I'm not sure I'd risk this. Anything controlled by computers can be hacked. Imagine what terrorists could do with an airplane in this way. It'd be 9/11 writ large. And they wouldn't even have to risk their own lives - they could hack into and divert planes on a whim. It'd be even worse than the flying car problem.
Hmm, yes, safeguards would need to be taken against antagonistic input. I was thinking it could be made failure-safe with triple-redundant independent computers and a large battery source to guard against alternator failure, but when you add antagonistic input to the picture you need to get more complicated.
Now, the only real threat from hackers (assuming they don't have maintenance access, which would be bad regardless) comes in the instructions from ATC.
A first level of safeguard would be simply: don't accept a clearance for other than a known route to the intended destination, without multiple independent verifications from several ATC facilities.
Even those messages could be protected with RSA.....or, if necessary, you could even generate a 1-time-pad (unbreakable) for each and every flight. (Of course, how you securely get that pad from the plane to every necessary ATC facility is still a problem, but it at least moves the issue to a different domain.)
Simple jamming of communications isn't really a problem; there are Lost Communications protocols in place already anyway, the plane would just follow them.