PALs seem to rely on cryptographic principles and tamper-proof design:
There are two basic means of foiling any lock, from an automobile ignition switch to a PAL: the first is to pick it, and the second is to bypass it. From the very beginning of the development of PAL technology, it was recognized that the real challenge was to build a system that afforded protection against the latter threat. Rather than attempting to build an indestructible lock, scientists at Livermore Laboratory in 1961 directed their efforts towards constructing a system that would render a weapon unusable if an attempt was made to interfere with its PAL. By 1964, it had been demonstrated that this approach would work. The design was perfected and incorporated into weapons that utilize CAT D and CAT F PALs. With this system, the insertion of too many false codes or an attempt to bypass the PAL will render the weapon permanently inoperative, and the weapon must then be returned to the weapons plant for reassembly. The protective system is designed to foil the probes of the most sophisticated unauthorized user. It is currently believed that even someone who gained possession of such a weapon, had a set of drawings, and enjoyed the technical capability of one of the national laboratories would be unable to successfully cause a detonation without knowing the code. [SF87].
The requirement for safety in the face of an enemy with full knowledge is eerily similar to the requirements for the security of a cipher system. An admiral was less convinced of their absolute safety, though this was 10 years earlier:
All nuclear weapons have some type of command and control mechanism which is designed to preclude unauthorized use, and all nuclear weapons are equipped with safety devices that meet rigid standards.... With regard to enemy capture of a nuclear weapon, similar safety and security devices thwart the arming, fuzing, and firing of the weapon, particularly if the enemy has little or no knowledge of the mechanical or electro-mechanical operation of the protective device. It is possible, however, that these mechanisms can be defeated by a sophisticated enemy over a period of time. Thus, emergency destruction devices and procedures have been developed so that nuclear weapons may be destroyed without producing a nuclear yield in the event that enemy capture is threatened.
The Permissive Action Link (PAL) Program consists of a code system and a family of devices integral or attached to nuclear weapons which have been developed to reduce the probability of an unauthorized nuclear detonation... [M76].
It was almost certainly possible to bypass early PALs: A technical solution to the issues raised by the Joint Committee on Atomic Energy was jointly worked out by the Sandia and Los Alamos Laboratories. The concept was to embed a mechanical or electromechanical code switch in the warhead in a location such that it could not be bypassed reasily. To foil any attempt to bypass the device, the switch's appearance and markings were disguised to make its function unclear unless the weaon's manual were also available. [J89]
[SF87] Stein, Peter and Feaver, Peter. Assuring Control of Nuclear Weapons. University Press, 1987.
[J89] "Safety, Security, and Control of Nuclear Weapons", in Technology and the Limitation of International Conflict, Blechman, Barry M., ed., Johns Hopkins Foreign Policy Institute, 1989
Now what do you know about Soviet era PALS? Do we even know what devices the Soviets built had PALS and which didn't?