key;
        }

    If your hash could have repeated values, the methods
    above will only find one of the associated keys.
    This may or may not worry you.

##</code><code>##

    package SpecialHash;
    use Tie::Hash;
    @SpecialHash::ISA = qw/Tie::StdHash/;

    sub FETCH {
        $_[1] eq "FLIPPED" ?
            { reverse %{ $_[0] } } :
            $_[0]->{$_[1]};
    }

    package main;
    tie my %hash, 'SpecialHash';
    @hash{ qw/foo bar/ } = qw/baz quux/;

    use Data::Dumper;
    print Dumper $hash{FLIPPED};