The recent Snowden disclosures about the NSA and GCHQ have revealed that there are no, nor have there ever been any secret 'Secret Santa' gift transactions. Such gift trades have been strictly monitored, and the subsequent data recorded and stored, since 1975.
In addition, in 1970s Scarfolk all Christmas presents had to go through a council clearance department that assessed each gift individually to decide whether or not it was appropriate for the intended recipient.
For example, if an intelligent child had revealed any potentially free-thinking tendencies he would not be allowed to receive books or any other form of educational materials. Such gifts might be substituted for depressants/sedatives, such as Comazepam, or he might receive a Cell Token which he could exchange for a prison term, irrespective of whether or not he had gone to the unnecessary effort of committing a crime.
Everyone at Scarfolk Council would like to wish you a very Merry Christmess, irrespective, or perhaps in spite of, your beliefs. All the very best for the new year; see you in 1974!