reCAPTCHA does not work on IE when using https://

I was no longer able to get it to work in IE at all:
http://groups.google.com/group/recaptcha/browse_thread/thread/57baacc2a0...

The quick fix for me was to change one line in my reCAPTCHA instance's recaptchalib.php file. I changed line 39 from this:

define("RECAPTCHA_API_SECURE_SERVER", "https://api-secure.recaptcha.net");

To this:

define("RECAPTCHA_API_SECURE_SERVER", "https://www.google.com/recaptcha/api");

This is also updated in the latest version (1.11) of the reCAPTCHA PHP plugin, which is available from this address:
http://code.google.com/p/recaptcha/downloads/detail?name=recaptcha-php-1...

I hope this helps someone else.

* Edit: after looking at this a little more, I would recommend upgrading to 1.11 since there are other connection strings that need to be updated.

see #1124950: reCAPTCHA uses a new HTTPS API URL

On a drupal website that was all https, I also have the issue of the recaptcha place on page being http not https.
I was using 7.x-1.7 2011-May-04

I changed to the dev module 7.x-1.x-dev 2011-May-27
and the https page with recaptcha now loads without complaint on MSIE 9,
I believe the lib may be fixed in the dev for drupal7 but not 7.x-1.7 ???

"reCAPTCHA: May 4, 2011 15:52
Commit b7e5410 on 5.x-2.x
by Rob Loach
Issue #1142150 by Misterw: New HTTPS API reCAPTCHA URL.
"

I was using 7.x-1.7 I had the same issue of the recaptcha place on page being http not https.

I found in the recaptcha.module using
drupal_add_js('http://api.recaptcha.net/js/recaptcha_ajax.js', array('type' => 'external'));

There is a secure version of this javascript file here:
https://www.google.com/recaptcha/api/js/recaptcha_ajax.js

When I replaced it with secure version of javascript file my issue got fixed.

drupal_add_js('https://www.google.com/recaptcha/api/js/recaptcha_ajax.js', array('type' => 'external'));

Hope this may help...

I hope core team have to fix it in the 7.x-1.7

So does one just always embed the https library or is there an elegant solution for switching to the js library when the site's viewed over https?

Nevermind, I figured out a Drupal 7.x compatible solution: http://drupal.org/node/1324932#comment-6246504