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"Typical design is two piles of uranium in a container, separated by a lead wall."

Even the simplest nuclear weapons design is slightly more involved than that - the gun-based design used in the "Little Boy" bomb that destroyed Hiroshima used an actual section of gun barrel to fire one chunk of uranium at the other.

More modern designs of fission bombs, either as stand-alone weapons or as primaries for H-bombs, are actually pretty complex - balancing the need to be efficient (plutonium and U235 are rather expensive), light, robust and safe is a non-trivial problem.

The W88 warhead with its prolate (egg-shaped) primary is the most advanced nuclear weapon that has had design details leaked to the public:


In the case of the Sum of All Fears the terrorists were trying to build a strategic level bomb (i.e. hundreds of kt) using a fusion boosted fission design to try and start a global war - so they were actually trying to build something relatively advanced, not just a basic bomb.

Edit: Another real problem with working with plutonium is that it is fairly nasty stuff to deal with - I can recommend the book "Making a Real Killing: Rocky Flats and the Nuclear West" to get some idea of the horrors of working with plutonium on an industrial scale:


True, but the prototypical modern terrorist doesn't need robust or safe, nor does he need to get the device airborne. He just needs a detonation, which (once you have the uranium) doesn't require sophisticated machining.

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