This answer is mostly based on the following article: https://www.theguardian.com/world/2003/jun/24/usa.science
In the 60's the U.S. wanted to know if it was possible for a random country to build a nuclear bomb. In order to test this, they recruited two people (one of which Dave Dobson) with physics PhDs, but no further knowledge of how to build a nuclear bomb. They gave them an office and helped them conduct 'experiments' (they told them the outcome), but gave them no access to classified information. After two and a half years they had designed a nuclear bomb of the more advanced implosion variety:
The whole works, in great detail, so that this thing could have been made by Joe's Machine Shop downtown.
They were told the destructive power would be similar to the bomb dropped on Nagasaki.
At the end of the article, Dave notes the following about a nuclear bomb:
It turns out it's not overwhelmingly difficult. There are some subtleties that are not trivial ... but an awful lot has been published. If you were a grad student today, and you reviewed the literature, a lot of pieces would fall into place.
So yes, if he's driven enough and has a solid physics background, he can most likely pull it off.
Another example, a student who designed a bomb as a physics term paper: http://people.com/archive/a-princeton-tiger-designs-an-atomic-bomb-in-a-physics-class-vol-6-no-17/ or this wiki article
He faced no criminal charges. However, part of his paper was confiscated, as well as his mockup. As for how difficult it was, he states:
It’s very simple. Any undergraduate physics major could have done what I did.