GameKitHelper.h

#import <GameKit/GameKit.h>
#import "GameCenterManager.h"

@interface GameKitHelper : NSObject <GameCenterManagerDelegate>

@property (nonatomic, readonly) UIViewController *window;
@property (nonatomic, readonly) UIViewController *topViewController;
@property (nonatomic, readonly) UIViewController *authenticationViewController;

+ (instancetype)sharedGameKitHelper;
- (void)showLeaderboard;
- (void)hideLeaderboard;
- (void)authenticatePlayer;
- (void)reportScore;

@end

GameKitHelper.m

#import "GameKitHelper.h"
#import "GameCenterManager.h"

@implementation GameKitHelper

NSString *const PresentAuthenticationViewController = @"present_authentication_view_controller";
UIWindow *window;

+ (instancetype)sharedGameKitHelper
{
	static GameKitHelper *sharedGameKitHelper;
	static dispatch_once_t onceToken;
	dispatch_once(&onceToken, ^{
		sharedGameKitHelper = [[GameKitHelper alloc] init];
	});

	return sharedGameKitHelper;
}

- (id)init
{
	self = [super init];
	if (self) {
		window = [[UIApplication sharedApplication] keyWindow];
		[[GameCenterManager sharedManager] setupManagerAndSetShouldCryptWithKey:@"YOUR_KEY_HERE" ];
		[[GameCenterManager sharedManager] setDelegate:self];
	}

	return self;
}

- (void) gameCenterManager:(GameCenterManager *)manager authenticateUser:(UIViewController *)gameCenterLoginController
{
	UIViewController *topController = window.rootViewController;
	[topController presentViewController:gameCenterLoginController animated:YES completion:nil];
}

- (void) gameCenterManager:(GameCenterManager *)manager availabilityChanged:(NSDictionary *)availabilityInformation
{
	//NSLog(@"%@", availabilityInformation);
}

- (void) showLeaderboard
{
	UIViewController *topController = window.rootViewController;
    [[GameCenterManager sharedManager] presentLeaderboardsOnViewController:topController];
}

- (void)leaderboardViewControllerDidFinish:(GKGameCenterViewController *)viewController
{
	UIViewController *topController = window.rootViewController;
	[topController dismissViewControllerAnimated:YES completion: nil];
}

- (void) hideLeaderboard
{
	UIViewController *topController = window.rootViewController;
	[topController dismissViewControllerAnimated:YES completion: nil];
}

- (void) reportScore: (int) score forLeaderboardID: (NSString*) identifier
{
	[[GameCenterManager sharedManager] saveAndReportScore:score leaderboard:identifier  sortOrder:GameCenterSortOrderHighToLow];
}	

- (BOOL) isAvailable
{
	BOOL isAvailable = [[GameCenterManager sharedManager] checkGameCenterAvailability];
	return isAvailable;
}

- (int) getScore: (NSString*) identifier
{
	int highScore = [[GameCenterManager sharedManager] highScoreForLeaderboard:identifier];
	return highScore;
}

- (NSString*) getIdentifier
{
	NSString *playerID = [[GameCenterManager sharedManager] localPlayerId];
	return playerID;
}

- (void)gameCenterManager:(GameCenterManager *)manager error:(NSError *)error
{
	//NSLog(@"%@", error);
}

- (void)openAppStore
{
	NSString *url = @"itms-apps://itunes.apple.com/WebObjects/MZStore.woa";
    url = [NSString stringWithFormat:@"%@/wa/viewContentsUserReviews?", url]; 
    url = [NSString stringWithFormat:@"%@type=Purple+Software&id=", url];
    url = [NSString stringWithFormat:@"%@YOUR_APP_ID", url]; 
    [[UIApplication sharedApplication] openURL:[NSURL URLWithString:url]];
	
}

- (BOOL)isInternetAvailable {
	BOOL isAvailable = [[GameCenterManager sharedManager] isInternetAvailable];
	return isAvailable;
}

@end