Read a TLS 1.3 handshake message by message, predict why a guessed key share closes it in one round trip while a rejected guess costs a second, and separate the certificate the server presents from the signature that actually proves it holds the key.

Type `https://` and your browser runs a whole conversation before the first HTTP byte leaves: a second round of messages that agrees a key nobody sent and proves the server is who it claims. Read what crosses the wire.

Climb a certificate chain from the leaf to a root already in your trust store, predict why a missing intermediate breaks curl and Firefox while Chrome silently refetches it, and watch a cross-signed intermediate give one leaf two valid paths to two different roots.

Your server's certificate is valid, in-date, and names the right host, yet `curl` still refuses it with `unable to get local issuer certificate`. Validity was never the question: someone has to vouch for it, all the way up.

Present a client certificate so a server running mutual TLS lets you in, then pin one expected key and watch a fully valid, freshly-issued certificate get refused on purpose, and see why the wrong pin locks out your own users.

`curl https://api.example.com` succeeds, but `curl` against an internal service stalls: the server sends a `certificate required` alert. It finished checking you, then asked the other way: prove who you are, or you are not coming in.