Comment 18 for bug 705988

Some of you might have a problem with missing PGP keys, which exposes this bug in a big way. That's because in that case all packages from an affected software source would be 'untrusted', as PGP keys are used to authenticate them.

If that's the case, you might get it fixed by:

cd /var/lib/apt
sudo mv lists lists.old
sudo mkdir -p lists/partial
sudo apt-get update

It worked fine for me. When you satisfy yourself that everything works fine, you can then delete the lists.old folder (it was taking about 70MB on my fresh 11:10 installation):

cd /var/lib/apt
sudo rm -r lists.old

Source:
http://askubuntu.com/questions/70553/software-center-not-downloading