Switch from your custom implementation of authentication (storing usernames and passwords in your data store) to a "Login using Google" in no-time. Below is an ultra-light authorization using Google OAuth 2.0. Visit https://cloud.google.com/console/project >> APIs & auth >> Credentials

google_oauth2_auth.php

<?php

define('GOOGLE_OAUTH2_CLIENT_ID', 'client id'); // this will be of form "<number>.apps.googleusercontent.com"
define('GOOGLE_OAUTH2_CLIENT_SECRET', 'client secret'); // this will be a base64 string
define('GOOGLE_OAUTH2_REDIRECT_URI', 'redirect url'); // This URL should be registered under "Redirect URIs"
define('YOUR_DOMAIN', 'your domain'); // your domain
define('OAUTH2_SESSION_DURATION', 90); //in seconds

require __DIR__ . "/url_get_contents.php"; // Use https://gist.github.com/m-manu/7462652

function getGoogleOAuthRedirectUrl($redirect_uri) {
	$required_permissions = array("https://www.googleapis.com/auth/userinfo.email", "https://www.googleapis.com/auth/userinfo.profile");
	$google_auth_url = "https://accounts.google.com/o/oauth2/auth?" . http_build_query(array(
			"redirect_uri" => $redirect_uri,
			"response_type" => "code",
			"client_id" => GOOGLE_OAUTH2_CLIENT_ID,
			"scope" => implode(' ', $required_permissions),
			"approval_prompt" => "force",
			"access_type" => "offline",
	));
	return $google_auth_url;
}

function redirect($url) {
	header("Location: $url");
	echo "<script type=\"text/javascript\">\nwindow.location.href = \"" . addslashes($url) . "\";\n</script>\n";
	exit;
}

if (isset($_REQUEST['code'])) {
	$code = $_REQUEST['code'];
	$response_token_rawstr = url_get_contents("https://accounts.google.com/o/oauth2/token", array(
		"code" => $code,
		"client_id" => GOOGLE_OAUTH2_CLIENT_ID,
		"client_secret" => GOOGLE_OAUTH2_CLIENT_SECRET,
		"redirect_uri" => GOOGLE_OAUTH2_REDIRECT_URI,
		"grant_type" => "authorization_code")
		, 'POST');
	$response_token = json_decode($response_token_rawstr, true);
	if (isset($response_token['access_token'])) {
		$token = $response_token['access_token'];
		$response_userinfo_rawstr = url_get_contents("https://www.googleapis.com/userinfo/v2/me", array('access_token' => $token));
		$response_userinfo = json_decode($response_userinfo_rawstr, true);
		setcookie('GOOGLE_OAUTH2', serialize($response_userinfo), time() + OAUTH2_SESSION_DURATION, '/', YOUR_DOMAIN);
		redirect($_COOKIE['url_goback']);
	}
	else {
		error_log("Google didn't return an access token for code \"$code\"");
		die("<h1>Login error</h1>");
	}
}
else {
	error_log("No parameter 'code' received");
	setcookie('url_goback', $_REQUEST['url_goback'], time() + 10);
	redirect(getGoogleOAuthRedirectUrl(GOOGLE_OAUTH2_REDIRECT_URI));
}