How to implement Google reCaptcha without installing a plugin?

WordPress noob here wondering how to include reCaptcha authentication in my login without a plugin?

So far I have added the captcha div into the login using a hook:

add_action('login_form','my_added_login_field');
  function my_added_login_field(){
?>
    <p>
        <div class="g-recaptcha" data-sitekey="mySiteKey"></div>
    </p>
<?php
}

The script is enqueued. Now I just need to add an authentication process to verify the captcha before loggin the user in. I know I need to use something like this filter:

add_filter( 'authenticate', 'my_custom_authenticate', 10, 3 );
function my_custom_authenticate( $user, $username, $password ){

$my_value = $_POST['g-captcha-response'];

if (!)

return $user;
}

But I’m a little stuck. According to google once the captcha is solved a field named “g-captcha-response” is populated and the response in a JSON object:

{
  "success": true|false,   
  "challenge_ts": timestamp,  // timestamp of the challenge load (ISO format yyyy-MM-dd'T'HH:mm:ssZZ)
  "hostname": string,         // the hostname of the site where the reCAPTCHA was solved
  "error-codes": [...]        // optional
}

I’m just a noob so I have no idea what to do with that info. Any help is appreciated!

you can use this function i think it works properly.

  add_filter( 'wp_authenticate_user', 'verify_recaptcha_on_login', 10, 3 );
function verify_recaptcha_on_login($user, $password) {
    $secretkey = "your secret key";
    if (isset($_POST['g-recaptcha-response'])) {
    $response = wp_remote_get( 'https://www.google.com/recaptcha/api/siteverify?secret=".$secretkey."&response=" . $_POST["g-recaptcha-response'] );

    $response = json_decode($response['body'], true);


    if (true == $response['success']) {


    return $user;


    } else {


    // FIXME: This one fires if your password is incorrect... Check if password was incorrect before returning this error...


     return new WP_Error( 'Captcha Invalid', __('<strong>ERROR</strong>: You are a bot') );


    }


    } else {


    return new WP_Error( 'Captcha Invalid', __('<strong>ERROR</strong>: You are a bot. If not then enable JavaScript.') );


    }
}