As merlyn points out, perl has string versions of the bitwise operators. permits becomes slightly different, since you need to test for non-null bytes:

sub permits { 
    my ($self, $mask) = @_;
    return (($self->{perms} & $mask) =~ y/\0//c);
}
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To retain the feature of having permits return not just a true or false value, but a usable bitmask of those permissions that were satisfied (untested):

sub permits {
    my ($self, $mask) = @_;
    $mask &= $self->{perms};
    return ($mask =~ y/\0//c ? $mask : "");
}
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