Remote Aircraft maintenance
It is totally obvious that airlines (and their service providers) want to monitor parameters of their aircraft more or less on a continous basis. So if any parameter of an aircraft moves out of the "good" interval, they want to have the spare parts, technicians and test/repair equipement already in place at the destination airport, ideally.
To facilitate that, data from all sorts of aircraft systems must be transmitted to the airline HQ (or service providers like MTU) while the plane is in the air on a continous basis.
I am not working for the aircraft/airline industry, so I do not know the details. It could be that such data transfers are strictly one-way, but I doubt this because it can be very useful for maintenance personell to change some critical parameters while an a/c is flying.
I have no doubt these systems are running over specially protected Virtual Private Networks (which can use the internet or other public telecom networks), but these VPNs also could contain flaws which could be a security issue. The crypto could be broken.
The A380 has an on-board network that includes the passender network and the avionics network. These two are NOT physically separate, but "separated" by a firewall.
A research project in 2005:
Airbus A380 avionics protected by "firewalls":
An Article on the Subject of Remote Maintenance:
Engine Manufacturer MTU offers "Engine condition monitoring (remote diagnostics)"