Add Class To Password Protected Posts http://wpsites.net/web-design/add-custom-class-to-style-password-protected-posts/

functions.php

add_filter( 'body_class', 'add_password_protected_body_class' );
function add_password_protected_body_class( $classes ) {
if ( post_password_required() ) 
   $classes[] = 'password-protected';
   return $classes;
}