Quoting the HTTPS RFC:
When the TLS handshake has finished. The client may then initiate the
first HTTP request. All HTTP data MUST be sent as TLS “application
data”.
Essentially, the secure SSL/TLS channel is established first. Only then the HTTP protocol is used. This will protect all the HTTP traffic with SSL, including HTTP headers (which contain the URL and cookies).
What may be visible in the handshake is the host name itself, since it’s contained in the server certificate which will be visible in clear in the handshake (and it’s often easy to guess the host name by looking at the destination IP address anyway).
When using Server Name Indication, the requested host name should also be visible in the server_name extension in the ClientHello message.
Otherwise, there may be a bit of ambiguity (for the eavesdropper) to guess the host name from the certificate if the certificate is valid for multiple host names (e.g. multiple Subject Alt. Names or wildcards). In this case eavesdropping the DNS request from the client might give the attacker a clue.
Reading other people’s answers and comments, some mention issues about Referer (lost an r in the spec) and logs.
- Referrers shouldn’t be sent when going from HTTPS to HTTP (but they are often sent when going from one HTTPS site to another HTTPS site).
- About the history: you’ll just have to trust whoever can potentially get that key legitimately (i.e. your users) not to spread it around. If needed, have a strategy to change it once in a while.
- About the logs: I was assuming you were after protection over the network. The URL (including query) will be in the logs indeed, but if someone is able to attack your machine so as to get the logs, you have more to worry about that your app keys.
One of the remaining potential weak points is how you give that link to the user. If it’s embedded in a web-page served over plain HTTP, anyone who can read that page would be able to see it. You should serve such a page over HTTPS too. If you send that link by e-mail instead, I’d say all bets are off, since mail servers rarely encrypt the connections between themselves and users also often to access their e-mail account without any encryption.
EDIT:
In addition, if you’re using client-certificate authentication, the client certificate will be visible if it is negotiated during the initial handshake. This may leak the name of the user accessing the website (often Subject DNs contain the user name). The client certificate will not be visible if it is sent during a re-negotiated handshake.