Add checkbox to login form

Hi guys,

I want to add a checkbox “Accept disclaimer” to default WordPress Login Form.
Look at this :

// Fields for redirect
function custom_login_fields() {
?>
	<p><label for="disclaimer"><input name="disclaimer" type="checkbox" id="disclaimer" tabindex="50"<?php checked( $disclaimer ); ?> /> J'accepte le <a href="<?php bloginfo('url'); ?>/disclaimer" target="_blank" title="Lien vers le disclaimer">disclaimer</label></p><br /><br />

<?php
}

// Add fields to the login form
add_action('login_form','custom_login_fields');

function check_field_disclaimer($errors) {
// validation function
global $disclaimer;
if (!isset($_POST['disclaimer'])) {
$errors->add('empty_realname', "<strong>Error：</strong> Vous devez accepter le disclaimer.");
}
}

But now I want to show the error when we submit it. If checkbox is not checked, i show error…

I know, it is just a piece of code but I cannot find it with Google. For register form we use :
add_action('register_post', check function here)

But for login form ?

Thanks