There are a large number of hashing algorithms you could use. Most of them work better in C / C++ than Perl, however, since you really need unsigned numbers, and there doesn't seem to be a simple way to tell Perl you don't want a signed variable. The following should work ok for strings of more than a few characters:

use strict;
use warnings;

print hash('dfsdgogmoerigre');

BEGIN {
    my @c = (0..9, 'A'..'F');
    my $c = $#c + 1;
    sub hash {
        my ($n, $r) = 0;
        for (split //, $_[0]) {
            $n = ord($_) + ($n << 6) + ($n << 16) - $n;
        }
        $n = abs($n);
        while ($n >= $c) {
            $r .= $c[$n % $c];
            $n /= $c;
        }
        return $r;
    }
}
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