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Along similar lines, Port knocking (https://en.wikipedia.org/wiki/Port_knocking) is something out-of-band used to allow access to a host (bypassing a firewall).

I think I'd sooner implement port knocking rather than port-hopping

Ooh, yep. This is definitely a better first line of defense than port-hopping.

Maybe you'd knock to get a number, and hash the number to get the real port.

Defense in depth! :)

I came here looking forward to upvote anyone mentionning port knocking.

This is THE way to go !