Generally when creating a page in SharePoint it inheritance from LayoutsPageBase, however a public page has to inheritance from UnsecuredLayoutsPageBase and overriding AllowAnonymousAccess property.

public partial class ForgotPassword: UnsecuredLayoutsPageBase

{

    protected override boolAllowAnonymousAccess { get{ return true; } }

    protected void Page_Load(objectsender, EventArgs e)

    {

    }

}