How to implement a secure login to the site?

Question

ubuntu

Good day!
Knowledgeable people, tell me which way to dig:
There is an office with a certain number of crooked users, who in turn, with a certain regularity, cling to all sorts of rubbish from the Internet.
There is a login and password to access the site to the registry of notaries.
The site is friendly only with IE and with the latest version of FF, it is terribly buggy in chrome, it does not open at all in opera. Under chromium and FF in ubuntu 12.04, it categorically refused to open.
Data is transmitted to the site without encryption.
Actually, the question is: how to organize access to this database for a certain number of users as safely as possible?
I came up with only one solution:
Hastily installed a wine server, installed a firewall, allowed access only to this resource and shared an RDP connection over the network.
Users connected to the machine via remote desktop, each under their own account, launched FF with the password already saved, and did their job.
But to keep a separate machine for only one site, somehow the toad presses, and it’s all not aesthetically pleasing - girls often confuse the open RDP connection window and the windows on their workstation, make mistakes, etc ...
There are two more servers in the office under Ubuntu, are any solutions possible on them?

Answer 1

Setting up an antivirus and appropriate security policies on each computer so that no one can stupidly turn it off is the best option in your situation, I think. Still it is possible to organize something like internal "proxy". The client makes a request to the site https://somesite.com/, your internal firewall redirects it to an internal proxy, which in turn simply redirects the same request without https. Receives data and returns it to the client over HTTPS. But then again...it won't save you from all sorts of keyloggers and stuff, so the first option is the best way out.