Alice and Bob Are Weird

Suppose Alice and Bob live in a country with 50 states. Alice is currently in state a and Bob is currently in state b. They can communicate with one another and Alice wants to test if she is currently in the same state as Bob. If they are in the same state, Alice should learn that fact and otherwise she should learn nothing else about Bob’s location. Bob should learn nothing about Alice’s location.

They agree on the following scheme:

  • They fix a group G of prime order p and generator g of G

Cryptographic problems. Gotta love ’em.

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