How to apt-update when apt is not accepting the repository?

Note: apt-key is deprecated

You could try updating the repository key. When I try to use the tor repository by adding this line to my sources.lst:

deb http://deb.torproject.org/torproject.org squeeze main

I get the following error:

W: GPG error: http://deb.torproject.org squeeze InRelease: The following 
signatures couldn't be verified because the public key is not available: 
NO_PUBKEY 74A941BA219EC810

So, the missing key is 74A941BA219EC810. To add (or update in your case) the key run:

sudo apt-key adv --recv-keys --keyserver keys.gnupg.net  74A941BA219EC810

You should now be able to run `apt-get update with no errors.

Note: apt-key is deprecated

To find any expired repository keys and their IDs, use apt-key as follows:

apt-key list --keyid-format short | fgrep expired

You will get a result similar to the following:

pub   4096R/BE1DB1F1 2011-03-29 [expired: 2014-03-28]

The key ID is the bit after the / i.e. BE1DB1F1 in this case.

To update the key, as terdon points out, run

sudo apt-key adv --recv-keys --keyserver keys.gnupg.net BE1DB1F1