post_to_third_party Authentication with Pyrix

I am integrating pyrix API with a form and had a question for my coding. Pyrix api requires authentication (http://code.google.com/p/piryx-api/wiki/Authentication). I am not a strong php coder. Where and what would I add to my code below to make it work?

<?php
add_action('gform_after_submission_2', 'post_to_third_party', 10, 2);
function post_to_third_party($entry, $form) {

    $post_url = 'https://secure.piryx.com/api/accounts/iLE6xTsx/payments';
    $body = array(
        'CampaignCode' => $entry[''],
        'Amount' => $entry['15'],
	'Payment' => $entry['24'],
        'Description' => $entry['21'],
        'CardNumber' => $entry['38'],
        'CardSecurityCode' => $entry['41'],
	'CardExpirationMonth' => $entry['39'],
        'CardExpirationYear' => $entry['40'],
        'RoutingNumber' => $entry['25'],
        'AccountNumber' => $entry['26'],
	'BillingAddress1' => $entry['31'],
        'BillingAddress2' => $entry['42'],
        'BillingCity' => $entry['32'],
        'BillingState' => $entry['33'],
	'BillingZip' => $entry['34'],
        'BillingPeriod' => $entry['28'],
        'TotalPayments' => $entry['29'],
        'Email' => $entry['36'],
	'FirstName' => $entry['2'],
        'MiddleName' => $entry['3'],
        'LastName' => $entry['4'],
        'Phone' => $entry['10'],
	'WorkPhone' => $entry['11'],
        'MobilePhone' => $entry['13'],
        'FaxPhone' => $entry['12']
        );

    $request = new WP_Http();
    $response = $request->post($post_url, array('body' => $body));

}
?>