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Let's assume there is a non-government actor willing to acquire nuclear weapons for some reason. Assume that the group has unlimited financing (or some significant amount of free and untraced money available -- e.g. 1 billion dollars in cryptocurrencies). What would be the best way for them to proceed, and what would be the most vulnerable points where they could be stopped?
Stealing existing nuclear weapons would probably not be an option (or will be of limited utility -- see below). Modern nuclear devices are all equipped with PALs (permissive action links), rendering them unusable without unlocking codes (the key idea of PAL is removing some small amount of explosives from the implosion shell, different for each detonator -- and compensating by adjusting precise timings when each detonator goes off; these timings are different for each device and can be released only by central command authority). Without knowing the entire set of PAL timings and the entire encrypted protocol between PAL controller and detonators, achieving a bona fide nuclear explosion is technically impossible. Some countries like Pakistan and perhaps North Korea do not possess sophisticated PAL systems for their devices; to compensate, their nuclear cores are tightly guarded by the military.
Therefore, even if weapon-grade nuclear materials are available (which is of course another near impossible problem), designing the nuclear explosive device de novo is still unavoidable. The principal design of nuclear weapons is not secret, and achieving the nuclear explosion is a clearly defined problem (in terms of timing, compression and explosion hydrodynamics) that can be solved by a small group of competent physicists. Indeed, the "Nth Country Experiment" by Lawrence Livermore National Laboratory in 1964 has shown that three bright physicists (without previous nuclear expertise) can deliver a plausible design for a working nuclear weapon (they were building an analogue of the Fat Man device, which is bulk and nearly undeliverable; today, more compact options should be pursued instead). A heavily redacted report is available at https://nsarchive2.gwu.edu//news/20030701/nth-country.pdf. With modern computers, open information about nuclear weapons, some OSINT and determination, the same feat could probably be accomplished in less than a year.
(Some open source software and libraries that can be useful in such an endeavor: OpenMC (http://web.mit.edu/smharper/www/) for criticality simulations, Castro (https://ccse.lbl.gov/Research/CASTRO/) for explosion hydrodynamics. There is also a book by a Brazilian physicist Dalton Ellery G. Barroso, "A Fisica dos Explosivos Nucleares" [only available in Portuguese so far], containing exhaustive calculations and e.g. parameters of equations of state, which is basically a guidebook for anyone with deep interest in the field). Many ideas for the critical part of the device, neutron initiator, are also discussed in the open literature (here I will refrain from mentioning exact books and papers, but the information is still publicly available). Again, the task is clearly formulated -- injecting the neutrons at the very precise moment during the explosion, this is only an engineering problem.
Assembling the device itself is no easy task, it requires precision engineering and e.g. casting high explosives, which cannot be done without significant pre-existing expertise. However, the brightest mechanical engineers and even explosives technicians can be legally hired on open market, if not for the direct participation in the project, then for training and knowledge transfer for the project team. Private organizations have achieved even more complicated engineering feats (e.g. rocket engines at SpaceX), so this part looks feasible.
All current nuclear devices require periodic maintenance and re-casting the plutonium pits with additional weapon-grade plutonium added every few years, otherwise their neutronic profile will gradually become too unfavorable to achieve a full nuclear explosion. If the group has acquired nuclear materials by stealing them, they will have to make use of them during the following few years. Nuclear programs of sovereign states, of course, have the entire weapon-grade plutonium production pipelines at their disposal, so the fresh plutonium is always available. This will be a much harder feat to achieve for a non-state actor. Ironically, the plutonium could be provided by disassembling PAL-equipped stolen or captured nuclear devices, which are less heavily guarded. While it is true that PAL will prevent their full scale explosion, they still can be the priceless source of weapon-grade plutonium.
Conclusion: safeguarding weapon-grade nuclear materials is the highest priority, as the design details of nuclear devices are hardly a secret these days, and can be readily reproduced by many competent and determined organizations. Emergence of nuclear production pipelines (isotope separation, SILEX, plutonium separation, plutonium-producing reactors) should be monitored everywhere. Even PAL-equipped weapons need to be closely guarded, as they can be the sources of these materials. Groups and non-state actors willing to acquire nuclear capabilities without building the full production pipeline need to act fast and have the design and device prototypes (sans cores) ready before acquiring nuclear materials, as their utility is diminishing every year since acquisition.