It looks like what you need to do is: get the last value you had, multiply it by 31, and add the next number; repeat. In Perl that would become:

sub hashing {
    my $s = shift;
    my $acc = 0;
    foreach my $c (unpack 'C*', $s) {
        $acc *= 31;
        $acc += $c;
    }
    return $acc;
}
[download]

You will have overflow problems, I think. Likely you should only retain the $n (<=32?) lower bits of $acc. Your remark on "using int arithmetic" also points in that direction. So I'll modify that into:

sub hashing {
    my $s = shift;
    my $acc = 0;
    foreach my $c (unpack 'C*', $s) {
        $acc *= 31;
        $acc += $c;
        $acc %= 0x100000000;
    }
    return $acc;
}
[download]