Curl on a Windows PHP installation does not know where to look for certificates. Hence when you try and curl a https url it fails. The default value for CURLOPT_SSL_VERIFYPEER is true which means curl will always try and validate ssl by default. I discovered this while working with an OpenID library (v1.2.3): http://openidenabled.com/php-openid/
There is the option of disabling the verfication.
$ch=curl_init;
// set URL and other appropriate options
curl_setopt($ch,CURLOPT_SSL_VERIFYPEER, false);
But thats ignoring the problem and opening a security hole! Instead download a reputable Certificate bundle file, for example: http://curl.haxx.se/docs/caextract.html
Then set CURLOPT_CAINFO with the location of your certificate bundle.
if( strtoupper (substr(PHP_OS, 0,3)) == 'WIN' ) {
curl_setopt($c, CURLOPT_CAINFO, 'C:/certificates/cacert.pem');
}