Cryptography’s most familiar use is perhaps the sending of coded messages: Alice wants to communicate some information to her distant confidant Bob. She worries that her message might be intercepted by an eavesdropper, so she encrypts it in a way that only Bob can decipher. A related task involves digital signatures: Alice wants to prove to Bob that her message came from her rather than an impostor.
There’s a broad range of complementary cryptographic tasks, though, in which Alice and Bob seek to guard against dishonesty not from intervening third parties but from each other. Examples include silent auctions and secret ballots: Participants want to ensure not only that their own bids or votes are kept private but also that the outcome isn’t being unfairly manipulated by any other participant.
To develop algorithms to perform those tasks, cryptographers use a building block called bit commitment. Alice chooses a secret bit...
