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They get a cookie and the proxy reads the cookie and allows the users to access the internet using http/https. At the same time, since the odds are the malware code can't properly authenticate against the proxy, it'll be stopped dead... If nothing else it will be another cog in the wheel to slow them down.
If I understand you correctly, you are suggesting a form of port authentication, where clients would be denied outbound access on specified ports based on an authentication mechanism. This would indeed stop this software, at least temporarily, if it was unable to gain permissions to use port 443. However, once a web browser had gained permission to use that port, the malware would then be able to use it as well if simple packet rules were used. A stateful firewall would be required which would authenticate each connection.