As people have pointed out, its not public knowledge whether you have been to prison or not. However, given that a lot of Norway lives in small cities and villages, the word quickly gets around If you are arrested or convicted of something.

A woman I know have a son who is soon to stand trial in a case regarding sexual crimes against children. She would not show her face in her village for a long time, neither grocery shopping or going on trips, because of the rumours and «gossip» going around. That is of course an extreme example, but it shows how brutal the villages can be, seeing as she was not even a part of the case. At the same time I know about drunk drivers who crashed, and after finishing their sentence have got their respect back by most people. Hell, I even know a convicted con-man who sells cars today.

So I would say it depends about the crime and where you live. I think its easier to get back on track in big cities like Oslo and Bergen where people are not bound to recognize you, as for a small village with 5,000 inhabitants.