Ugh? Yes, fake news is about a trust problem - people trusting sources which spread nefariously incorrect or distorted views. But no, public key cryptography or blockchain does not solve this problem. I am not sure what do you even propose exactly but think for a moment what differentiates a "real news" and "fake news" source from each other, and you are back to square one. People who read fake news already now choose to trust and subscribe to their reporting.