Controller Class Security
Like other Apex classes, you can specify whether a user can execute methods in a custom controller or controller extension class based on the user's profile.
Permission for an Apex class is checked only at the top level. For example, class A calls class B. User X has a profile that can access class A but not class B. User X can execute the code in class B, but only through class A; user X cannot invoke class B directly. Likewise, if a Visualforce page uses a custom component with an associated controller, security is only checked for the controller associated with the page. The controller associated with the custom component executes regardless of permissions.
To set Apex class security from the class list page:
Set Apex Class Access from the Class List Page
To set Apex class security from the class detail page: Set Apex Class Access from the Class Detail Page