Generate JWT for Apple Push Notification

apn.php

<?php

require_once 'vendor/autoload.php';

use Jose\Factory\JWKFactory;
use Jose\Factory\JWSFactory;

$key_file = '/PATH/TO/KEY/FILE';
$secret = null; // If the key is encrypted, the secret must be set in this variable

$private_key = JWKFactory::createFromKeyFile($key_file, $secret, [
    'kid' => 'ABC123DEFG', // The Key ID obtained from your developer account
    'alg' => 'ES256',      // Not mandatory but recommended
    'use' => 'sig',        // Not mandatory but recommended
]);

var_dump('We show our private EC key');
var_dump(json_encode($private_key));

var_dump('We prepare the payload (claims to sign).');
$payload = [
    'iss' => 'DEF123GHIJ',
    'iat' => time(),
];
var_dump($payload);

var_dump('We prepare the protected header.');
$header = [
    'alg' => 'ES256',
    'kid' => $private_key->get('kid'),
];
var_dump($header);

var_dump('We create our JWS using the private key, the payload and the header');
$jws = JWSFactory::createJWSToCompactJSON(
    $payload,
    $private_key,
    $header
);

var_dump('We show our JWS.');
var_dump($jws);



/***************************************/
/* Same code as above without comments */
/***************************************/

$key_file = '/PATH/TO/KEY/FILE';
$secret = null;
$private_key = JWKFactory::createFromKeyFile($key_file, $secret, ['kid' => 'ABC123DEFG', alg' => 'ES256', 'use' => 'sig']);
$payload = ['iss' => 'DEF123GHIJ', 'iat' => time()];
$header = ['alg' => 'ES256', 'kid' => $private_key->get('kid')];
$jws = JWSFactory::createJWSToCompactJSON($payload, $private_key, $header);

I have a valid certificate cert.p12 exported from Mac Keychain. How can I know private and public key for alg ES256?