Lets say I create a self-signed X509 certificate A and use it to issue certificate B. I put certificate A in my trusted root authorities so that all certificates signed by it are accepted. My question is:
When I then use a service protected by cert B, how does my computer know it was actually signed by cert A? Is the parent certificate somehow embedded into its child?
In a X.509 certificate, the name of the issuer (in your example, A's name) is also included (as issuerDN). Also, a certificate can contain an extension which points to a place where the issuer's certificate can be downloaded (the "Authority Information Access", section 4.2.2.1 of RFC 5280); note that since all certificates are signed entities which are accepted and use only after having verified these signatures, they can be downloaded and transported with little care. Finally, it is customary, in protocols where a party can show a certificate, to actually show a list of certificates containing needed intermediate CA certificates. This is what happens, for instance, in an SSL Certificate message.
All this gives a lot of ways for a computer to do certification path building, i.e. reconstructing chains of certificate on which validation (including verifying cryptographic signatures) seems relevant.
When the CA issues the certificate, they sign it using their private key. Only the CA's public key can verify that the signature is authentic and the certificate has not been tampered with.
What is odd is that the signature property seems to be missing in a lot of instances (.NET's X509Certificate class and when viewing a certificate in Windows). I've found that even though it is not always displayed, it is still inside the certificate. Given a certificate in DER binary format, you can decode it into plain text which DOES show the signer's signature.
openssl x509 -text -noout -inform DER -in certFile.der
Signature Algorithm: sha1WithRSAEncryption
30:d9:40:ac:d8:0d:46:81:68:14:8a:c6:a7:29:96:4e:b4:58:
7b:e6:12:3f:45:4f:c6:9b:18:aa:f2:99:23:ee:48:df:5f:c0:
a3:c7:e4:ba:3a:bc:6f:58:57:fe:a8:a7:23:d0:d1:9a:47:a6:
42:1a:d8:20:e8:f1:ec:76:43:47:0b:75:d6:a1:d2:71:2b:f7:
19:96:e3:48:57:e2:36:0f:0c:25:5d:7f:f8:26:50:c2:5e:80:
8e:17:ac:37:ad:f1:e3:3c:6f:a3:20:a6:16:93:df:2b:04:9c:
22:d3:01:33:f9:4c:3b:f8:a8:39:f1:6c:41:74:de:ba:96:6a:
0b:f1:e6:f0:7b:d8:1f:42:ec:b5:73:d1:94:1b:01:4a:4c:13:
ca:5e:2b:af:fd:2c:eb:43:d3:fc:2f:ea:5a:8d:db:a9:6a:f6:
b6:9b:58:e1:b7:94:7f:14:6d:11:8b:2c:b7:4e:f3:82:ad:c4:
92:04:c4:97:a3:7a:52:e5:a0:b1:1b:8f:47:bb:43:a3:2c:1a:
fb:31:d9:51:7c:23:7b:57:8e:73:46:81:c4:25:f3:48:c5:a1:
8f:0d:3d:f2:e1:4b:fd:7f:49:b9:f9:b1:2a:c2:22:9e:8a:85:
61:bd:b7:18:8e:56:33:a4:6e:d2:7d:db:2e:37:d0:fb:9a:35:
87:c8:2a:69
From http://en.wikipedia.org/wiki/X.509
To validate this certificate, one needs a second certificate that matches the Issuer (Thawte Server CA) of the first certificate. First, one verifies that the second certificate is of a CA kind; that is, that it can be used to issue other certificates. This is done by inspecting a value of the CA attribute in the X509v3 extension section. Then the RSA public key from the CA certificate is used to decode the signature on the first certificate to obtain a MD5 hash, which must match an actual MD5 hash computed over the rest of the certificate.
