I was getting errors when trying to update a LInux system that had not been updated in quite a while.
I got the error that stated that the "Signatures are invalid" when trying to "apt-get update".
The fix is simple...
For Kali LInux just run: wget -q -O - https://archive.kali.org/archive-key.asc | apt-key add
After that, run: sudo apt-get update && apt-get upgrade
That should fix the issues.
Hope this helps.