A Cryptographically Secret Santa

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2024-12-25 19:30:04

Twas about 4-6 weeks before Christmas, and all through the math department, not a creature was stirring, not even a plucky young undergrad. Cryptography professors Alice and Bob sat at the elliptically-curved conference table to plan the department’s secret Santa. Mallory, the department secretary, had been given the task of organizing last year, and somehow managed to get three gifts while leaving several people disappointed. This year’s math department thus resolved to do their secret Santa without a trusted party.

As Alice and Bob went to the blackboard to think, they began to decide on the properties of their secret Santa. They came to several conclusions:

After some research, and much to their dismay, even Matt Parker could not find such an algorithm. Nor could the kind elves of Math Stack Exchange, although they gave a valiant effort. Thus, Alice and Bob sat down to plan their own cryptographically secret Santa.

Thankfully, Alice and Bob had many constructs from modern cryptography available, and they sat down at the blackboard to start each step.

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