I am looking for something like https, but backwards. The user generates their own private key (in advance) and then (only later) provides the web application with the associated public key. This part of the exchange should (if necessary) occur out-of-band. Communication is then encrypted/decrypted with these keys.
I've thought of some strange JavaScript approaches to implement this (From the client perspective: form submissions are encrypted on their way out while (on ajax response) web content is decrypted. I recognize this is horrible, but you can't deny that it would be a fun hack. However, I wondered if there was already something out there... something commonly implemented in browsers and web/application servers.
Primarily this is to address compromised security when (unknowingly) communicating through a rogue access point that may be intercepting https connections and issuing its own certificates. Recently (in my own network) I recreated this and (with due horror) soon saw my gmail password in plain text! I have a web application going that only I and a few others use, but where security (from a learning stand point) needs to be top notch.
I should add, the solution does not need to be practical
Also, if there is something intrinsically wrong with my thought process, I would greatly appreciate it if someone set me on the right track or directed me to the proper literature. Science is not about finding better answers; science is about forming better questions.
Thank you for your time, O∴D