Some improvements, questions and fixes

This PR contains a number of issues. Please feel free to comment what I should remove, I will make a PR which contains only the things you accept as contributions, so you do not need to hand-merge them.
the key was not "used to verify", so if you think "verify" is correct, it should be "key which can be used to verify". Hower I typically think protocols are described from the point of the sender of a message?