Ie sign the current data package plus the current time. Receivers ignore everything with an incorrect timestamp and/or wrong signature.
Now you only have to make sure that you don't lose your private keys.
Mental model tweak: The signals aren't for a specific location, they are world-wide. So the "for Las Vegas" part doesn't work.
Replay attacks are just a kind of denial of service. In that case, you may as well just use jamming. Spoofing attacks are far more dangerous, and cryptographic signing defeats them effectively.
The whole point of GPS is that the differential in signal timing between the signals from the transmitters on different satellites tells you how far you are from those satellites, and thus if you know where the satellites are supposed to be, that tells you where you must be.
As a result, recording the signals in a desert outside Las Vegas three weeks ago is by far the easiest way to get... drum roll... the signals which when received by your GPS receiver right now will convince it that right now it's three weeks ago and it is just outside Las Vegas.
> Replay attacks are just a kind of denial of service
Nope, as explained they're actually a very common and effective spoofing tactic. The receiver doesn't say "No service" it will tell you that you're outside Las Vegas three weeks ago.
> Spoofing attacks are far more dangerous, and cryptographic signing defeats them effectively.
Spoofing attacks use the same principle (although of course they'll tell your receiver it's a few milli-seconds ago and it is somewhere nearby, not outside Las Vegas three weeks ago).
Signatures make no major difference, this data is authentic it's just second hand. Everything checks out, that's why they do it.
The thing with GPS is that it is also a time source, so you'd need a secondary source for your time to confirm that you are not off by three weeks.
I wonder if the problem lies in a different aspect of needing to authenticate messages quickly enough and thus requiring more processing power.
Also, be careful with assuming that late = imposter. The whole point of GPS is that signals take time to travel over distance, so, maybe the signal is late because you're further from that satellite instead, which is what you were trying to measure when you got distracted trying to prevent spoofing.
> got distracted trying to prevent spoofing
Indeed overwhelming the processing power with junk seems the important issue if crypto is added.