I had a system crash with my Raspberry Pi during an update process. As a result the disk was corrupted and I needed to fix the trusted GPG keys as well as the cache for apt-get.
I got the following error after running apt-get update, so if you get:
W: GPG error: http://archive.raspberrypi.org jessie InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 82B129927FA3303E
First, check your filesystem:
sudo touch /forcefsck sudo reboot
Try update again, if it fails, update the keys:
sudo cp /etc/apt/trusted.gpg ~ sudo rm /etc/apt/trusted.gpg sudo apt-key adv --keyserver http://archive.raspbian.org/raspbian.public.key --recv-keys 90FDDD2E sudo apt-key adv --keyserver http://archive.raspbian.org/raspbian.public.key --recv-keys 7FA3303E sudo apt-key adv --keyserver http://archive.raspbian.org/raspbian.public.key --recv-keys 78661FA5
Note that if you had other keys you had installed, you will have to reinstall them manually.
Restart the operation:
sudo apt-get clean sudo apt-get update
If this does not solve your solution, replace the /etc/apt/trusted.gpg file with a fresh one.