Here are the IP ranges used by Duo Security for authentication purposes – list correct as of September 2016. Duo don’t make this list public (security through obscurity?) but they do give it to customers on request so here they are:
You can use this information to tighten up your firewall policies and rules. Previously, as per Duo Security’s instructions on their knowledge base articles, you would have had to allow access from your servers to anywhere on the internet on port 443 – not really acceptable in my opinion.
Hopefully that comes in handy.