One brief additional piece of information. The 'Smart Gun' that
Smith & Wesson produced for police use worked slightly differently. It, too, relied on a ring-mounted
transponder. However, the algorithm was slightly different; in this unit's case, it would only fire if the ring was
not in front of the gun, as defined by a plane intersecting the middle of the barrel perpendicular to the weapon - spreading out away from the gun to all sides. This was done so that if someone managed to wrestle the gun away from the officer and point it at him or her, the presence of the transponder in front of the gun would cause it to lock. AFAIK, however, the gun would still fire if no ring was anywhere to be seen.
Furthermore, the final prototype of this gun was exhibited by Smith & Wesson on several television 'technology' shows; in those appearances, they were careful to state that while the technology worked, it was not robust enough to survive the gun actually firing. I don't buy that; it's plausible that the prototype didn't have a robust electronics package in it, but there is no good reason one couldn't be produced cheaply. Embedded solid-state electronics
are a mature technology, and have demonstrated the ability to withstand much nastier shocks than a pistol shot's recoil.
A 'wishful thinking' version of this showed up in the James Bond film License to Kill as the 'Signature gun'.