I am searching the algorithm about how SSL validation process is performed, but almost everywhere, they explain the certificate validation step as "certificate is checked by client" or something like that, but I wonder what is the scenario behind this.
What I know is:
When the client receives a copy of the certificate that belongs to which website/server you wanna attempt to handshake, there are some indicators that shows the public information of webserver (I think this is for matching the entries in your cached certificate entries, which your browser has installed.)
Once the client matchs a cached-certificate with the webserver's one, it starts validating it. It uses the public key of cached-certificate to decrypt the signature of webserver's one.(? [Not sure this because public keys are used to "encrypt" the data, not decrypt. Also this step may be totally wrong.])
Once it decrypts, it compares the signature between cached one and webserver's one. If it is same, certificate is valid.
I also heard about chains. I really wonder how a chain is known, and how to determine if the webserver's certificate just belongs to a chain.(?)
How SSL certificates are checked by client? I need the answer as step by step and clarified. Thanks :)
Edit:
I think the public key here is used for "decrypting" instead of "encrypting". So a public key is not responsible for encrypting everytime, it can also decrypt and don't encrypt some data. The magic here is that since the public key decrypts here, if you want to fake the certificate, you should have that CA's private key to apply the changes as encrypted (because only private key can encrypt the data). But now, another question comes... What if we decrypt it using webserver's public key, then change the entries in the signature, then encrypt it again using our own private key (we generate it manually, it doesn't belong to server.), which actually make us behave like a CA; and finally overwrite the certificate to hold our own public key which is able to decrypt the data encrypted with our own private key?