To implement Google authentication in a Windows Forms application, you can make use of the Google Sign-In API provided by Google. Here’s an example of how you can create a simple Google authentication class in WinForms:

using Google.Apis.Auth.OAuth2;
using Google.Apis.Auth.OAuth2.Flows;
using Google.Apis.Auth.OAuth2.Responses;
using Google.Apis.Services;
using Google.Apis.Util.Store;
using System;
using System.Collections.Generic;
using System.IO;
using System.Threading;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace GoogleAuthenticationExample
{
    public class GoogleAuthenticator
    {
        private const string ClientSecretsFile = "client_secrets.json";
        private const string TokenFile = "token.json";
        private readonly string[] Scopes = { "https://www.googleapis.com/auth/userinfo.email" };

        private UserCredential credential;

        public bool IsAuthenticated { get; private set; }

        public string AccessToken => credential.Token.AccessToken;

        public async Task<bool> Authenticate()
        {
            try
            {
                var credPath = Path.Combine(Application.StartupPath, TokenFile);

                var clientSecrets = GetClientSecrets();

                var flow = new GoogleAuthorizationCodeFlow(new GoogleAuthorizationCodeFlow.Initializer
                {
                    ClientSecrets = clientSecrets,
                    Scopes = Scopes,
                    DataStore = new FileDataStore(credPath, true),
                });

                var token = await GetStoredToken(flow, credPath);
                if (token == null)
                {
                    var authResult = await new AuthorizationCodeInstalledApp(flow, new LocalServerCodeReceiver()).AuthorizeAsync("user", CancellationToken.None);
                    token = authResult.Credential.Token;
                    await SaveToken(token, flow, credPath);
                }

                credential = new UserCredential(flow, "user", token);
                IsAuthenticated = await credential.RefreshTokenAsync(CancellationToken.None);
                return IsAuthenticated;
            }
            catch (Exception ex)
            {
                // Handle authentication errors
                MessageBox.Show($"Authentication failed: {ex.Message}", "Authentication Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
                return false;
            }
        }

        private ClientSecrets GetClientSecrets()
        {
            using (var stream = new FileStream(ClientSecretsFile, FileMode.Open, FileAccess.Read))
            {
                return GoogleClientSecrets.Load(stream).Secrets;
            }
        }

        private async Task<TokenResponse> GetStoredToken(GoogleAuthorizationCodeFlow flow, string credPath)
        {
            try
            {
                var token = await flow.LoadTokenAsync("user", CancellationToken.None);
                return token;
            }
            catch (IOException)
            {
                return null;
            }
        }

        private async Task SaveToken(TokenResponse token, GoogleAuthorizationCodeFlow flow, string credPath)
        {
            await flow.StoreTokenAsync("user", token, CancellationToken.None);
        }
    }
}

In this example, the GoogleAuthenticator class encapsulates the authentication logic. It uses the GoogleAuthorizationCodeFlow class to handle the authorization flow, and the UserCredential class to manage the user’s credentials.

To use this class in your Windows Forms application, you can create an instance of GoogleAuthenticator and call the Authenticate method. If the authentication is successful, the IsAuthenticated property will be set to true, and you can access the user’s access token using the AccessToken property.

Here’s an example of how you can use the GoogleAuthenticator class in your Windows Forms application:

using System;
using System.Windows.Forms;

namespace GoogleAuthenticationExample
{
    public partial class MainForm : Form
    {
        private GoogleAuthenticator authenticator;

        public MainForm()
        {
            InitializeComponent();
        }

        private async void MainForm_Load(object sender, EventArgs e)
        {
            authenticator = new GoogleAuthenticator();
            var isAuthenticated = await authenticator.Authenticate();

            if (isAuthenticated)
            {
                // Authentication successful
                var accessToken = authenticator.AccessToken;
                // Use the access token for further API requests
                // ...
            }
            else
            {
                // Authentication failed
                // Handle the failure case
                // ...
            }

            // Close the form
            Close();
        }
    }
}

In this example, the MainForm_Load event handler initiates the authentication process by calling the Authenticate method of the GoogleAuthenticator instance. After the authentication is completed, you can access the access token and use it for further API requests.