If you visit https://billing.microsoft.com/ with Firefox, you will be confronted with an error message that the certificate is invalid. The reason is that the website is vouched by a new root certificate by Microsoft, that Microsoft appears not to have done the proper procedure to contact the Mozilla Foundation and add the root certificate.
Using CertWatch we managed to extract the certificate file (other methods also exist).
Here are the details of this billing.microsoft.com root certificate:
Certificate:
Data:
Version: 3 (0x2)
Serial Number:
6a:80:24:5c:00:08:00:01:9c:18
Signature Algorithm: sha1WithRSAEncryption
Issuer: DC=com, DC=microsoft, DC=corp, DC=redmond,
CN=Microsoft Secure Server Authority
Validity
Not Before: Jul 9 03:16:55 2010 GMT
Not After : Jul 9 03:16:55 2011 GMT
Subject: C=US, ST=Washington, L=Redmond, O=Microsoft,
OU=Windows Live Operations, CN=billing.microsoft.com
Subject Public Key Info:
Public Key Algorithm: rsaEncryption
RSA Public Key: (1024 bit)
Modulus (1024 bit):
00:ab:d7:34:a7:58:eb:89:b8:a0:3c:5a:d4:fb:d5:
49:1e:6c:51:79:d0:dc:49:03:3d:11:e8:79:2c:e2:
c8:24:e4:d0:a8:45:57:c1:fd:b9:9e:ed:c0:c5:e6:
94:ae:96:45:db:ce:14:29:63:34:55:f4:e9:3a:d1:
4e:be:45:06:db:ef:f0:95:7d:dd:63:21:81:6e:d6:
1f:8a:7d:59:80:83:df:59:a8:a6:6e:b3:82:ea:af:
80:43:79:45:45:af:fb:5e:66:83:4d:b2:23:13:ff:
bc:67:5d:a5:7b:03:81:e5:24:7f:31:2d:5b:1d:98:
ed:c5:53:73:17:2e:7e:c4:cd
Exponent: 65537 (0x10001)
X509v3 extensions:
X509v3 Key Usage:
Digital Signature, Key Encipherment, Data Encipherment
S/MIME Capabilities:
......0...+....0050...*.H..
..*.H..
X509v3 Extended Key Usage:
TLS Web Client Authentication, TLS Web Server Authentication
X509v3 Subject Key Identifier:
69:47:71:B7:BA:81:B5:35:50:69:AC:DB:46:18:F2:5F:82:83:9B:D5
X509v3 Authority Key Identifier:
keyid:08:42:E3:DB:4E:11:66:F3:B5:08:C5:40:DB:55:7C:33:46:11:83:38
X509v3 CRL Distribution Points:
URI:http://mscrl.microsoft.com/pki/mscorp/crl/Microsoft%20Secure%20Server%20Authority(8).crl
URI:http://crl.microsoft.com/pki/mscorp/crl/Microsoft%20Secure%20Server%20Authority(8).crl
URI:http://corppki/crl/Microsoft%20Secure%20Server%20Authority(8).crl
Authority Information Access:
CA Issuers - URI:http://www.microsoft.com/pki/mscorp/Microsoft%20Secure%20Server%20Authority(8).crt
CA Issuers - URI:http://corppki/aia/Microsoft%20Secure%20Server%20Authority(8).crt
1.3.6.1.4.1.311.21.7:
00.(+.....7.....M..........}...t.O.........c..d...
1.3.6.1.4.1.311.21.10:
0.0
..+.......0
..+.......
Signature Algorithm: sha1WithRSAEncryption
77:62:04:97:b2:38:c5:90:1e:9f:8d:03:16:bd:79:c9:c9:54:
cb:f3:94:b4:7a:fa:18:de:95:54:20:1f:3a:bd:72:c2:d9:46:
d5:af:b9:72:5a:a2:52:5f:42:89:16:b8:60:f7:00:74:19:e8:
de:23:64:0c:a2:6e:64:7c:22:aa:58:a0:25:59:24:b5:30:54:
2f:a3:be:db:b7:6d:ce:02:37:37:d8:c0:11:c5:62:d8:81:84:
cd:c3:e3:15:36:33:56:97:7f:68:d9:ab:d4:ac:5a:9b:f5:99:
be:52:4d:f1:c4:32:40:0d:ed:27:59:36:75:3c:a5:27:6e:66:
43:b8:82:56:74:eb:ab:62:5f:5d:96:b8:ba:0d:59:f7:1f:f4:
8d:e1:ff:88:0d:5d:76:10:3e:90:46:85:5e:f9:a7:13:b8:11:
e8:39:79:49:c6:5a:04:55:c9:bf:fb:b9:6a:ea:2a:2b:ab:0a:
97:3b:86:78:5c:2e:28:39:19:c6:29:66:32:a8:60:d8:55:2b:
71:4c:ff:e1:69:7c:40:a0:6c:86:49:fe:f8:0d:f4:8c:2c:03:
e2:45:16:fd:0a:72:c1:90:4e:8c:ff:b0:e8:9b:1f:0f:51:f0:
3e:40:a2:4a:10:70:48:6e:a7:08:8f:59:bc:61:96:1e:85:11:
ea:db:63:64
The public key in decimal is
120670606144085109719219572194923534474923017051023017296322634692 625135745151055829730471725822826389243527648003600042874496534246 318211937373035306269108919094913609992115753070424083618544501290 818141600949585344863493055281433804504288287861848308627219396986 992979141910834747175772631763346288615015629
If you can factorise this number, then you have broken the certificate.
Apparently this certificate is accepted by recent versions of Internet Explorer and Chrome. With this information at hand, I do not see how these browsers accept the root certificate which is also a website certificate (an oddity). Currently, the only explanation at hand would be that those browsers either have a copy of this root certificate or they use another (unknown to me) cryptographic mechanism to verify the certificate.